From c0dcf7c2bc72b370bc1d85f16c4231433bf71c7c Mon Sep 17 00:00:00 2001 From: Lou Quillio Date: Sun, 9 Jul 2017 18:33:42 -0700 Subject: [PATCH] Port Draco bitstream spec to Markdown. This represents the grunt-work of porting the gDocs document to plaintext. There are decisions to make and polish to be applied. --- docs/Gemfile.lock | 199 ++ docs/_config.yml | 34 + docs/_layouts/spec.html | 29 + docs/_site/DracoLogo.jpeg | Bin 0 -> 20683 bytes docs/_site/artwork/draco3d-horiz-320x79.png | Bin 0 -> 8622 bytes docs/_site/artwork/draco3d-horiz-640x158.png | Bin 0 -> 19412 bytes docs/_site/artwork/draco3d-horiz.ai | 348 +++ docs/_site/artwork/draco3d-horiz.svg | 323 +++ docs/_site/artwork/draco3d-mark-180x180.png | Bin 0 -> 13055 bytes docs/_site/artwork/draco3d-mark-360x360.png | Bin 0 -> 29971 bytes docs/_site/artwork/draco3d-mark.ai | 364 ++++ docs/_site/artwork/draco3d-mark.svg | 306 +++ docs/_site/artwork/draco3d-vert-180x137.png | Bin 0 -> 9189 bytes docs/_site/artwork/draco3d-vert-360x274.png | Bin 0 -> 19836 bytes docs/_site/artwork/draco3d-vert-452x344.png | Bin 0 -> 25782 bytes docs/_site/artwork/draco3d-vert.ai | 424 ++++ docs/_site/artwork/draco3d-vert.svg | 374 ++++ docs/_site/assets/css/pygments/README.md | 23 + docs/_site/assets/css/pygments/UNLICENSE.txt | 24 + docs/_site/assets/css/pygments/autumn.css | 58 + docs/_site/assets/css/pygments/borland.css | 46 + docs/_site/assets/css/pygments/bw.css | 34 + docs/_site/assets/css/pygments/colorful.css | 61 + docs/_site/assets/css/pygments/default.css | 61 + docs/_site/assets/css/pygments/emacs.css | 61 + docs/_site/assets/css/pygments/friendly.css | 61 + docs/_site/assets/css/pygments/fruity.css | 70 + docs/_site/assets/css/pygments/github.css | 61 + docs/_site/assets/css/pygments/index.html | 27 + docs/_site/assets/css/pygments/manni.css | 61 + docs/_site/assets/css/pygments/monokai.css | 66 + docs/_site/assets/css/pygments/murphy.css | 61 + docs/_site/assets/css/pygments/native.css | 70 + docs/_site/assets/css/pygments/pastie.css | 60 + docs/_site/assets/css/pygments/perldoc.css | 58 + docs/_site/assets/css/pygments/tango.css | 69 + docs/_site/assets/css/pygments/trac.css | 59 + docs/_site/assets/css/pygments/vim.css | 70 + docs/_site/assets/css/pygments/vs.css | 33 + docs/_site/assets/css/pygments/zenburn.css | 136 ++ docs/_site/assets/css/spec-style.css | 1 + docs/_site/assets/favicon.ico | Bin 0 -> 1406 bytes docs/_site/assets/js/ASCIIMathML.js | 1127 ++++++++++ ...igation-For-Your-Long-Document-autoTOC.zip | Bin 0 -> 5047 bytes docs/_site/assets/js/jquery.autotoc.js | 58 + docs/_site/spec/00.00.00.title.html | 2 + docs/_site/spec/00.00.00.title.md | 3 + docs/_site/spec/00.00.01.version.html | 3 + docs/_site/spec/00.00.01.version.md | 3 + docs/_site/spec/00.00.02.authors.html | 4 + docs/_site/spec/00.00.02.authors.md | 4 + docs/_site/spec/00.00.03.last.modified.html | 2 + docs/_site/spec/00.00.03.last.modified.md | 2 + docs/_site/spec/00.00.04.abstract.html | 5 + docs/_site/spec/00.00.04.abstract.md | 6 + docs/_site/spec/00.00.05.toc.html | 3 + docs/_site/spec/00.00.05.toc.md | 5 + docs/_site/spec/01.00.00.scope.html | 5 + docs/_site/spec/01.00.00.scope.md | 5 + docs/_site/spec/02.00.00.terms.html | 19 + docs/_site/spec/02.00.00.terms.md | 8 + docs/_site/spec/03.00.00.symbols.html | 30 + docs/_site/spec/03.00.00.symbols.md | 18 + docs/_site/spec/04.00.00.conventions.html | 42 + docs/_site/spec/04.00.00.conventions.md | 26 + docs/_site/spec/draco.decoder.html | 43 + docs/_site/spec/draco.decoder.md | 45 + docs/_site/spec/edgebreaker.decoder.html | 1556 +++++++++++++ docs/_site/spec/edgebreaker.decoder.md | 1674 ++++++++++++++ docs/_site/spec/index.html | 1927 +++++++++++++++++ docs/_site/spec/mesh.decoder.html | 11 + docs/_site/spec/mesh.decoder.md | 11 + docs/assets/css/pygments/README.md | 23 + docs/assets/css/pygments/UNLICENSE.txt | 24 + docs/assets/css/pygments/autumn.css | 58 + docs/assets/css/pygments/borland.css | 46 + docs/assets/css/pygments/bw.css | 34 + docs/assets/css/pygments/colorful.css | 61 + docs/assets/css/pygments/default.css | 61 + docs/assets/css/pygments/emacs.css | 61 + docs/assets/css/pygments/friendly.css | 61 + docs/assets/css/pygments/fruity.css | 70 + docs/assets/css/pygments/github.css | 61 + docs/assets/css/pygments/manni.css | 61 + docs/assets/css/pygments/monokai.css | 66 + docs/assets/css/pygments/murphy.css | 61 + docs/assets/css/pygments/native.css | 70 + docs/assets/css/pygments/pastie.css | 60 + docs/assets/css/pygments/perldoc.css | 58 + docs/assets/css/pygments/tango.css | 69 + docs/assets/css/pygments/trac.css | 59 + docs/assets/css/pygments/vim.css | 70 + docs/assets/css/pygments/vs.css | 33 + docs/assets/css/pygments/zenburn.css | 136 ++ docs/assets/css/spec-style.sass | 99 + docs/assets/favicon.ico | Bin 0 -> 1406 bytes docs/assets/js/ASCIIMathML.js | 1127 ++++++++++ ...igation-For-Your-Long-Document-autoTOC.zip | Bin 0 -> 5047 bytes docs/assets/js/jquery.autotoc.js | 58 + docs/spec/00.00.00.title.md | 3 + docs/spec/00.00.01.version.md | 3 + docs/spec/00.00.02.authors.md | 4 + docs/spec/00.00.03.last.modified.md | 2 + docs/spec/00.00.04.abstract.md | 6 + docs/spec/00.00.05.toc.md | 5 + docs/spec/01.00.00.scope.md | 5 + docs/spec/02.00.00.terms.md | 8 + docs/spec/03.00.00.symbols.md | 18 + docs/spec/04.00.00.conventions.md | 26 + docs/spec/draco.decoder.md | 45 + docs/spec/edgebreaker.decoder.md | 1674 ++++++++++++++ docs/spec/index.md | 32 + docs/spec/mesh.decoder.md | 11 + 113 files changed, 14808 insertions(+) create mode 100644 docs/Gemfile.lock create mode 100644 docs/_config.yml create mode 100644 docs/_layouts/spec.html create mode 100644 docs/_site/DracoLogo.jpeg create mode 100644 docs/_site/artwork/draco3d-horiz-320x79.png create mode 100644 docs/_site/artwork/draco3d-horiz-640x158.png create mode 100644 docs/_site/artwork/draco3d-horiz.ai create mode 100644 docs/_site/artwork/draco3d-horiz.svg create mode 100644 docs/_site/artwork/draco3d-mark-180x180.png create mode 100644 docs/_site/artwork/draco3d-mark-360x360.png create mode 100644 docs/_site/artwork/draco3d-mark.ai create mode 100644 docs/_site/artwork/draco3d-mark.svg create mode 100644 docs/_site/artwork/draco3d-vert-180x137.png create mode 100644 docs/_site/artwork/draco3d-vert-360x274.png create mode 100644 docs/_site/artwork/draco3d-vert-452x344.png create mode 100644 docs/_site/artwork/draco3d-vert.ai create mode 100644 docs/_site/artwork/draco3d-vert.svg create mode 100644 docs/_site/assets/css/pygments/README.md create mode 100644 docs/_site/assets/css/pygments/UNLICENSE.txt create mode 100644 docs/_site/assets/css/pygments/autumn.css create mode 100644 docs/_site/assets/css/pygments/borland.css create mode 100644 docs/_site/assets/css/pygments/bw.css create mode 100644 docs/_site/assets/css/pygments/colorful.css create mode 100644 docs/_site/assets/css/pygments/default.css create mode 100644 docs/_site/assets/css/pygments/emacs.css create mode 100644 docs/_site/assets/css/pygments/friendly.css create mode 100644 docs/_site/assets/css/pygments/fruity.css create mode 100644 docs/_site/assets/css/pygments/github.css create mode 100644 docs/_site/assets/css/pygments/index.html create mode 100644 docs/_site/assets/css/pygments/manni.css create mode 100644 docs/_site/assets/css/pygments/monokai.css create mode 100644 docs/_site/assets/css/pygments/murphy.css create mode 100644 docs/_site/assets/css/pygments/native.css create mode 100644 docs/_site/assets/css/pygments/pastie.css create mode 100644 docs/_site/assets/css/pygments/perldoc.css create mode 100644 docs/_site/assets/css/pygments/tango.css create mode 100644 docs/_site/assets/css/pygments/trac.css create mode 100644 docs/_site/assets/css/pygments/vim.css create mode 100644 docs/_site/assets/css/pygments/vs.css create mode 100644 docs/_site/assets/css/pygments/zenburn.css create mode 100644 docs/_site/assets/css/spec-style.css create mode 100644 docs/_site/assets/favicon.ico create mode 100644 docs/_site/assets/js/ASCIIMathML.js create mode 100644 docs/_site/assets/js/Generating-An-In-page-Navigation-For-Your-Long-Document-autoTOC.zip create mode 100644 docs/_site/assets/js/jquery.autotoc.js create mode 100644 docs/_site/spec/00.00.00.title.html create mode 100644 docs/_site/spec/00.00.00.title.md create mode 100644 docs/_site/spec/00.00.01.version.html create mode 100644 docs/_site/spec/00.00.01.version.md create mode 100644 docs/_site/spec/00.00.02.authors.html create mode 100644 docs/_site/spec/00.00.02.authors.md create mode 100644 docs/_site/spec/00.00.03.last.modified.html create mode 100644 docs/_site/spec/00.00.03.last.modified.md create mode 100644 docs/_site/spec/00.00.04.abstract.html create mode 100644 docs/_site/spec/00.00.04.abstract.md create mode 100644 docs/_site/spec/00.00.05.toc.html create mode 100644 docs/_site/spec/00.00.05.toc.md create mode 100644 docs/_site/spec/01.00.00.scope.html create mode 100644 docs/_site/spec/01.00.00.scope.md create mode 100644 docs/_site/spec/02.00.00.terms.html create mode 100644 docs/_site/spec/02.00.00.terms.md create mode 100644 docs/_site/spec/03.00.00.symbols.html create mode 100644 docs/_site/spec/03.00.00.symbols.md create mode 100644 docs/_site/spec/04.00.00.conventions.html create mode 100644 docs/_site/spec/04.00.00.conventions.md create mode 100644 docs/_site/spec/draco.decoder.html create mode 100644 docs/_site/spec/draco.decoder.md create mode 100644 docs/_site/spec/edgebreaker.decoder.html create mode 100644 docs/_site/spec/edgebreaker.decoder.md create mode 100644 docs/_site/spec/index.html create mode 100644 docs/_site/spec/mesh.decoder.html create mode 100644 docs/_site/spec/mesh.decoder.md create mode 100644 docs/assets/css/pygments/README.md create mode 100644 docs/assets/css/pygments/UNLICENSE.txt create mode 100644 docs/assets/css/pygments/autumn.css create mode 100644 docs/assets/css/pygments/borland.css create mode 100644 docs/assets/css/pygments/bw.css create mode 100644 docs/assets/css/pygments/colorful.css create mode 100644 docs/assets/css/pygments/default.css create mode 100644 docs/assets/css/pygments/emacs.css create mode 100644 docs/assets/css/pygments/friendly.css create mode 100644 docs/assets/css/pygments/fruity.css create mode 100644 docs/assets/css/pygments/github.css create mode 100644 docs/assets/css/pygments/manni.css create mode 100644 docs/assets/css/pygments/monokai.css create mode 100644 docs/assets/css/pygments/murphy.css create mode 100644 docs/assets/css/pygments/native.css create mode 100644 docs/assets/css/pygments/pastie.css create mode 100644 docs/assets/css/pygments/perldoc.css create mode 100644 docs/assets/css/pygments/tango.css create mode 100644 docs/assets/css/pygments/trac.css create mode 100644 docs/assets/css/pygments/vim.css create mode 100644 docs/assets/css/pygments/vs.css create mode 100644 docs/assets/css/pygments/zenburn.css create mode 100644 docs/assets/css/spec-style.sass create mode 100644 docs/assets/favicon.ico create mode 100644 docs/assets/js/ASCIIMathML.js create mode 100644 docs/assets/js/Generating-An-In-page-Navigation-For-Your-Long-Document-autoTOC.zip create mode 100644 docs/assets/js/jquery.autotoc.js create mode 100644 docs/spec/00.00.00.title.md create mode 100644 docs/spec/00.00.01.version.md create mode 100644 docs/spec/00.00.02.authors.md create mode 100644 docs/spec/00.00.03.last.modified.md create mode 100644 docs/spec/00.00.04.abstract.md create mode 100644 docs/spec/00.00.05.toc.md create mode 100644 docs/spec/01.00.00.scope.md create mode 100644 docs/spec/02.00.00.terms.md create mode 100644 docs/spec/03.00.00.symbols.md create mode 100644 docs/spec/04.00.00.conventions.md create mode 100644 docs/spec/draco.decoder.md create mode 100644 docs/spec/edgebreaker.decoder.md create mode 100644 docs/spec/index.md create mode 100644 docs/spec/mesh.decoder.md diff --git a/docs/Gemfile.lock b/docs/Gemfile.lock new file mode 100644 index 0000000..eceddc5 --- /dev/null +++ b/docs/Gemfile.lock @@ -0,0 +1,199 @@ +GEM + remote: https://rubygems.org/ + specs: + activesupport (4.2.8) + i18n (~> 0.7) + minitest (~> 5.1) + thread_safe (~> 0.3, >= 0.3.4) + tzinfo (~> 1.1) + addressable (2.5.1) + public_suffix (~> 2.0, >= 2.0.2) + coffee-script (2.4.1) + coffee-script-source + execjs + coffee-script-source (1.12.2) + colorator (1.1.0) + ethon (0.10.1) + ffi (>= 1.3.0) + execjs (2.7.0) + faraday (0.12.1) + multipart-post (>= 1.2, < 3) + ffi (1.9.18) + forwardable-extended (2.6.0) + gemoji (3.0.0) + github-pages (141) + activesupport (= 4.2.8) + github-pages-health-check (= 1.3.4) + jekyll (= 3.4.3) + jekyll-avatar (= 0.4.2) + jekyll-coffeescript (= 1.0.1) + jekyll-default-layout (= 0.1.4) + jekyll-feed (= 0.9.2) + jekyll-gist (= 1.4.0) + jekyll-github-metadata (= 2.4.0) + jekyll-mentions (= 1.2.0) + jekyll-optional-front-matter (= 0.1.2) + jekyll-paginate (= 1.1.0) + jekyll-readme-index (= 0.1.0) + jekyll-redirect-from (= 0.12.1) + jekyll-relative-links (= 0.4.1) + jekyll-sass-converter (= 1.5.0) + jekyll-seo-tag (= 2.2.3) + jekyll-sitemap (= 1.0.0) + jekyll-swiss (= 0.4.0) + jekyll-theme-architect (= 0.0.4) + jekyll-theme-cayman (= 0.0.4) + jekyll-theme-dinky (= 0.0.4) + 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jekyll-avatar (0.4.2) + jekyll (~> 3.0) + jekyll-coffeescript (1.0.1) + coffee-script (~> 2.2) + jekyll-default-layout (0.1.4) + jekyll (~> 3.0) + jekyll-feed (0.9.2) + jekyll (~> 3.3) + jekyll-gist (1.4.0) + octokit (~> 4.2) + jekyll-github-metadata (2.4.0) + jekyll (~> 3.1) + octokit (~> 4.0, != 4.4.0) + jekyll-mentions (1.2.0) + activesupport (~> 4.0) + html-pipeline (~> 2.3) + jekyll (~> 3.0) + jekyll-optional-front-matter (0.1.2) + jekyll (~> 3.0) + jekyll-paginate (1.1.0) + jekyll-readme-index (0.1.0) + jekyll (~> 3.0) + jekyll-redirect-from (0.12.1) + jekyll (~> 3.3) + jekyll-relative-links (0.4.1) + jekyll (~> 3.3) + jekyll-sass-converter (1.5.0) + sass (~> 3.4) + jekyll-seo-tag (2.2.3) + jekyll (~> 3.3) + jekyll-sitemap (1.0.0) + jekyll (~> 3.3) + jekyll-swiss (0.4.0) + jekyll-theme-architect (0.0.4) + jekyll (~> 3.3) + jekyll-theme-cayman (0.0.4) + jekyll (~> 3.3) + jekyll-theme-dinky (0.0.4) + jekyll (~> 3.3) + jekyll-theme-hacker (0.0.4) + jekyll (~> 3.3) + 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(0.14.0) + forwardable-extended (~> 2.6) + public_suffix (2.0.5) + rb-fsevent (0.10.2) + rb-inotify (0.9.10) + ffi (>= 0.5.0, < 2) + rouge (1.11.1) + safe_yaml (1.0.4) + sass (3.4.25) + sawyer (0.8.1) + addressable (>= 2.3.5, < 2.6) + faraday (~> 0.8, < 1.0) + terminal-table (1.8.0) + unicode-display_width (~> 1.1, >= 1.1.1) + thread_safe (0.3.6) + typhoeus (0.8.0) + ethon (>= 0.8.0) + tzinfo (1.2.3) + thread_safe (~> 0.1) + unicode-display_width (1.3.0) + +PLATFORMS + ruby + +DEPENDENCIES + github-pages + +BUNDLED WITH + 1.14.6 diff --git a/docs/_config.yml b/docs/_config.yml new file mode 100644 index 0000000..06dd47f --- /dev/null +++ b/docs/_config.yml @@ -0,0 +1,34 @@ +# Welcome to Jekyll! +# +# This config file is meant for settings that affect your whole blog, values +# which you are expected to set up once and rarely edit after that. If you find +# yourself editing this file very often, consider using Jekyll's data files +# feature for the data you need to update frequently. +# +# For technical reasons, this file is *NOT* reloaded automatically when you use +# 'bundle exec jekyll serve'. If you change this file, please restart the server process. + +# Site settings +# These are used to personalize your new site. If you look in the HTML files, +# you will see them accessed via {{ site.title }}, {{ site.email }}, and so on. +# You can create any custom variable you would like, and they will be accessible +# in the templates via {{ site.myvariable }}. +title: Draco 3D Data Compression + +email: webmaster@webmproject.org +description: > + Description here +baseurl: "/docs" # the subpath of your site, e.g. /blog +url: "" # the base hostname & protocol for your site, e.g. http://example.com +twitter_username: webm +github_username: webmproject +timezone: America/Los_Angeles + +# Build settings +markdown: kramdown +gems: +exclude: + - Gemfile + - Gemfile.lock +sass: + style: compressed diff --git a/docs/_layouts/spec.html b/docs/_layouts/spec.html new file mode 100644 index 0000000..1181d44 --- /dev/null +++ b/docs/_layouts/spec.html @@ -0,0 +1,29 @@ + + + + + {{ page.title }} + + + + + +{{ content }} + + + + diff --git a/docs/_site/DracoLogo.jpeg b/docs/_site/DracoLogo.jpeg new file mode 100644 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We make this dedication for the benefit +of the public at large and to the detriment of our heirs and +successors. We intend this dedication to be an overt act of +relinquishment in perpetuity of all present and future rights to this +software under copyright law. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, +EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF +MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. +IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR +OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, +ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR +OTHER DEALINGS IN THE SOFTWARE. + +For more information, please refer to diff --git a/docs/_site/assets/css/pygments/autumn.css b/docs/_site/assets/css/pygments/autumn.css new file mode 100644 index 0000000..a5f3d4c --- /dev/null +++ b/docs/_site/assets/css/pygments/autumn.css @@ -0,0 +1,58 @@ +.highlight .hll { background-color: #ffffcc } +.highlight .c { color: #aaaaaa; font-style: italic } /* Comment */ +.highlight .err { color: #F00000; 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jekyll-pygments-themes

+ +

A set of CSS theme files for Pygments (Python-based code highlighting tool) +created from the original built-in Pygments styles, ready for use with Jekyll.

+ +

Theme Previews and Custom Theme Builder

+ + +

Using Themes Without Jekyll

+

If you want to use the themes with something other than Jekyll, you may need to +remove or change the CSS style prefix of .highlight.

+ + + + + +

Hacking

+ +

If you want to hack on the site, check out the gh-pages branch.

+ +

Acknowledgements

+

Forked from richleland/pygments-css.

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+} + +.highlight .m,.preview-zenburn .highlight .mf,.preview-zenburn .highlight .mh,.preview-zenburn .highlight .mi,.preview-zenburn .highlight .mo,.preview-zenburn .highlight .il { +color:#8cd0d3; +} + +.highlight .na,.preview-zenburn .highlight .nt { +color:#9ac39f; +} + +.highlight .nb,.preview-zenburn .highlight .nc,.preview-zenburn .highlight .nf,.preview-zenburn .highlight .bp,.preview-zenburn .highlight .vc { +color:#efef8f; +} diff --git a/docs/_site/assets/css/spec-style.css b/docs/_site/assets/css/spec-style.css new file mode 100644 index 0000000..513a264 --- /dev/null +++ b/docs/_site/assets/css/spec-style.css @@ -0,0 +1 @@ +@import url("https://fonts.googleapis.com/css?family=Inconsolata");body{font-family:Arial,sans-serif;margin:10% 25% 10% 10%;line-height:1.3}a{color:navy;text-decoration:none}a:visited{color:navy;text-decoration:none}a:hover{text-decoration:underline}pre{font-family:"Inconsolata",monospace;border:2px solid #ddd;padding:1em;margin-left:1em;overflow-x:auto}code{font-family:"Inconsolata",monospace}table{border-collapse:collapse;min-width:50%;margin-left:1em}th,td{border:2px solid #ccc;padding:.5em}th{background-color:#333;color:#fff}table.terms th{display:none}table.terms td{vertical-align:top}table.conventions th{display:none}table.conventions td{vertical-align:top}table.conventions td:first-child{white-space:nowrap}table.nohead th{display:none}table.xyhead th,table.xyhead td:first-child{background-color:#9bbb59}table.xyhead th{color:#000;font-weight:normal}figure.highlight{background-color:#f2f2f2;padding-left:1em;padding-right:1em;border:2px solid #ccc}div.syntax{background-color:#fff;background-image:linear-gradient(90deg, transparent 540px, #abced4 540px, #abced4 542px, transparent 542px),linear-gradient(#ddd .1em, transparent .1em);background-size:100% 1.3em;border-left:2px solid #ddd;border-right:2px solid #ddd;border-bottom:2px solid #ddd;white-space:pre;font-family:"Inconsolata",monospace;font-size:1em;padding-left:1em;margin-left:1em;width:720px} diff --git a/docs/_site/assets/favicon.ico b/docs/_site/assets/favicon.ico new file mode 100644 index 0000000000000000000000000000000000000000..4ca5dba1fb70dad00b67cf10e092bea8fcb9caf5 GIT binary patch literal 1406 zcmeHH>r;$z6nkUTum9-(T zKnFIz6|$r|-KhV$iW zh;1_=$ZUY?>&n|5_EK+Aes!F(Rz47jp7!Q3ssPl|d-XrTGRpB+y;+ z4e*ayp8J@dmq>x8k%ll$uN5a zW}8>7J>=s%FYy!`zMn?S+~CMhm_JK)YR&AR?Zo$~9F#}MGq!V9aBgqhapwsETr^@k z!)&HRD0cm(Oz={>Shpz2AI_{h>gu;>(_elvI{dW9+`pWewk&enZ`%J8DE0%?Gim$g Z1TzBtC)FG%Y~e6KNT<3na4`q2_ZQ8$6zl*1 literal 0 HcmV?d00001 diff --git a/docs/_site/assets/js/ASCIIMathML.js b/docs/_site/assets/js/ASCIIMathML.js new file mode 100644 index 0000000..727111c --- /dev/null +++ b/docs/_site/assets/js/ASCIIMathML.js @@ -0,0 +1,1127 @@ +/* +ASCIIMathML.js +============== +This file contains JavaScript functions to convert ASCII math notation +and (some) LaTeX to Presentation MathML. The conversion is done while the +HTML page loads, and should work with Firefox and other browsers that can +render MathML. + +Just add the next line to your HTML page with this file in the same folder: + + + +Version 2.2 Mar 3, 2014. +Latest version at https://github.com/mathjax/asciimathml +If you use it on a webpage, please send the URL to jipsen@chapman.edu + +Copyright (c) 2014 Peter Jipsen and other ASCIIMathML.js contributors + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ +var asciimath = {}; + +(function(){ +var mathcolor = "blue"; // change it to "" (to inherit) or another color +var mathfontsize = "1em"; // change to e.g. 1.2em for larger math +var mathfontfamily = "serif"; // change to "" to inherit (works in IE) + // or another family (e.g. "arial") +var automathrecognize = false; // writing "amath" on page makes this true +var checkForMathML = true; // check if browser can display MathML +var notifyIfNoMathML = true; // display note at top if no MathML capability +var alertIfNoMathML = false; // show alert box if no MathML capability +var translateOnLoad = true; // set to false to do call translators from js +var translateASCIIMath = true; // false to preserve `..` +var displaystyle = true; // puts limits above and below large operators +var showasciiformulaonhover = true; // helps students learn ASCIIMath +var decimalsign = "."; // change to "," if you like, beware of `(1,2)`! +var AMdelimiter1 = "`", AMescape1 = "\\\\`"; // can use other characters +var AMdocumentId = "wikitext" // PmWiki element containing math (default=body) +var fixphi = true; //false to return to legacy phi/varphi mapping + +/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++*/ + +var isIE = (navigator.appName.slice(0,9)=="Microsoft"); +var noMathML = false, translated = false; + +if (isIE) { // add MathPlayer info to IE webpages + document.write(""); + document.write(""); +} + +// Add a stylesheet, replacing any previous custom stylesheet (adapted from TW) +function setStylesheet(s) { + var id = "AMMLcustomStyleSheet"; + var n = document.getElementById(id); + if(document.createStyleSheet) { + // Test for IE's non-standard createStyleSheet method + if(n) + n.parentNode.removeChild(n); + // This failed without the   + document.getElementsByTagName("head")[0].insertAdjacentHTML("beforeEnd"," "); + } else { + if(n) { + n.replaceChild(document.createTextNode(s),n.firstChild); + } else { + n = document.createElement("style"); + n.type = "text/css"; + n.id = id; + n.appendChild(document.createTextNode(s)); + document.getElementsByTagName("head")[0].appendChild(n); + } + } +} + +setStylesheet("#AMMLcloseDiv \{font-size:0.8em; padding-top:1em; color:#014\}\n#AMMLwarningBox \{position:absolute; width:100%; top:0; left:0; z-index:200; text-align:center; font-size:1em; font-weight:bold; padding:0.5em 0 0.5em 0; color:#ffc; background:#c30\}"); + +function init(){ + var msg, warnings = new Array(); + if (document.getElementById==null){ + alert("This webpage requires a recent browser such as Mozilla Firefox"); + return null; + } + if (checkForMathML && (msg = checkMathML())) warnings.push(msg); + if (warnings.length>0) displayWarnings(warnings); + if (!noMathML) initSymbols(); + return true; +} + +function checkMathML(){ + if (navigator.appName.slice(0,8)=="Netscape") + if (navigator.appVersion.slice(0,1)>="5") noMathML = null; + else noMathML = true; + else if (navigator.appName.slice(0,9)=="Microsoft") + try { + var ActiveX = new ActiveXObject("MathPlayer.Factory.1"); + noMathML = null; + } catch (e) { + noMathML = true; + } + else if (navigator.appName.slice(0,5)=="Opera") + if (navigator.appVersion.slice(0,3)>="9.5") noMathML = null; + else noMathML = true; +//noMathML = true; //uncomment to check + if (noMathML && notifyIfNoMathML) { + var msg = "To view the ASCIIMathML notation use Internet Explorer + MathPlayer or Mozilla Firefox 2.0 or later."; + if (alertIfNoMathML) + alert(msg); + else return msg; + } +} + +function hideWarning(){ + var body = document.getElementsByTagName("body")[0]; + body.removeChild(document.getElementById('AMMLwarningBox')); + body.onclick = null; +} + +function displayWarnings(warnings) { + var i, frag, nd = createElementXHTML("div"); + var body = document.getElementsByTagName("body")[0]; + body.onclick=hideWarning; + nd.id = 'AMMLwarningBox'; + for (i=0; i<", tag:"mo", output:"\u22C9", tex:"ltimes", ttype:CONST}, +{input:"><|", tag:"mo", output:"\u22CA", tex:"rtimes", ttype:CONST}, +{input:"|><|", tag:"mo", output:"\u22C8", tex:"bowtie", ttype:CONST}, +{input:"-:", tag:"mo", output:"\u00F7", tex:"div", ttype:CONST}, +{input:"divide", tag:"mo", output:"-:", tex:null, ttype:DEFINITION}, +{input:"@", tag:"mo", output:"\u2218", tex:"circ", ttype:CONST}, +{input:"o+", tag:"mo", output:"\u2295", tex:"oplus", ttype:CONST}, +{input:"ox", tag:"mo", output:"\u2297", tex:"otimes", ttype:CONST}, +{input:"o.", tag:"mo", output:"\u2299", tex:"odot", ttype:CONST}, +{input:"sum", tag:"mo", output:"\u2211", tex:null, ttype:UNDEROVER}, +{input:"prod", tag:"mo", output:"\u220F", tex:null, ttype:UNDEROVER}, +{input:"^^", tag:"mo", output:"\u2227", tex:"wedge", ttype:CONST}, +{input:"^^^", tag:"mo", output:"\u22C0", tex:"bigwedge", ttype:UNDEROVER}, +{input:"vv", tag:"mo", output:"\u2228", tex:"vee", ttype:CONST}, +{input:"vvv", tag:"mo", output:"\u22C1", tex:"bigvee", ttype:UNDEROVER}, +{input:"nn", tag:"mo", output:"\u2229", tex:"cap", ttype:CONST}, +{input:"nnn", tag:"mo", output:"\u22C2", tex:"bigcap", ttype:UNDEROVER}, +{input:"uu", tag:"mo", output:"\u222A", tex:"cup", ttype:CONST}, +{input:"uuu", tag:"mo", output:"\u22C3", tex:"bigcup", ttype:UNDEROVER}, + +//binary relation symbols +{input:"!=", tag:"mo", output:"\u2260", tex:"ne", ttype:CONST}, +{input:":=", tag:"mo", output:":=", tex:null, ttype:CONST}, +{input:"lt", tag:"mo", output:"<", tex:null, ttype:CONST}, +{input:"<=", tag:"mo", output:"\u2264", tex:"le", ttype:CONST}, +{input:"lt=", tag:"mo", output:"\u2264", tex:"leq", ttype:CONST}, +{input:"gt", tag:"mo", output:">", tex:null, ttype:CONST}, +{input:">=", tag:"mo", output:"\u2265", tex:"ge", ttype:CONST}, +{input:"gt=", tag:"mo", output:"\u2265", tex:"geq", ttype:CONST}, +{input:"-<", tag:"mo", output:"\u227A", tex:"prec", ttype:CONST}, +{input:"-lt", tag:"mo", output:"\u227A", tex:null, ttype:CONST}, +{input:">-", tag:"mo", output:"\u227B", tex:"succ", ttype:CONST}, +{input:"-<=", tag:"mo", output:"\u2AAF", tex:"preceq", ttype:CONST}, +{input:">-=", tag:"mo", output:"\u2AB0", tex:"succeq", ttype:CONST}, +{input:"in", tag:"mo", output:"\u2208", tex:null, ttype:CONST}, +{input:"!in", tag:"mo", output:"\u2209", tex:"notin", ttype:CONST}, +{input:"sub", tag:"mo", output:"\u2282", tex:"subset", ttype:CONST}, +{input:"sup", tag:"mo", output:"\u2283", tex:"supset", ttype:CONST}, +{input:"sube", tag:"mo", output:"\u2286", tex:"subseteq", ttype:CONST}, +{input:"supe", tag:"mo", output:"\u2287", tex:"supseteq", ttype:CONST}, +{input:"-=", tag:"mo", output:"\u2261", tex:"equiv", ttype:CONST}, +{input:"~=", tag:"mo", output:"\u2245", tex:"cong", ttype:CONST}, +{input:"~~", tag:"mo", output:"\u2248", tex:"approx", ttype:CONST}, +{input:"prop", tag:"mo", output:"\u221D", tex:"propto", ttype:CONST}, + +//logical symbols +{input:"and", tag:"mtext", output:"and", tex:null, ttype:SPACE}, +{input:"or", tag:"mtext", output:"or", tex:null, ttype:SPACE}, +{input:"not", tag:"mo", output:"\u00AC", tex:"neg", ttype:CONST}, +{input:"=>", tag:"mo", output:"\u21D2", tex:"implies", ttype:CONST}, +{input:"if", tag:"mo", output:"if", tex:null, ttype:SPACE}, +{input:"<=>", tag:"mo", output:"\u21D4", tex:"iff", ttype:CONST}, +{input:"AA", tag:"mo", output:"\u2200", tex:"forall", ttype:CONST}, +{input:"EE", tag:"mo", output:"\u2203", tex:"exists", ttype:CONST}, +{input:"_|_", tag:"mo", output:"\u22A5", tex:"bot", ttype:CONST}, +{input:"TT", tag:"mo", output:"\u22A4", tex:"top", ttype:CONST}, +{input:"|--", tag:"mo", output:"\u22A2", tex:"vdash", ttype:CONST}, +{input:"|==", tag:"mo", output:"\u22A8", tex:"models", ttype:CONST}, + +//grouping brackets +{input:"(", tag:"mo", output:"(", tex:null, ttype:LEFTBRACKET}, +{input:")", tag:"mo", output:")", tex:null, ttype:RIGHTBRACKET}, +{input:"[", tag:"mo", output:"[", tex:null, ttype:LEFTBRACKET}, +{input:"]", tag:"mo", output:"]", tex:null, ttype:RIGHTBRACKET}, +{input:"{", tag:"mo", output:"{", tex:null, ttype:LEFTBRACKET}, +{input:"}", tag:"mo", output:"}", tex:null, ttype:RIGHTBRACKET}, +{input:"|", tag:"mo", output:"|", tex:null, ttype:LEFTRIGHT}, +//{input:"||", tag:"mo", output:"||", tex:null, ttype:LEFTRIGHT}, +{input:"(:", tag:"mo", output:"\u2329", tex:"langle", ttype:LEFTBRACKET}, +{input:":)", tag:"mo", output:"\u232A", tex:"rangle", ttype:RIGHTBRACKET}, +{input:"<<", tag:"mo", output:"\u2329", tex:null, ttype:LEFTBRACKET}, +{input:">>", tag:"mo", output:"\u232A", tex:null, ttype:RIGHTBRACKET}, +{input:"{:", tag:"mo", output:"{:", tex:null, ttype:LEFTBRACKET, invisible:true}, +{input:":}", tag:"mo", output:":}", tex:null, ttype:RIGHTBRACKET, invisible:true}, + +//miscellaneous symbols +{input:"int", tag:"mo", output:"\u222B", tex:null, ttype:CONST}, +{input:"dx", tag:"mi", output:"{:d x:}", tex:null, ttype:DEFINITION}, +{input:"dy", tag:"mi", output:"{:d y:}", tex:null, ttype:DEFINITION}, +{input:"dz", tag:"mi", output:"{:d z:}", tex:null, ttype:DEFINITION}, +{input:"dt", tag:"mi", output:"{:d t:}", tex:null, ttype:DEFINITION}, +{input:"oint", tag:"mo", output:"\u222E", tex:null, ttype:CONST}, +{input:"del", tag:"mo", output:"\u2202", tex:"partial", ttype:CONST}, +{input:"grad", tag:"mo", output:"\u2207", tex:"nabla", ttype:CONST}, +{input:"+-", tag:"mo", output:"\u00B1", tex:"pm", ttype:CONST}, +{input:"O/", tag:"mo", output:"\u2205", tex:"emptyset", ttype:CONST}, +{input:"oo", tag:"mo", output:"\u221E", tex:"infty", ttype:CONST}, +{input:"aleph", tag:"mo", output:"\u2135", tex:null, ttype:CONST}, +{input:"...", tag:"mo", output:"...", tex:"ldots", ttype:CONST}, +{input:":.", tag:"mo", output:"\u2234", tex:"therefore", ttype:CONST}, +{input:":'", tag:"mo", output:"\u2235", tex:"because", ttype:CONST}, +{input:"/_", tag:"mo", output:"\u2220", tex:"angle", ttype:CONST}, +{input:"/_\\", tag:"mo", output:"\u25B3", tex:"triangle", ttype:CONST}, +{input:"'", tag:"mo", output:"\u2032", tex:"prime", ttype:CONST}, +{input:"tilde", tag:"mover", output:"~", tex:null, ttype:UNARY, acc:true}, +{input:"\\ ", tag:"mo", output:"\u00A0", tex:null, ttype:CONST}, +{input:"frown", tag:"mo", output:"\u2322", tex:null, ttype:CONST}, +{input:"quad", tag:"mo", output:"\u00A0\u00A0", tex:null, ttype:CONST}, +{input:"qquad", tag:"mo", output:"\u00A0\u00A0\u00A0\u00A0", tex:null, ttype:CONST}, +{input:"cdots", tag:"mo", output:"\u22EF", tex:null, ttype:CONST}, +{input:"vdots", tag:"mo", output:"\u22EE", tex:null, ttype:CONST}, +{input:"ddots", tag:"mo", output:"\u22F1", tex:null, ttype:CONST}, +{input:"diamond", tag:"mo", output:"\u22C4", tex:null, ttype:CONST}, +{input:"square", tag:"mo", output:"\u25A1", tex:null, ttype:CONST}, +{input:"|__", tag:"mo", output:"\u230A", tex:"lfloor", ttype:CONST}, +{input:"__|", tag:"mo", output:"\u230B", tex:"rfloor", ttype:CONST}, +{input:"|~", tag:"mo", output:"\u2308", tex:"lceiling", ttype:CONST}, +{input:"~|", tag:"mo", output:"\u2309", tex:"rceiling", ttype:CONST}, +{input:"CC", tag:"mo", output:"\u2102", tex:null, ttype:CONST}, +{input:"NN", tag:"mo", output:"\u2115", tex:null, ttype:CONST}, +{input:"QQ", tag:"mo", output:"\u211A", tex:null, ttype:CONST}, +{input:"RR", tag:"mo", output:"\u211D", tex:null, ttype:CONST}, +{input:"ZZ", tag:"mo", output:"\u2124", tex:null, ttype:CONST}, +{input:"f", tag:"mi", output:"f", tex:null, ttype:UNARY, func:true}, +{input:"g", tag:"mi", output:"g", tex:null, ttype:UNARY, func:true}, + +//standard functions +{input:"lim", tag:"mo", output:"lim", tex:null, ttype:UNDEROVER}, +{input:"Lim", tag:"mo", output:"Lim", tex:null, ttype:UNDEROVER}, +{input:"sin", tag:"mo", output:"sin", tex:null, ttype:UNARY, func:true}, +{input:"cos", tag:"mo", output:"cos", tex:null, ttype:UNARY, func:true}, +{input:"tan", tag:"mo", output:"tan", tex:null, ttype:UNARY, func:true}, +{input:"sinh", tag:"mo", output:"sinh", tex:null, ttype:UNARY, func:true}, +{input:"cosh", tag:"mo", output:"cosh", tex:null, ttype:UNARY, func:true}, +{input:"tanh", tag:"mo", output:"tanh", tex:null, ttype:UNARY, func:true}, +{input:"cot", tag:"mo", output:"cot", tex:null, ttype:UNARY, func:true}, +{input:"sec", tag:"mo", output:"sec", tex:null, ttype:UNARY, func:true}, +{input:"csc", tag:"mo", output:"csc", tex:null, ttype:UNARY, func:true}, +{input:"arcsin", tag:"mo", output:"arcsin", tex:null, ttype:UNARY, func:true}, +{input:"arccos", tag:"mo", output:"arccos", tex:null, ttype:UNARY, func:true}, +{input:"arctan", tag:"mo", output:"arctan", tex:null, ttype:UNARY, func:true}, +{input:"coth", tag:"mo", output:"coth", tex:null, ttype:UNARY, func:true}, +{input:"sech", tag:"mo", output:"sech", tex:null, ttype:UNARY, func:true}, +{input:"csch", tag:"mo", output:"csch", tex:null, ttype:UNARY, func:true}, +{input:"exp", tag:"mo", output:"exp", tex:null, ttype:UNARY, func:true}, +{input:"abs", tag:"mo", output:"abs", tex:null, ttype:UNARY, rewriteleftright:["|","|"]}, +{input:"norm", tag:"mo", output:"norm", tex:null, ttype:UNARY, rewriteleftright:["\u2225","\u2225"]}, +{input:"floor", tag:"mo", output:"floor", tex:null, ttype:UNARY, rewriteleftright:["\u230A","\u230B"]}, +{input:"ceil", tag:"mo", output:"ceil", tex:null, ttype:UNARY, rewriteleftright:["\u2308","\u2309"]}, +{input:"log", tag:"mo", output:"log", tex:null, ttype:UNARY, func:true}, +{input:"ln", tag:"mo", output:"ln", tex:null, ttype:UNARY, func:true}, +{input:"det", tag:"mo", output:"det", tex:null, ttype:UNARY, func:true}, +{input:"dim", tag:"mo", output:"dim", tex:null, ttype:CONST}, +{input:"mod", tag:"mo", output:"mod", tex:null, ttype:CONST}, +{input:"gcd", tag:"mo", output:"gcd", tex:null, ttype:UNARY, func:true}, +{input:"lcm", tag:"mo", output:"lcm", tex:null, ttype:UNARY, func:true}, +{input:"lub", tag:"mo", output:"lub", tex:null, ttype:CONST}, +{input:"glb", tag:"mo", output:"glb", tex:null, ttype:CONST}, +{input:"min", tag:"mo", output:"min", tex:null, ttype:UNDEROVER}, +{input:"max", tag:"mo", output:"max", tex:null, ttype:UNDEROVER}, + +//arrows +{input:"uarr", tag:"mo", output:"\u2191", tex:"uparrow", ttype:CONST}, +{input:"darr", tag:"mo", output:"\u2193", tex:"downarrow", ttype:CONST}, +{input:"rarr", tag:"mo", output:"\u2192", tex:"rightarrow", ttype:CONST}, +{input:"->", tag:"mo", output:"\u2192", tex:"to", ttype:CONST}, +{input:">->", tag:"mo", output:"\u21A3", tex:"rightarrowtail", ttype:CONST}, +{input:"->>", tag:"mo", output:"\u21A0", tex:"twoheadrightarrow", ttype:CONST}, +{input:">->>", tag:"mo", output:"\u2916", tex:"twoheadrightarrowtail", ttype:CONST}, +{input:"|->", tag:"mo", output:"\u21A6", tex:"mapsto", ttype:CONST}, +{input:"larr", tag:"mo", output:"\u2190", tex:"leftarrow", ttype:CONST}, +{input:"harr", tag:"mo", output:"\u2194", tex:"leftrightarrow", ttype:CONST}, +{input:"rArr", tag:"mo", output:"\u21D2", tex:"Rightarrow", ttype:CONST}, +{input:"lArr", tag:"mo", output:"\u21D0", tex:"Leftarrow", ttype:CONST}, +{input:"hArr", tag:"mo", output:"\u21D4", tex:"Leftrightarrow", ttype:CONST}, +//commands with argument +{input:"sqrt", tag:"msqrt", output:"sqrt", tex:null, ttype:UNARY}, +{input:"root", tag:"mroot", output:"root", tex:null, ttype:BINARY}, +{input:"frac", tag:"mfrac", output:"/", tex:null, ttype:BINARY}, +{input:"/", tag:"mfrac", output:"/", tex:null, ttype:INFIX}, +{input:"stackrel", tag:"mover", output:"stackrel", tex:null, ttype:BINARY}, +{input:"overset", tag:"mover", output:"stackrel", tex:null, ttype:BINARY}, +{input:"underset", tag:"munder", output:"stackrel", tex:null, ttype:BINARY}, +{input:"_", tag:"msub", output:"_", tex:null, ttype:INFIX}, +{input:"^", tag:"msup", output:"^", tex:null, ttype:INFIX}, +{input:"hat", tag:"mover", output:"\u005E", tex:null, ttype:UNARY, acc:true}, +{input:"bar", tag:"mover", output:"\u00AF", tex:"overline", ttype:UNARY, acc:true}, +{input:"vec", tag:"mover", output:"\u2192", tex:null, ttype:UNARY, acc:true}, +{input:"dot", tag:"mover", output:".", tex:null, ttype:UNARY, acc:true}, +{input:"ddot", tag:"mover", output:"..", tex:null, ttype:UNARY, acc:true}, +{input:"ul", tag:"munder", output:"\u0332", tex:"underline", ttype:UNARY, acc:true}, +{input:"ubrace", tag:"munder", output:"\u23DF", tex:"underbrace", ttype:UNARYUNDEROVER, acc:true}, +{input:"obrace", tag:"mover", output:"\u23DE", tex:"overbrace", ttype:UNARYUNDEROVER, acc:true}, +{input:"text", tag:"mtext", output:"text", tex:null, ttype:TEXT}, +{input:"mbox", tag:"mtext", output:"mbox", tex:null, ttype:TEXT}, +{input:"color", tag:"mstyle", ttype:BINARY}, +{input:"cancel", tag:"menclose", output:"cancel", tex:null, ttype:UNARY}, +AMquote, +{input:"bb", tag:"mstyle", atname:"mathvariant", atval:"bold", output:"bb", tex:null, ttype:UNARY}, +{input:"mathbf", tag:"mstyle", atname:"mathvariant", atval:"bold", output:"mathbf", tex:null, ttype:UNARY}, +{input:"sf", tag:"mstyle", atname:"mathvariant", atval:"sans-serif", output:"sf", tex:null, ttype:UNARY}, +{input:"mathsf", tag:"mstyle", atname:"mathvariant", atval:"sans-serif", output:"mathsf", tex:null, ttype:UNARY}, +{input:"bbb", tag:"mstyle", atname:"mathvariant", atval:"double-struck", output:"bbb", tex:null, ttype:UNARY, codes:AMbbb}, +{input:"mathbb", tag:"mstyle", atname:"mathvariant", atval:"double-struck", output:"mathbb", tex:null, ttype:UNARY, codes:AMbbb}, +{input:"cc", tag:"mstyle", atname:"mathvariant", atval:"script", output:"cc", tex:null, ttype:UNARY, codes:AMcal}, +{input:"mathcal", tag:"mstyle", atname:"mathvariant", atval:"script", output:"mathcal", tex:null, ttype:UNARY, codes:AMcal}, +{input:"tt", tag:"mstyle", atname:"mathvariant", atval:"monospace", output:"tt", tex:null, ttype:UNARY}, +{input:"mathtt", tag:"mstyle", atname:"mathvariant", atval:"monospace", output:"mathtt", tex:null, ttype:UNARY}, +{input:"fr", tag:"mstyle", atname:"mathvariant", atval:"fraktur", output:"fr", tex:null, ttype:UNARY, codes:AMfrk}, +{input:"mathfrak", tag:"mstyle", atname:"mathvariant", atval:"fraktur", output:"mathfrak", tex:null, ttype:UNARY, codes:AMfrk} +]; + +function compareNames(s1,s2) { + if (s1.input > s2.input) return 1 + else return -1; +} + +var AMnames = []; //list of input symbols + +function initSymbols() { + var i; + var symlen = AMsymbols.length; + for (i=0; i=n where str appears or would be inserted +// assumes arr is sorted + if (n==0) { + var h,m; + n = -1; + h = arr.length; + while (n+1> 1; + if (arr[m]=str +} + +function AMgetSymbol(str) { +//return maximal initial substring of str that appears in names +//return null if there is none + var k = 0; //new pos + var j = 0; //old pos + var mk; //match pos + var st; + var tagst; + var match = ""; + var more = true; + for (var i=1; i<=str.length && more; i++) { + st = str.slice(0,i); //initial substring of length i + j = k; + k = position(AMnames, st, j); + if (k=AMnames[k]; + } + AMpreviousSymbol=AMcurrentSymbol; + if (match!=""){ + AMcurrentSymbol=AMsymbols[mk].ttype; + return AMsymbols[mk]; + } +// if str[0] is a digit or - return maxsubstring of digits.digits + AMcurrentSymbol=CONST; + k = 1; + st = str.slice(0,1); + var integ = true; + while ("0"<=st && st<="9" && k<=str.length) { + st = str.slice(k,k+1); + k++; + } + if (st == decimalsign) { + st = str.slice(k,k+1); + if ("0"<=st && st<="9") { + integ = false; + k++; + while ("0"<=st && st<="9" && k<=str.length) { + st = str.slice(k,k+1); + k++; + } + } + } + if ((integ && k>1) || k>2) { + st = str.slice(0,k-1); + tagst = "mn"; + } else { + k = 2; + st = str.slice(0,1); //take 1 character + tagst = (("A">st || st>"Z") && ("a">st || st>"z")?"mo":"mi"); + } + if (st=="-" && AMpreviousSymbol==INFIX) { + AMcurrentSymbol = INFIX; //trick "/" into recognizing "-" on second parse + return {input:st, tag:tagst, output:st, ttype:UNARY, func:true}; + } + return {input:st, tag:tagst, output:st, ttype:CONST}; +} + +function AMremoveBrackets(node) { + var st; + if (!node.hasChildNodes()) { return; } + if (node.firstChild.hasChildNodes() && (node.nodeName=="mrow" || node.nodeName=="M:MROW")) { + st = node.firstChild.firstChild.nodeValue; + if (st=="(" || st=="[" || st=="{") node.removeChild(node.firstChild); + } + if (node.lastChild.hasChildNodes() && (node.nodeName=="mrow" || node.nodeName=="M:MROW")) { + st = node.lastChild.firstChild.nodeValue; + if (st==")" || st=="]" || st=="}") node.removeChild(node.lastChild); + } +} + +/*Parsing ASCII math expressions with the following grammar +v ::= [A-Za-z] | greek letters | numbers | other constant symbols +u ::= sqrt | text | bb | other unary symbols for font commands +b ::= frac | root | stackrel binary symbols +l ::= ( | [ | { | (: | {: left brackets +r ::= ) | ] | } | :) | :} right brackets +S ::= v | lEr | uS | bSS Simple expression +I ::= S_S | S^S | S_S^S | S Intermediate expression +E ::= IE | I/I Expression +Each terminal symbol is translated into a corresponding mathml node.*/ + +var AMnestingDepth,AMpreviousSymbol,AMcurrentSymbol; + +function AMparseSexpr(str) { //parses str and returns [node,tailstr] + var symbol, node, result, i, st,// rightvert = false, + newFrag = document.createDocumentFragment(); + str = AMremoveCharsAndBlanks(str,0); + symbol = AMgetSymbol(str); //either a token or a bracket or empty + if (symbol == null || symbol.ttype == RIGHTBRACKET && AMnestingDepth > 0) { + return [null,str]; + } + if (symbol.ttype == DEFINITION) { + str = symbol.output+AMremoveCharsAndBlanks(str,symbol.input.length); + symbol = AMgetSymbol(str); + } + switch (symbol.ttype) { case UNDEROVER: + case CONST: + str = AMremoveCharsAndBlanks(str,symbol.input.length); + return [createMmlNode(symbol.tag, //its a constant + document.createTextNode(symbol.output)),str]; + case LEFTBRACKET: //read (expr+) + AMnestingDepth++; + str = AMremoveCharsAndBlanks(str,symbol.input.length); + result = AMparseExpr(str,true); + AMnestingDepth--; + if (typeof symbol.invisible == "boolean" && symbol.invisible) + node = createMmlNode("mrow",result[0]); + else { + node = createMmlNode("mo",document.createTextNode(symbol.output)); + node = createMmlNode("mrow",node); + node.appendChild(result[0]); + } + return [node,result[1]]; + case TEXT: + if (symbol!=AMquote) str = AMremoveCharsAndBlanks(str,symbol.input.length); + if (str.charAt(0)=="{") i=str.indexOf("}"); + else if (str.charAt(0)=="(") i=str.indexOf(")"); + else if (str.charAt(0)=="[") i=str.indexOf("]"); + else if (symbol==AMquote) i=str.slice(1).indexOf("\"")+1; + else i = 0; + if (i==-1) i = str.length; + st = str.slice(1,i); + if (st.charAt(0) == " ") { + node = createMmlNode("mspace"); + node.setAttribute("width","1ex"); + newFrag.appendChild(node); + } + newFrag.appendChild( + createMmlNode(symbol.tag,document.createTextNode(st))); + if (st.charAt(st.length-1) == " ") { + node = createMmlNode("mspace"); + node.setAttribute("width","1ex"); + newFrag.appendChild(node); + } + str = AMremoveCharsAndBlanks(str,i+1); + return [createMmlNode("mrow",newFrag),str]; + case UNARYUNDEROVER: + case UNARY: + str = AMremoveCharsAndBlanks(str,symbol.input.length); + result = AMparseSexpr(str); + if (result[0]==null) return [createMmlNode(symbol.tag, + document.createTextNode(symbol.output)),str]; + if (typeof symbol.func == "boolean" && symbol.func) { // functions hack + st = str.charAt(0); + if (st=="^" || st=="_" || st=="/" || st=="|" || st=="," || + (symbol.input.length==1 && symbol.input.match(/\w/) && st!="(")) { + return [createMmlNode(symbol.tag, + document.createTextNode(symbol.output)),str]; + } else { + node = createMmlNode("mrow", + createMmlNode(symbol.tag,document.createTextNode(symbol.output))); + node.appendChild(result[0]); + return [node,result[1]]; + } + } + AMremoveBrackets(result[0]); + if (symbol.input == "sqrt") { // sqrt + return [createMmlNode(symbol.tag,result[0]),result[1]]; + } else if (typeof symbol.rewriteleftright != "undefined") { // abs, floor, ceil + node = createMmlNode("mrow", createMmlNode("mo",document.createTextNode(symbol.rewriteleftright[0]))); + node.appendChild(result[0]); + node.appendChild(createMmlNode("mo",document.createTextNode(symbol.rewriteleftright[1]))); + return [node,result[1]]; + } else if (symbol.input == "cancel") { // cancel + node = createMmlNode(symbol.tag,result[0]); + node.setAttribute("notation","updiagonalstrike"); + return [node,result[1]]; + } else if (typeof symbol.acc == "boolean" && symbol.acc) { // accent + node = createMmlNode(symbol.tag,result[0]); + node.appendChild(createMmlNode("mo",document.createTextNode(symbol.output))); + return [node,result[1]]; + } else { // font change command + if (!isIE && typeof symbol.codes != "undefined") { + for (i=0; i64 && st.charCodeAt(j)<91) + newst = newst + symbol.codes[st.charCodeAt(j)-65]; + else if (st.charCodeAt(j)>96 && st.charCodeAt(j)<123) + newst = newst + symbol.codes[st.charCodeAt(j)-71]; + else newst = newst + st.charAt(j); + if (result[0].nodeName=="mi") + result[0]=createMmlNode("mo"). + appendChild(document.createTextNode(newst)); + else result[0].replaceChild(createMmlNode("mo"). + appendChild(document.createTextNode(newst)), + result[0].childNodes[i]); + } + } + node = createMmlNode(symbol.tag,result[0]); + node.setAttribute(symbol.atname,symbol.atval); + return [node,result[1]]; + } + case BINARY: + str = AMremoveCharsAndBlanks(str,symbol.input.length); + result = AMparseSexpr(str); + if (result[0]==null) return [createMmlNode("mo", + document.createTextNode(symbol.input)),str]; + AMremoveBrackets(result[0]); + var result2 = AMparseSexpr(result[1]); + if (result2[0]==null) return [createMmlNode("mo", + document.createTextNode(symbol.input)),str]; + AMremoveBrackets(result2[0]); + if (symbol.input=="color") { + if (str.charAt(0)=="{") i=str.indexOf("}"); + else if (str.charAt(0)=="(") i=str.indexOf(")"); + else if (str.charAt(0)=="[") i=str.indexOf("]"); + st = str.slice(1,i); + node = createMmlNode(symbol.tag,result2[0]); + node.setAttribute("mathcolor",st); + return [node,result2[1]]; + } + if (symbol.input=="root" || symbol.output=="stackrel") + newFrag.appendChild(result2[0]); + newFrag.appendChild(result[0]); + if (symbol.input=="frac") newFrag.appendChild(result2[0]); + return [createMmlNode(symbol.tag,newFrag),result2[1]]; + case INFIX: + str = AMremoveCharsAndBlanks(str,symbol.input.length); + return [createMmlNode("mo",document.createTextNode(symbol.output)),str]; + case SPACE: + str = AMremoveCharsAndBlanks(str,symbol.input.length); + node = createMmlNode("mspace"); + node.setAttribute("width","1ex"); + newFrag.appendChild(node); + newFrag.appendChild( + createMmlNode(symbol.tag,document.createTextNode(symbol.output))); + node = createMmlNode("mspace"); + node.setAttribute("width","1ex"); + newFrag.appendChild(node); + return [createMmlNode("mrow",newFrag),str]; + case LEFTRIGHT: +// if (rightvert) return [null,str]; else rightvert = true; + AMnestingDepth++; + str = AMremoveCharsAndBlanks(str,symbol.input.length); + result = AMparseExpr(str,false); + AMnestingDepth--; + st = ""; + if (result[0].lastChild!=null) + st = result[0].lastChild.firstChild.nodeValue; + if (st == "|") { // its an absolute value subterm + node = createMmlNode("mo",document.createTextNode(symbol.output)); + node = createMmlNode("mrow",node); + node.appendChild(result[0]); + return [node,result[1]]; + } else { // the "|" is a \mid so use unicode 2223 (divides) for spacing + node = createMmlNode("mo",document.createTextNode("\u2223")); + node = createMmlNode("mrow",node); + return [node,str]; + } + default: +//alert("default"); + str = AMremoveCharsAndBlanks(str,symbol.input.length); + return [createMmlNode(symbol.tag, //its a constant + document.createTextNode(symbol.output)),str]; + } +} + +function AMparseIexpr(str) { + var symbol, sym1, sym2, node, result, underover; + str = AMremoveCharsAndBlanks(str,0); + sym1 = AMgetSymbol(str); + result = AMparseSexpr(str); + node = result[0]; + str = result[1]; + symbol = AMgetSymbol(str); + if (symbol.ttype == INFIX && symbol.input != "/") { + str = AMremoveCharsAndBlanks(str,symbol.input.length); +// if (symbol.input == "/") result = AMparseIexpr(str); else ... + result = AMparseSexpr(str); + if (result[0] == null) // show box in place of missing argument + result[0] = createMmlNode("mo",document.createTextNode("\u25A1")); + else AMremoveBrackets(result[0]); + str = result[1]; +// if (symbol.input == "/") AMremoveBrackets(node); + underover = (sym1.ttype == UNDEROVER || sym1.ttype == UNARYUNDEROVER); + if (symbol.input == "_") { + sym2 = AMgetSymbol(str); + if (sym2.input == "^") { + str = AMremoveCharsAndBlanks(str,sym2.input.length); + var res2 = AMparseSexpr(str); + AMremoveBrackets(res2[0]); + str = res2[1]; + node = createMmlNode((underover?"munderover":"msubsup"),node); + node.appendChild(result[0]); + node.appendChild(res2[0]); + node = createMmlNode("mrow",node); // so sum does not stretch + } else { + node = createMmlNode((underover?"munder":"msub"),node); + node.appendChild(result[0]); + } + } else if (symbol.input == "^" && underover) { + node = createMmlNode("mover",node); + node.appendChild(result[0]); + } else { + node = createMmlNode(symbol.tag,node); + node.appendChild(result[0]); + } + if (typeof sym1.func != 'undefined' && sym1.func) { + sym2 = AMgetSymbol(str); + if (sym2.ttype != INFIX && sym2.ttype != RIGHTBRACKET) { + result = AMparseIexpr(str); + node = createMmlNode("mrow",node); + node.appendChild(result[0]); + str = result[1]; + } + } + } + return [node,str]; +} + +function AMparseExpr(str,rightbracket) { + var symbol, node, result, i, + newFrag = document.createDocumentFragment(); + do { + str = AMremoveCharsAndBlanks(str,0); + result = AMparseIexpr(str); + node = result[0]; + str = result[1]; + symbol = AMgetSymbol(str); + if (symbol.ttype == INFIX && symbol.input == "/") { + str = AMremoveCharsAndBlanks(str,symbol.input.length); + result = AMparseIexpr(str); + if (result[0] == null) // show box in place of missing argument + result[0] = createMmlNode("mo",document.createTextNode("\u25A1")); + else AMremoveBrackets(result[0]); + str = result[1]; + AMremoveBrackets(node); + node = createMmlNode(symbol.tag,node); + node.appendChild(result[0]); + newFrag.appendChild(node); + symbol = AMgetSymbol(str); + } + else if (node!=undefined) newFrag.appendChild(node); + } while ((symbol.ttype != RIGHTBRACKET && + (symbol.ttype != LEFTRIGHT || rightbracket) + || AMnestingDepth == 0) && symbol!=null && symbol.output!=""); + if (symbol.ttype == RIGHTBRACKET || symbol.ttype == LEFTRIGHT) { +// if (AMnestingDepth > 0) AMnestingDepth--; + var len = newFrag.childNodes.length; + if (len>0 && newFrag.childNodes[len-1].nodeName == "mrow" + && newFrag.childNodes[len-1].lastChild + && newFrag.childNodes[len-1].lastChild.firstChild ) { //matrix + //removed to allow row vectors: //&& len>1 && + //newFrag.childNodes[len-2].nodeName == "mo" && + //newFrag.childNodes[len-2].firstChild.nodeValue == "," + var right = newFrag.childNodes[len-1].lastChild.firstChild.nodeValue; + if (right==")" || right=="]") { + var left = newFrag.childNodes[len-1].firstChild.firstChild.nodeValue; + if (left=="(" && right==")" && symbol.output != "}" || + left=="[" && right=="]") { + var pos = []; // positions of commas + var matrix = true; + var m = newFrag.childNodes.length; + for (i=0; matrix && i1) matrix = pos[i].length == pos[i-2].length; + } + matrix = matrix && (pos.length>1 || pos[0].length>0); + if (matrix) { + var row, frag, n, k, table = document.createDocumentFragment(); + for (i=0; i(-,-,...,-,-) + n = node.childNodes.length; + k = 0; + node.removeChild(node.firstChild); //remove ( + for (j=1; j2) { + newFrag.removeChild(newFrag.firstChild); //remove ) + newFrag.removeChild(newFrag.firstChild); //remove , + } + table.appendChild(createMmlNode("mtr",row)); + } + node = createMmlNode("mtable",table); + if (typeof symbol.invisible == "boolean" && symbol.invisible) node.setAttribute("columnalign","left"); + newFrag.replaceChild(node,newFrag.firstChild); + } + } + } + } + str = AMremoveCharsAndBlanks(str,symbol.input.length); + if (typeof symbol.invisible != "boolean" || !symbol.invisible) { + node = createMmlNode("mo",document.createTextNode(symbol.output)); + newFrag.appendChild(node); + } + } + return [newFrag,str]; +} + +function parseMath(str,latex) { + var frag, node; + AMnestingDepth = 0; + //some basic cleanup for dealing with stuff editors like TinyMCE adds + str = str.replace(/ /g,""); + str = str.replace(/>/g,">"); + str = str.replace(/</g,"<"); + str = str.replace(/(Sin|Cos|Tan|Arcsin|Arccos|Arctan|Sinh|Cosh|Tanh|Cot|Sec|Csc|Log|Ln|Abs)/g, function(v) { return v.toLowerCase(); }); + frag = AMparseExpr(str.replace(/^\s+/g,""),false)[0]; + node = createMmlNode("mstyle",frag); + if (mathcolor != "") node.setAttribute("mathcolor",mathcolor); + if (mathfontfamily != "") node.setAttribute("fontfamily",mathfontfamily); + if (displaystyle) node.setAttribute("displaystyle","true"); + node = createMmlNode("math",node); + if (showasciiformulaonhover) //fixed by djhsu so newline + node.setAttribute("title",str.replace(/\s+/g," "));//does not show in Gecko + return node; +} + +function strarr2docFrag(arr, linebreaks, latex) { + var newFrag=document.createDocumentFragment(); + var expr = false; + for (var i=0; i,\\|!:;'~]|\\.(?!(?:\x20|$))|"+ambigAMtoken+englishAMtoken+simpleAMtoken; + var re = new RegExp("(^|\\s)((("+token+")\\s?)(("+token+secondenglishAMtoken+")\\s?)+)([,.?]?(?=\\s|$))","g"); + str = str.replace(re," `$2`$7"); + var arr = str.split(AMdelimiter1); + var re1 = new RegExp("(^|\\s)([b-zB-HJ-Z+*<>]|"+texcommand+ambigAMtoken+simpleAMtoken+")(\\s|\\n|$)","g"); + var re2 = new RegExp("(^|\\s)([a-z]|"+texcommand+ambigAMtoken+simpleAMtoken+")([,.])","g"); // removed |\d+ for now + for (i=0; i1 || mtch) { + if (!noMathML) { + frg = strarr2docFrag(arr,n.nodeType==8,latex); + var len = frg.childNodes.length; + n.parentNode.replaceChild(frg,n); + return len-1; + } else return 0; + } + } + } else return 0; + } else if (n.nodeName!="math") { + for (i=0; igCniQG(FtL6Gs5B_neCZ(TfY`b|RTNM52 zdiKpdwZcQ~7mEsDhn76cy7!~&2WOp&^AfZB;V%MNme!?Y#60boeXX>=A@{HZV z0THs_c~1!Xgxlj1Apy_dBrv!67o(n=Xs9wQgAJ43f3eNqEZYZS4nNr@Ra$a1`!9jB zYm`O%Y+3mB?+O{p59!y)+WC!I_z#Kt-#@-1JOEsLHq3fg9pYX*hOy|@4bSv(tb3oZ z+@G+dmTO#FQ?rM?yOtu6;^Qz&p&(K9jG({?Ri0UCQMjj9j(i-X0G849v_~6d!W^ovkkFtV#d)W2HRr2@g)8NhK;gA zGtpLkbX;oh3Z|{kX4*Gu5BgBaQiVTuhN+tr!h_AKaRVhLkv}%^CZorF&Nm{yqxTTW z>v^?NN9&!~Z8}_6ej+Q5wj0TvbvamJ($;qgEHBJI`(@?jn8U|`4McLBBy3{a2bIh! zR?_}*fU3Gt>3-mG`q_u`jwmVNLw`I4BK3wsQE+2a%eZ4W?uZjU4}TaWSdCTP<=xcL}_qFkD}ccU9MXX_7hQm^a*Cz zNxm)VVXT2H@65I3-2OdRrjOaAG;U2EZD!r}BG9cF&N!Z@rv=8OBhR?@qlkR@)K0Ch z$7Fg~;*mlpjs3P=m+?w>u~}9UC%5u8K{HP`15?%9+rIb>LS!lez%(VpauK5<9}I%c z^sxo6Xe+o)j@Nc?_n-3(eL1+)lI`HZ5_6bW2bY`{YVs^Q8{_LBxs`^_`B2xf&%i;$CL 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z54~=Yp^8SvtkPYXQD4CYD^eC8Urgqz#Ie!N-w4RD7H3)b!B?!4C1OvYVa*9SE@v9d zb?pcFlO~Qx4A?9j6Ny9z$m)?@t5D@lTe&j9R%wVgRBKp&tT3iz-SF(CR;?Lp9EQ$D zftKCXsRp#-<~Mgl;&16nuH#6ykc@hh>A~sTN0Dzz=TxJ0AGoq|J^Ddgv!mB!g3R{V zQ_B#?F=3l?V%)OqL&znR(CmEc^a)x~#lUVDN7pK|_=rg8rid6>!nO3kFn&|Jr~EZ$ z#|t@5GCJq1h2n?&TTfD}Qx@Z^nI$A?iClEl)h|2Q^~RSrP^h_&{2xGk1Btj>gJRDsv>kuW@wf^|Bk->P literal 0 HcmV?d00001 diff --git a/docs/_site/assets/js/jquery.autotoc.js b/docs/_site/assets/js/jquery.autotoc.js new file mode 100644 index 0000000..20a2bd4 --- /dev/null +++ b/docs/_site/assets/js/jquery.autotoc.js @@ -0,0 +1,58 @@ +// jQuery AutoTOC +// Dynamically create a table of contents for a page with semantically correct HTML headings. +// Version 1.0, December 30, 2016 +// By Craig D. Cocca + +jQuery.fn.extend({ + autoTOC: function(options) { + + var monitoredDOMElements = new Array(); + var windowHeight = $(window).height(); + + // Make sure we keep tabs on the window height as the user changes the browser window dimensions + $(window).on("resize", function() { + windowHeight = $(window).height(); + }); + + // Bind monitor to scroll event to keep an eye which heading element is in the top quarter of the page + $(window).on("scroll",function() { + topOfWindow = $(window).scrollTop(); + bottomOfWindow = $(window).scrollTop() + (windowHeight * .25); + for(element in monitoredDOMElements) { + if( monitoredDOMElements[element].offset > topOfWindow && + monitoredDOMElements[element].offset < bottomOfWindow) { + $(monitoredDOMElements[element].anchor).addClass("selected"); + $(".autotoc li").not(monitoredDOMElements[element].anchor).removeClass("selected"); + break; + } + } + }); + + + // Default settings + var settings = $.extend({ + toc: "#toc" + },options); + + var toc = $('
    '); + + $(settings.toc).append(toc); + + return this.each(function() { + tocEntry = $('
  • ' + $(this).html() + '
    • '); + tocEntry.data("parentHeading",this); + tocEntry.on("click", function() { + $('html, body').animate({ + scrollTop: $($(this).data("parentHeading")).offset().top - (windowHeight * .2) + }, 750 ); + }); + + $(".autotoc").append(tocEntry); + + monitoredDOMElements.push({ + offset: $(this).offset().top, + anchor: tocEntry + }); + }); + } +}); \ No newline at end of file diff --git a/docs/_site/spec/00.00.00.title.html b/docs/_site/spec/00.00.00.title.html new file mode 100644 index 0000000..3b73c4f --- /dev/null +++ b/docs/_site/spec/00.00.00.title.html @@ -0,0 +1,2 @@ + +

    {{ page.title }}

    diff --git a/docs/_site/spec/00.00.00.title.md b/docs/_site/spec/00.00.00.title.md new file mode 100644 index 0000000..fffa716 --- /dev/null +++ b/docs/_site/spec/00.00.00.title.md @@ -0,0 +1,3 @@ + +# {{ page.title }} +{:.no_toc} diff --git a/docs/_site/spec/00.00.01.version.html b/docs/_site/spec/00.00.01.version.html new file mode 100644 index 0000000..ecfa653 --- /dev/null +++ b/docs/_site/spec/00.00.01.version.html @@ -0,0 +1,3 @@ + +

    __
    +__

    diff --git a/docs/_site/spec/00.00.01.version.md b/docs/_site/spec/00.00.01.version.md new file mode 100644 index 0000000..1796d22 --- /dev/null +++ b/docs/_site/spec/00.00.01.version.md @@ -0,0 +1,3 @@ + +_{{ page.version }}_ +_{{ page.version_date }}_ diff --git a/docs/_site/spec/00.00.02.authors.html b/docs/_site/spec/00.00.02.authors.html new file mode 100644 index 0000000..289d69f --- /dev/null +++ b/docs/_site/spec/00.00.02.authors.html @@ -0,0 +1,4 @@ + +

    Frank Galligan, Google
    +[author]
    +[author]

    diff --git a/docs/_site/spec/00.00.02.authors.md b/docs/_site/spec/00.00.02.authors.md new file mode 100644 index 0000000..2cf7726 --- /dev/null +++ b/docs/_site/spec/00.00.02.authors.md @@ -0,0 +1,4 @@ + +_Frank Galligan, Google +\[author] +\[author]_ diff --git a/docs/_site/spec/00.00.03.last.modified.html b/docs/_site/spec/00.00.03.last.modified.html new file mode 100644 index 0000000..124fa6d --- /dev/null +++ b/docs/_site/spec/00.00.03.last.modified.html @@ -0,0 +1,2 @@ + +

    Last modified: 2017-07-09 18:30:06 -0700

    diff --git a/docs/_site/spec/00.00.03.last.modified.md b/docs/_site/spec/00.00.03.last.modified.md new file mode 100644 index 0000000..092b08c --- /dev/null +++ b/docs/_site/spec/00.00.03.last.modified.md @@ -0,0 +1,2 @@ + +_Last modified: {{ site.time }}_ diff --git a/docs/_site/spec/00.00.04.abstract.html b/docs/_site/spec/00.00.04.abstract.html new file mode 100644 index 0000000..595ec74 --- /dev/null +++ b/docs/_site/spec/00.00.04.abstract.html @@ -0,0 +1,5 @@ + +

    Abstract

    + +

    This document defines the bitstream format and decoding process for the +Draco 3D Data Compression scheme.

    diff --git a/docs/_site/spec/00.00.04.abstract.md b/docs/_site/spec/00.00.04.abstract.md new file mode 100644 index 0000000..2fc4a46 --- /dev/null +++ b/docs/_site/spec/00.00.04.abstract.md @@ -0,0 +1,6 @@ + +## Abstract +{:.no_toc .nocount} + +This document defines the bitstream format and decoding process for the +Draco 3D Data Compression scheme. diff --git a/docs/_site/spec/00.00.05.toc.html b/docs/_site/spec/00.00.05.toc.html new file mode 100644 index 0000000..09409a6 --- /dev/null +++ b/docs/_site/spec/00.00.05.toc.html @@ -0,0 +1,3 @@ + +

    Contents

    + diff --git a/docs/_site/spec/00.00.05.toc.md b/docs/_site/spec/00.00.05.toc.md new file mode 100644 index 0000000..9ce6baf --- /dev/null +++ b/docs/_site/spec/00.00.05.toc.md @@ -0,0 +1,5 @@ + +**Contents** + +* TOC +{:toc} diff --git a/docs/_site/spec/01.00.00.scope.html b/docs/_site/spec/01.00.00.scope.html new file mode 100644 index 0000000..d0e1a2e --- /dev/null +++ b/docs/_site/spec/01.00.00.scope.html @@ -0,0 +1,5 @@ + +

    Scope

    + +

    This document specifies the open-source Draco #D Data Compression bitstream +format and decoding process.

    diff --git a/docs/_site/spec/01.00.00.scope.md b/docs/_site/spec/01.00.00.scope.md new file mode 100644 index 0000000..d17eff9 --- /dev/null +++ b/docs/_site/spec/01.00.00.scope.md @@ -0,0 +1,5 @@ + +## Scope + +This document specifies the open-source Draco #D Data Compression bitstream +format and decoding process. diff --git a/docs/_site/spec/02.00.00.terms.html b/docs/_site/spec/02.00.00.terms.html new file mode 100644 index 0000000..2ecb3a9 --- /dev/null +++ b/docs/_site/spec/02.00.00.terms.html @@ -0,0 +1,19 @@ + +

    Terms and Definitions

    + +

    For the purposes of this document, the following terms and definitions apply:

    + + + + + + + + + + + + + + +
    TermDefinition
      
    diff --git a/docs/_site/spec/02.00.00.terms.md b/docs/_site/spec/02.00.00.terms.md new file mode 100644 index 0000000..cfca0dd --- /dev/null +++ b/docs/_site/spec/02.00.00.terms.md @@ -0,0 +1,8 @@ + +## Terms and Definitions + +For the purposes of this document, the following terms and definitions apply: + +| Term | Definition | +| ------- | ---------------- | +| | | diff --git a/docs/_site/spec/03.00.00.symbols.html b/docs/_site/spec/03.00.00.symbols.html new file mode 100644 index 0000000..550b9e4 --- /dev/null +++ b/docs/_site/spec/03.00.00.symbols.html @@ -0,0 +1,30 @@ + +

    Symbols (and abbreviated terms)

    + +

    DCT: Discrete Cosine Transform

    + +

    FIXME

    + +

    The specification makes use of a number of constant integers. Constants that +relate to the semantics of a particular syntax element are defined in section +7.

    + +

    Additional constants are defined below:

    + + + + + + + + + + + + + + + + +
    Symbol nameValueDescription
    SYMBOL  
    + diff --git a/docs/_site/spec/03.00.00.symbols.md b/docs/_site/spec/03.00.00.symbols.md new file mode 100644 index 0000000..58b42cf --- /dev/null +++ b/docs/_site/spec/03.00.00.symbols.md @@ -0,0 +1,18 @@ + +## Symbols (and abbreviated terms) + +**DCT:** Discrete Cosine Transform + +FIXME + +The specification makes use of a number of constant integers. Constants that +relate to the semantics of a particular syntax element are defined in section +7. + +Additional constants are defined below: + + +| Symbol name | Value | Description | +| ------------------------ |:-----:| ----------- | +| `SYMBOL` | | + diff --git a/docs/_site/spec/04.00.00.conventions.html b/docs/_site/spec/04.00.00.conventions.html new file mode 100644 index 0000000..80fc2b5 --- /dev/null +++ b/docs/_site/spec/04.00.00.conventions.html @@ -0,0 +1,42 @@ +

    Conventions

    + +
      +
    • +

      When bit reading is finished it will always pad the read to the current +byte.

      +
      • +
    • +

      Draco encoded mesh files are comprised of three main sections. This first +section is the header. The second section contains the connectivity data. +The third section contains the attribute data. The header must be decoded +first, then the connectivity section, and then the attribute section.

      +
      • +
    • +

      The Connectivity section is composed of the following sections in order:

      + +
        +
      • +

        Connectivity header

        +
        • +
      • +

        EdgeBreaker symbol buffer

        +
        • +
      • +

        Start face buffer

        +
        • +
      • +

        EdgeBreaker valence header

        +
        • +
      • +

        Context data for the valence prediction

        +
        • +
      • +

        Hole and Split data

        +
        • +
      +
      • +
    • +

      The hole and split data must be decoded before the EdgeBreaker symbols are +decoded.

      +
      • +
    diff --git a/docs/_site/spec/04.00.00.conventions.md b/docs/_site/spec/04.00.00.conventions.md new file mode 100644 index 0000000..767de7c --- /dev/null +++ b/docs/_site/spec/04.00.00.conventions.md @@ -0,0 +1,26 @@ +## Conventions + + * When bit reading is finished it will always pad the read to the current + byte. + + * Draco encoded mesh files are comprised of three main sections. This first + section is the header. The second section contains the connectivity data. + The third section contains the attribute data. The header must be decoded + first, then the connectivity section, and then the attribute section. + + * The Connectivity section is composed of the following sections in order: + + * Connectivity header + + * EdgeBreaker symbol buffer + + * Start face buffer + + * EdgeBreaker valence header + + * Context data for the valence prediction + + * Hole and Split data + + * The hole and split data must be decoded before the EdgeBreaker symbols are + decoded. diff --git a/docs/_site/spec/draco.decoder.html b/docs/_site/spec/draco.decoder.html new file mode 100644 index 0000000..114ff0c --- /dev/null +++ b/docs/_site/spec/draco.decoder.html @@ -0,0 +1,43 @@ +

    Draco Decoder

    + +

    Decode()

    + +
    +Decode() { Type + DecodeHeader() + DecodeConnectivityData() + DecodeAttributeData()} + +
    + +

    DecodeHeader()

    + +
    +DecodeHeader() { Type + draco_string UI8[5] + major_version UI8 + minor_version UI8 + encoder_type UI8 + encoder_method UI8 + flags +} + +
    + +

    DecodeAttributeData()

    + +
    +DecodeAttributeData() { Type + num_attributes_decoders UI8 + for (i = 0; i < num_attributes_decoders; ++i) { + CreateAttributesDecoder(i); + } + for (auto &att_dec : attributes_decoders_) { + att_dec->Initialize(this, point_cloud_) + } + for (i = 0; i < num_attributes_decoders; ++i) { + attributes_decoders_[i]->DecodeAttributesDecoderData(buffer_) + } + DecodeAllAttributes() + OnAttributesDecoded() +
    diff --git a/docs/_site/spec/draco.decoder.md b/docs/_site/spec/draco.decoder.md new file mode 100644 index 0000000..99c8096 --- /dev/null +++ b/docs/_site/spec/draco.decoder.md @@ -0,0 +1,45 @@ +## Draco Decoder + +### Decode() + +
    +Decode() { Type + DecodeHeader() + DecodeConnectivityData() + DecodeAttributeData()} + +
    + + +### DecodeHeader() + +
    +DecodeHeader() { Type + draco_string UI8[5] + major_version UI8 + minor_version UI8 + encoder_type UI8 + encoder_method UI8 + flags +} + +
    + + +### DecodeAttributeData() + +
    +DecodeAttributeData() { Type + num_attributes_decoders UI8 + for (i = 0; i < num_attributes_decoders; ++i) { + CreateAttributesDecoder(i); + } + for (auto &att_dec : attributes_decoders_) { + att_dec->Initialize(this, point_cloud_) + } + for (i = 0; i < num_attributes_decoders; ++i) { + attributes_decoders_[i]->DecodeAttributesDecoderData(buffer_) + } + DecodeAllAttributes() + OnAttributesDecoded() +
    diff --git a/docs/_site/spec/edgebreaker.decoder.html b/docs/_site/spec/edgebreaker.decoder.html new file mode 100644 index 0000000..d5a7db7 --- /dev/null +++ b/docs/_site/spec/edgebreaker.decoder.html @@ -0,0 +1,1556 @@ +

    EdgeBreaker Decoder

    + +

    InitializeDecoder()

    + +
    +InitializeDecoder() { Type + edgebreaker_decoder_type UI8 +} + +
    + +

    DecodeConnectivity()

    + +
    +DecodeConnectivity() { Type + num_new_verts UI32 + num_encoded_vertices UI32 + num_faces UI32 + num_attribute_data I8 + num_encoded_symbols UI32 + num_encoded_split_symbols UI32 + encoded_connectivity_size UI32 + // file pointer must be set to current position + encoded_connectivity_size + hole_and_split_bytes = DecodeHoleAndTopologySplitEvents() + // file pointer must be set to old current position + EdgeBreakerTraversalValence_Start() + DecodeConnectivity(num_symbols) + if (attribute_data_.size() > 0) { + for (ci = 0; ci < corner_table_->num_corners(); ci += 3) { + DecodeAttributeConnectivitiesOnFace(ci) + } + } + for (i = 0; i < corner_table_->num_vertices(); ++i) { + if (is_vert_hole_[i]) { + corner_table_->UpdateVertexToCornerMap(i); + } + } + // Decode attribute connectivity. + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + attribute_data_[i].connectivity_data.InitEmpty(corner_table_.get()); + for (int32_t c : attribute_data_[i].attribute_seam_corners) { + attribute_data_[i].connectivity_data.AddSeamEdge(c); + } + attribute_data_[i].connectivity_data.RecomputeVertices(nullptr, nullptr); + } + // Preallocate vertex to value mapping + AssignPointsToCorners() +} + +
    + +

    AssignPointsToCorners()

    + +
    +AssignPointsToCorners() { Type + decoder_->mesh()->SetNumFaces(corner_table_->num_faces()); + if (attribute_data_.size() == 0) { + for (f = 0; f < decoder_->mesh()->num_faces(); ++f) { + for (c = 0; c < 3; ++c) { + vert_id = corner_table_->Vertex(3 * f + c); + if (point_id == -1) + point_id = num_points++; + face[c] = point_id; + } + decoder_->mesh()->SetFace(f, face); + } + decoder_->point_cloud()->set_num_points(num_points); + Return true; + } + for (v = 0; v < corner_table_->num_vertices(); ++v) { + c = corner_table_->LeftMostCorner(v); + if (c < 0) + continue; + deduplication_first_corner = c; + if (!is_vert_hole_[v]) { + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + if (!attribute_data_[i].connectivity_data.IsCornerOnSeam(c)) + continue; + vert_id = attribute_data_[i].connectivity_data.Vertex(c); + act_c = corner_table_->SwingRight(c); + seam_found = false; + while (act_c != c) { + if (attribute_data_[i].connectivity_data.Vertex(act_c) != vert_id) { + deduplication_first_corner = act_c; + seam_found = true; + break; + } + act_c = corner_table_->SwingRight(act_c); + } + if (seam_found) + break; + } + } + c = deduplication_first_corner; + corner_to_point_map[c] = point_to_corner_map.size(); + point_to_corner_map.push_back(c); + prev_c = c; + c = corner_table_->SwingRight(c); + while (c >= 0 && c != deduplication_first_corner) { + attribute_seam = false; + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + if (attribute_data_[i].connectivity_data.Vertex(c) != + attribute_data_[i].connectivity_data.Vertex(prev_c)) { + attribute_seam = true; + break; + } + } + if (attribute_seam) { + corner_to_point_map[c] = point_to_corner_map.size(); + point_to_corner_map.push_back(c); + } else { + corner_to_point_map[c] = corner_to_point_map[prev_c]; + } + prev_c = c; + c = corner_table_->SwingRight(c); + } + } + for (f = 0; f < decoder_->mesh()->num_faces(); ++f) { + for (c = 0; c < 3; ++c) { + face[c] = corner_to_point_map[3 * f + c]; + } + decoder_->mesh()->SetFace(f, face); + } + decoder_->point_cloud()->set_num_points(point_to_corner_map.size()); +} + +
    + +

    DecodeConnectivity()

    + +
    +DecodeConnectivity(num_symbols) { Type + for (i = 0; i < num_symbols; ++i) { + symbol = TraversalValence_DecodeSymbol() + corner = 3 * num_faces++ + if (symbol == TOPOLOGY_C) { + vertex_x = UpdateCornerTableForSymbolC() + is_vert_hole_[vertex_x] = false; + } else if (symbol == TOPOLOGY_R || symbol == TOPOLOGY_L) { + UpdateCornerTableForSymbolLR() + check_topology_split = true; + } else if (symbol == TOPOLOGY_S) { + HandleSymbolS() + } else if (symbol == TOPOLOGY_E) { + UpdateCornerTableForSymbolE() + check_topology_split = true; + } + active_corner_stack.back() = corner; + traversal_decoder_.NewActiveCornerReached(corner); + if (check_topology_split) { + encoder_symbol_id = num_symbols - symbol_id - 1; + while (true) { + split = IsTopologySplit(encoder_symbol_id, &split_edge, + &encoder_split_symbol_id); + if (!split) { + break; + } + act_top_corner = corner; + if (split_edge == RIGHT_FACE_EDGE) { + new_active_corner = corner_table_->Next(act_top_corner); + } else { + new_active_corner = corner_table_->Previous(act_top_corner); + } + decoder_split_symbol_id = num_symbols - encoder_split_symbol_id - 1; + topology_split_active_corners[decoder_split_symbol_id] = + new_active_corner; + } + } + } + while (active_corner_stack.size() > 0) { + corner = active_corner_stack.pop_back(); + interior_face = traversal_decoder_.DecodeStartFaceConfiguration(); + if (interior_face == true) { + UpdateCornerTableForInteriorFace() + for (ci = 0; ci < 3; ++ci) { + is_vert_hole_[corner_table_->Vertex(new_corner + ci)] = false; + } + init_face_configurations_.push_back(true); + init_corners_.push_back(new_corner); + } else { + init_face_configurations_.push_back(false); + init_corners_.push_back(corner); + } + } + Return num_vertices; +} + +
    + +

    UpdateCornerTableForSymbolC()

    + +
    +UpdateCornerTableForSymbolC(corner) { Type + corner_a = active_corner_stack.back(); + corner_b = corner_table_->Previous(corner_a); + while (corner_table_->Opposite(corner_b) >= 0) { + corner_b = corner_table_->Previous(corner_table_->Opposite(corner_b)); + } + SetOppositeCorners(corner_a, corner + 1); + SetOppositeCorners(corner_b, corner + 2); + vertex_x = corner_table_->Vertex(corner_table_->Next(corner_a)); + corner_table_->MapCornerToVertex(corner, vertex_x); + corner_table_->MapCornerToVertex( + corner + 1, corner_table_->Vertex(corner_table_->Next(corner_b))); + corner_table_->MapCornerToVertex( + corner + 2, corner_table_->Vertex(corner_table_->Previous(corner_a))); + return vertex_x; +} + +
    + +

    UpdateCornerTableForSymbolLR()

    + +
    +UpdateCornerTableForSymbolLR(corner, symbol) { Type + if (symbol == TOPOLOGY_R) { + opp_corner = corner + 2; + } else { + opp_corner = corner + 1; + } + SetOppositeCorners(opp_corner, corner_a); + corner_table_->MapCornerToVertex(opp_corner,num_vertices++); + corner_table_->MapCornerToVertex( + corner_table_->Next(opp_corner), + corner_table_->Vertex(corner_table_->Previous(corner_a))); + corner_table_->MapCornerToVertex( + corner_table_->Previous(opp_corner), + corner_table_->Vertex(corner_table_->Next(corner_a))); +} + +
    + +

    HandleSymbolS()

    + +
    +HandleSymbolS(corner) { Type + corner_b = active_corner_stack.pop_back(); + it = topology_split_active_corners.find(symbol_id); + if (it != topology_split_active_corners.end()) { + active_corner_stack.push_back(it->second); + } + corner_a = active_corner_stack.back(); + SetOppositeCorners(corner_a, corner + 2); + SetOppositeCorners(corner_b, corner + 1); + vertex_p = corner_table_->Vertex(corner_table_->Previous(corner_a)); + corner_table_->MapCornerToVertex(corner, vertex_p); + corner_table_->MapCornerToVertex( + corner + 1, corner_table_->Vertex(corner_table_->Next(corner_a))); + corner_table_->MapCornerToVertex(corner + 2, + corner_table_->Vertex(corner_table_->Previous(corner_b))); + corner_n = corner_table_->Next(corner_b); + vertex_n = corner_table_->Vertex(corner_n); + traversal_decoder_.MergeVertices(vertex_p, vertex_n); + // TraversalValence_MergeVertices + while (corner_n >= 0) { + corner_table_->MapCornerToVertex(corner_n, vertex_p); + corner_n = corner_table_->SwingLeft(corner_n); + } + corner_table_->MakeVertexIsolated(vertex_n); +} + +
    + +

    UpdateCornerTableForSymbolE()

    + +
    +UpdateCornerTableForSymbolE() { Type + corner_table_->MapCornerToVertex(corner, num_vertices++); + corner_table_->MapCornerToVertex(corner + 1, num_vertices++); + corner_table_->MapCornerToVertex(corner + 2, num_vertices++); +} + +
    + +

    UpdateCornerTableForInteriorFace()

    + +
    +UpdateCornerTableForInteriorFace() { Type + corner_b = corner_table_->Previous(corner); + while (corner_table_->Opposite(corner_b) >= 0) { + corner_b = corner_table_->Previous(corner_table_->Opposite(corner_b)); + } + corner_c = corner_table_->Next(corner); + while (corner_table_->Opposite(corner_c) >= 0) { + corner_c = corner_table_->Next(corner_table_->Opposite(corner_c)); + } + face(num_faces++); + corner_table_->MapCornerToVertex( + new_corner, corner_table_->Vertex(corner_table_->Next(corner_b))); + corner_table_->MapCornerToVertex( + new_corner + 1, corner_table_->Vertex(corner_table_->Next(corner_c))); + corner_table_->MapCornerToVertex( + new_corner + 2, corner_table_->Vertex(corner_table_->Next(corner))); +} + +
    + +

    IsTopologySplit()

    + +
    +IsTopologySplit(encoder_symbol_id, *out_face_edge, Type + + *out_encoder_split_symbol_id) { + if (topology_split_data_.size() == 0) + return false; + if (topology_split_data_.back().source_symbol_id != encoder_symbol_id) + return false; + *out_face_edge = topology_split_data_.back().source_edge; + *out_encoder_split_symbol_id = + topology_split_data_.back().split_symbol_id; + topology_split_data_.pop_back(); + return true; +} + +
    + +

    DecodeAttributeConnectivitiesOnFace()

    + +
    +DecodeAttributeConnectivitiesOnFace(corner) { Type + corners[3] = {corner, corner_table_->Next(corner), + corner_table_->Previous(corner)} + for (c = 0; c < 3; ++c) { + opp_corner = corner_table_->Opposite(corners[c]); + if (opp_corner < 0) { + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + attribute_data_[i].attribute_seam_corners.push_back(corners[c]); + } + continue + } + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + bool is_seam = traversal_decoder_.DecodeAttributeSeam(i); + if (is_seam) { + attribute_data_[i].attribute_seam_corners.push_back(corners[c]); + } + } + } +} + +
    + +

    SetOppositeCorners()

    + +
    +SetOppositeCorners(corner_0, corner_1) { Type + corner_table_->SetOppositeCorner(corner_0, corner_1); + corner_table_->SetOppositeCorner(corner_1, corner_0); +} + +
    + +

    EdgeBreaker Hole and Topology Split Events

    + +

    DecodeHoleAndTopologySplitEvents()

    + +

    FIXME: Escaping angle brackets

    + +
    +DecodeHoleAndTopologySplitEvents() { Type + num_topologoy_splits UI32 + source_symbol_id = 0 + for (i = 0; i < num_topologoy_splits; ++i) { + DecodeVarint\<UI32\>(&delta) + split_data[i].source_symbol_id = delta + source_symbol_id + DecodeVarint\<UI32\>(&delta) + split_data[i].split_symbol_id = source_symbol_id - delta + } + for (i = 0; i < num_topologoy_splits; ++i) { + split_data[i].split_edge bits1 + split_data[i].source_edge bits1 + } + num_hole_events UI32 + symbol_id = 0 + for (i = 0; i < num_hole_events; ++i) { + DecodeVarint\<UI32\>(&delta) + hole_data[i].symbol_id = delta + symbol_id + } + return bytes_decoded; +} + +
    + +

    CreateAttributesDecoder

    + +

    FIXME: Escaping angle brackets

    + +
    +CreateAttributesDecoder() { Type + att_data_id I8 + decoder_type UI8 + if (att_data_id >= 0) { + attribute_data_[att_data_id].decoder_id = att_decoder_id; + } + traversal_method_encoded UI8 + if (decoder_type == MESH_VERTEX_ATTRIBUTE) { + if (att_data_id < 0) { + encoding_data = &pos_encoding_data_; + } else { + encoding_data = &attribute_data_[att_data_id].encoding_data; + attribute_data_[att_data_id].is_connectivity_used = false; + } + if (traversal_method == MESH_TRAVERSAL_DEPTH_FIRST) { + typedef EdgeBreakerTraverser\<AttProcessor, AttObserver\> AttTraverser; + sequencer = CreateVertexTraversalSequencer\<AttTraverser\>(encoding_data); + } else if (traversal_method == MESH_TRAVERSAL_PREDICTION_DEGREE) { + typedef PredictionDegreeTraverser\<AttProcessor, AttObserver\> AttTraverser; + sequencer = CreateVertexTraversalSequencer\<AttTraverser\>(encoding_data); + } + } else { + // TODO + } + att_controller(new SequentialAttributeDecodersController(std::move(sequencer))) + decoder_->SetAttributesDecoder(att_decoder_id, std::move(att_controller)); +} + +
    + +

    Edgebreaker Traversal Decoder

    + +

    EdgebreakerTraversal_Start()

    + +
    +EdgebreakerTraversal_Start() { Type + size UI64 + symbol_buffer_ size * UI8 + size UI64 + start_face_buffer_ size * UI8 + if (num_attribute_data_ > 0) { + attribute_connectivity_decoders_ = std::unique_ptr<BinaryDecoder[]>( + new BinaryDecoder[num_attribute_data_]); + for (i = 0; i < num_attribute_data_; ++i) { + attribute_connectivity_decoders_[i].StartDecoding() + // RansBitDecoder_StartDecoding + } +} + +
    + +

    Traversal_DecodeSymbol()

    + +
    Traversal_DecodeSymbol() {
+  symbol_buffer_.DecodeLeastSignificantBits32(1, &symbol);                   bits1
+  if (symbol != TOPOLOGY_C) {
+    symbol_buffer_.DecodeLeastSignificantBits32(2, &symbol_suffix);          bits2
+    symbol |= (symbol_suffix << 1);
+  }
+  return symbol
+}
+
    +
    + +

    DecodeAttributeSeam()

    + +
    DecodeAttributeSeam(int attribute) {
+  return attribute_connectivity_decoders_[attribute].DecodeNextBit();
+}
+
    +
    + +

    EdgeBreaker Traversal Valence Decoder

    + +

    EdgeBreakerTraversalValence_Start()

    + +
    EdgeBreakerTraversalValence_Start(num_vertices, num_attribute_data) {
+  out_buffer = EdgebreakerTraversal_Start()
+  num_split_symbols                                                          I32
+  mode == 0                                                                  I8
+  num_vertices_ += num_split_symbols
+  vertex_valences_ init to 0
+  vertex_valences_.resize(num_vertices_, 0);
+  min_valence_ = 2;
+  max_valence_ = 7;
+  num_unique_valences = 6 (max_valence_ - min_valence_ + 1)
+  for (i = 0; i < num_unique_valences; ++i) {
+    DecodeVarint<UI32>(&num_symbols, out_buffer)
+    If (num_symbols > 0) {
+      DecodeSymbols(num_symbols, out_buffer, &context_symbols_[i])
+    }
+    context_counters_[i] = num_symbols
+  }
+  return out_buffer;
+}
+
    +
    + +

    TraversalValence_DecodeSymbol()

    + +
    TraversalValence_DecodeSymbol() {
+  if (active_context_ != -1) {
+    symbol_id  = context_symbols_[active_context_]
+                                                      [--context_counters_[active_context_]]
+    last_symbol_ = edge_breaker_symbol_to_topology_id[symbol_id]
+  } else {
+    last_symbol_ = Traversal_DecodeSymbol()
+  }
+  return last_symbol_
+}
+
    +
    + +

    TraversalValence_NewActiveCornerReached()

    + +
    TraversalValence_NewActiveCornerReached(corner) {
+  switch (last_symbol_) {
+    case TOPOLOGY_C:
+    case TOPOLOGY_S:
+      vertex_valences_[ct(next)] += 1;
+      vertex_valences_[ct(prev)] += 1;
+      break;
+    case TOPOLOGY_R:
+      vertex_valences_[corner] += 1;
+      vertex_valences_[ct(next)] += 1;
+      vertex_valences_[ct(prev)] += 2;
+      break;
+    case TOPOLOGY_L:
+      vertex_valences_[corner] += 1;
+      vertex_valences_[ct(next)] += 2;
+      vertex_valences_[ct(prev)] += 1;
+      break;
+    case TOPOLOGY_E:
+      vertex_valences_[corner] += 2;
+      vertex_valences_[ct(next)] += 2;
+      vertex_valences_[ct(prev)] += 2;
+      break;
+  }
+  valence = vertex_valences_[ct(next)]
+  valence = max(valence, min_valence_)
+  valence = min(valence, max_valence_)
+  active_context_ = (valence - min_valence_);
+}
+
    +
    + +

    TraversalValence_MergeVertices()

    + +
    TraversalValence_MergeVertices(dest, source) {
+  vertex_valences_[dest] += vertex_valences_[source];
+}
+
    +
    + +

    Attributes Decoder

    + +

    DecodeAttributesDecoderData()

    + +
    DecodeAttributesDecoderData(buffer) {
+  num_attributes                                                             I32
+  point_attribute_ids_.resize(num_attributes);
+  for (i = 0; i < num_attributes; ++i) {
+    att_type                                                                 UI8
+    data_type                                                                UI8
+    components_count                                                         UI8
+    normalized                                                               UI8
+    custom_id                                                                UI16
+    Initialize GeometryAttribute ga
+    att_id = pc->AddAttribute(new PointAttribute(ga));
+    point_attribute_ids_[i] = att_id;
+}
+
    +
    + +

    Sequential Attributes Decoders Controller

    + +

    DecodeAttributesDecoderData()

    + +
    DecodeAttributesDecoderData(buffer) {
+  AttributesDecoder_DecodeAttributesDecoderData(buffer)
+  sequential_decoders_.resize(num_attributes());
+  for (i = 0; i < num_attributes(); ++i) {
+    decoder_type                                                             UI8
+    sequential_decoders_[i] = CreateSequentialDecoder(decoder_type);
+    sequential_decoders_[i]->Initialize(decoder(), GetAttributeId(i))
+}
+
    +
    + +

    DecodeAttributes()

    + +
    DecodeAttributes(buffer) {
+  sequencer_->GenerateSequence(&point_ids_)
+  for (i = 0; i < num_attributes(); ++i) {
+    pa = decoder()->point_cloud()->attribute(GetAttributeId(i));
+    sequencer_->UpdatePointToAttributeIndexMapping(pa)
+  }
+  for (i = 0; i < num_attributes(); ++i) {
+    sequential_decoders_[i]->Decode(point_ids_, buffer)
+    //SequentialAttributeDecoder_Decode()
+  }
+}
+
    +
    + +

    CreateSequentialDecoder()

    + +
    CreateSequentialDecoder(type) {
+  switch (type) {
+    case SEQUENTIAL_ATTRIBUTE_ENCODER_GENERIC:
+      return new SequentialAttributeDecoder()
+    case SEQUENTIAL_ATTRIBUTE_ENCODER_INTEGER:
+      return new SequentialIntegerAttributeDecoder()
+    case SEQUENTIAL_ATTRIBUTE_ENCODER_QUANTIZATION:
+      return new SequentialQuantizationAttributeDecoder()
+    case SEQUENTIAL_ATTRIBUTE_ENCODER_NORMALS:
+      return new SequentialNormalAttributeDecoder()
+  }
+}
+
    +
    + +

    Sequential Attribute Decoder

    + +
    Initialize(...) {
+  // Init some members
+}
+
    +
    + +

    DecodeValues()

    + +
    DecodeValues(const std::vector<PointIndex> &point_ids) {
+  num_values = point_ids.size();
+  entry_size = attribute_->byte_stride();
+  std::unique_ptr<uint8_t[]> value_data_ptr(new uint8_t[entry_size]);
+  out_byte_pos = 0;
+  for (i = 0; i < num_values; ++i) {
+   value_data                                                         UI8 * entry_size
+    attribute_->buffer()->Write(out_byte_pos, value_data, entry_size);
+    out_byte_pos += entry_size;
+  }
+}
+
    +
    + +

    Sequential Integer Attribute Decoder

    + +
    Initialize(...) {
+  SequentialAttributeDecoder_Initialize()
+}
+
    +
    + +

    DecodeValues()

    + +
    DecodeValues(point_ids) {
+  prediction_scheme_method                                                   I8
+  if (prediction_scheme_method != PREDICTION_NONE) {
+    prediction_transform_type                                                I8
+    prediction_scheme_ = CreateIntPredictionScheme(...)
+  }
+  if (prediction_scheme_) {
+  }
+  DecodeIntegerValues(point_ids)
+  //SequentialQuantizationAttributeDecoder_DecodeIntegerValues()
+  //StoreValues()
+  DequantizeValues(num_values)
+}
+
    +
    + +

    DecodeIntegerValues()

    + +
    DecodeIntegerValues(point_ids) {
+  compressed                                                                 UI8
+  if (compressed) {
+    DecodeSymbols(..., values_.data())
+  } else {
+  // TODO
+  }
+  if (!prediction_scheme_->AreCorrectionsPositive()) {
+    ConvertSymbolsToSignedInts(...)
+  }
+  if (prediction_scheme_) {
+    prediction_scheme_->DecodePredictionData(buffer)
+    // DecodeTransformData(buffer)
+    if (!values_.empty()) {
+      prediction_scheme_->Decode(values_.data(), &values_[0],
+                                      values_.size(), num_components, point_ids.data())
+      // MeshPredictionSchemeParallelogram_Decode()
+}
+
    +
    + +

    Sequential Quantization Attribute Decoder

    + +
    Initialize(...) {
+  SequentialIntegerAttributeDecoder_Initialize()
+}
+
    +
    + +

    DecodeIntegerValues()

    + +
    DecodeIntegerValues(point_ids) {
+  // DecodeQuantizedDataInfo()
+  num_components = attribute()->components_count();
+  for (i = 0; i < num_components; ++i) {
+    min_value_[i]                                                            F32
+  }
+  max_value_dif_                                                             F32
+  quantization_bits_                                                         UI8
+  SequentialIntegerAttributeDecoder::DecodeIntegerValues()
+}
+
    +
    + +

    DequantizeValues()

    + +
    DequantizeValues(num_values) {
+  max_quantized_value = (1 << (quantization_bits_)) - 1;
+  num_components = attribute()->components_count();
+  entry_size = sizeof(float) * num_components;
+  quant_val_id = 0;
+  out_byte_pos = 0;
+  for (i = 0; i < num_values; ++i) {
+    for (c = 0; c < num_components; ++c) {
+      value = dequantizer.DequantizeFloat(values()->at(quant_val_id++));
+      value = value + min_value_[c];
+      att_val[c] = value;
+    }
+    attribute()->buffer()->Write(out_byte_pos, att_val.get(), entry_size);
+    out_byte_pos += entry_size;
+  }
+}
+
    +
    + +

    Prediction Scheme Transform

    + +

    ComputeOriginalValue()

    + +
    ComputeOriginalValue(const DataTypeT *predicted_vals,
+                                   const CorrTypeT *corr_vals,
+                                   DataTypeT *out_original_vals, int val_id) {
+  for (i = 0; i < num_components_; ++i) {
+    out_original_vals[i] = predicted_vals[i] + corr_vals[val_id + i];
+  }
+}
+
    +
    + +

    Prediction Scheme Wrap Transform

    + +

    DecodeTransformData()

    + +
    DecodeTransformData(buffer) {
+  min_value_                                                                 DT
+  max_value_                                                                 DT
+}
+
    +
    + +

    ComputeOriginalValue()

    + +
    ComputeOriginalValue(const DataTypeT *predicted_vals,
+                                   const CorrTypeT *corr_vals,
+                                   DataTypeT *out_original_vals, int val_id) {
+  clamped_vals = ClampPredictedValue(predicted_vals);
+  ComputeOriginalValue(clamped_vals, corr_vals, out_original_vals, val_id)
+  // PredictionSchemeTransform_ComputeOriginalValue()
+  for (i = 0; i < this->num_components(); ++i) {
+    if (out_original_vals[i] > max_value_) {
+      out_original_vals[i] -= max_dif_;
+    } else if (out_original_vals[i] < min_value_) {
+      out_original_vals[i] += max_dif_;
+    }
+}
+
    +
    + +

    ClampPredictedValue()

    + +
    ClampPredictedValue(const DataTypeT *predicted_val) {
+  for (i = 0; i < this->num_components(); ++i) {
+    clamped_value_[i] = min(predicted_val[i], max_value_)
+    clamped_value_[i] = max(predicted_val[i], min_value_)
+  }
+  return &clamped_value_[0];
+}
+
    +
    + +

    Mesh Prediction Scheme Parallelogram

    + +

    Decode()

    + +
    Decode(...) {
+  this->transform().InitializeDecoding(num_components);
+  // restore the first value
+  this->transform().ComputeOriginalValue(pred_vals.get(),
+                                       in_corr, out_data, 0);
+  // PredictionSchemeWrapTransform_ComputeOriginalValue()
+  corner_map_size = this->mesh_data().data_to_corner_map()->size();
+  for (p = 1; p < corner_map_size; ++p) {
+    corner_id = this->mesh_data().data_to_corner_map()->at(p);
+    dst_offset = p * num_components;
+    b= ComputeParallelogramPrediction(p, corner_id, table,
+                                        *vertex_to_data_map, out_data,
+                                        num_components, pred_vals.get())
+    if (!b) {
+      src_offset = (p - 1) * num_components;
+      this->transform().ComputeOriginalValue(out_data + src_offset, in_corr,
+                                             out_data + dst_offset, dst_offset);
+      // PredictionSchemeWrapTransform_ComputeOriginalValue()
+    } else {
+      this->transform().ComputeOriginalValue(pred_vals.get(), in_corr,
+                                             out_data + dst_offset, dst_offset);
+      // PredictionSchemeWrapTransform_ComputeOriginalValue()
+    }
+  }
+}
+
    +
    + +

    MeshPredictionSchemeParallelogramShared

    + +

    ComputeParallelogramPrediction()

    + +
    ComputeParallelogramPrediction(...) {
+  oci = table->Opposite(ci);
+  vert_opp = vertex_to_data_map[table->Vertex(ci)];
+  vert_next = vertex_to_data_map[table->Vertex(table->Next(ci))];
+  vert_prev = vertex_to_data_map[table->Vertex(table->Previous(ci))];
+  if (vert_opp < data_entry_id && vert_next < data_entry_id &&
+      vert_prev < data_entry_id) {
+    v_opp_off = vert_opp * num_components;
+    v_next_off = vert_next * num_components;
+    v_prev_off = vert_prev * num_components;
+    for (c = 0; c < num_components; ++c) {
+      out_prediction[c] = (in_data[v_next_off + c] + in_data[v_prev_off + c]) -
+                          in_data[v_opp_off + c];
+    }
+    Return true;
+  }
+  return false;
+}
+
    +
    + +

    CornerTable Traversal Processor

    + +

    IsFaceVisited()

    + +
    IsFaceVisited(corner_id) {
+  if (corner_id < 0)
+    return true
+  return is_face_visited_[corner_id / 3];
+}
+
    +
    + +

    MarkFaceVisited()

    + +
    MarkFaceVisited(face_id) {
+  is_face_visited_[face_id] = true;
+}
+
    +
    + +

    IsVertexVisited()

    + +
    IsVertexVisited(vert_id) {
+  return is_vertex_visited_[vert_id];
+}
+
    +
    + +

    MarkVertexVisited()

    + +
    MarkVertexVisited(vert_id) {
+  is_vertex_visited_[vert_id] = true;
+}
+
    +
    + +

    Mesh Attribute Indices Encoding Observer

    + +

    OnNewVertexVisited()

    + +
    OnNewVertexVisited(vertex, corner) {
+  point_id = mesh_->face(corner / 3)[corner % 3];
+  sequencer_->AddPointId(point_id);
+  // Keep track of visited corners.
+  encoding_data_->encoded_attribute_value_index_to_corner_map.push_back(corner);
+  encoding_data_
+        ->vertex_to_encoded_attribute_value_index_map[vertex] =
+        encoding_data_->num_values;
+  encoding_data_->num_values++;
+}
+
    +
    + +

    EdgeBreaker Traverser

    + +

    TraverseFromCorner()

    + +
    TraverseFromCorner(corner_id) {
+  if (processor_.IsFaceVisited(corner_id))
+    return
+  corner_traversal_stack_.clear();
+  corner_traversal_stack_.push_back(corner_id);
+  next_vert = corner_table_->Vertex(corner_table_->Next(corner_id));
+  prev_vert = corner_table_->Vertex(corner_table_->Previous(corner_id));
+  if (!processor_.IsVertexVisited(next_vert)) {
+    processor_.MarkVertexVisited(next_vert);
+    traversal_observer_.OnNewVertexVisited(next_vert,
+                                        corner_table_->Next(corner_id));
+  }
+  if (!processor_.IsVertexVisited(prev_vert)) {
+    processor_.MarkVertexVisited(prev_vert);
+    traversal_observer_.OnNewVertexVisited(prev_vert,
+                                        corner_table_->Previous(corner_id));
+  }
+  while (!corner_traversal_stack_.empty()) {
+    corner_id = corner_traversal_stack_.back();
+    face_id =corner_id / 3;
+    if (processor_.IsFaceVisited(face_id)) {
+      corner_traversal_stack_.pop_back();
+      continue
+    }
+    while(true) {
+      face_id = corner_id / 3;
+      processor_.MarkFaceVisited(face_id);
+      traversal_observer_.OnNewFaceVisited(face_id);
+      vert_id = corner_table_->Vertex(corner_id);
+      on_boundary = corner_table_->IsOnBoundary(vert_id);
+      if (!processor_.IsVertexVisited(vert_id)) {
+        processor_.MarkVertexVisited(vert_id);
+        traversal_observer_.OnNewVertexVisited(vert_id, corner_id);
+        if (!on_boundary) {
+          corner_id = corner_table_->GetRightCorner(corner_id);
+          continue;
+        }
+      }
+      // The current vertex has been already visited or it was on a boundary.
+      right_corner_id = corner_table_->GetRightCorner(corner_id);
+      left_corner_id = corner_table_->GetLeftCorner(corner_id);
+      right_face_id((right_corner_id < 0 ? -1 : right_corner_id / 3));
+      left_face_id((left_corner_id < 0 ? -1 : left_corner_id / 3));
+      if (processor_.IsFaceVisited(right_face_id)) {
+        if (processor_.IsFaceVisited(left_face_id)) {
+          corner_traversal_stack_.pop_back();
+          break; // Break from while(true) loop
+        } else {
+          corner_id = left_corner_id;
+        }
+      } else {
+        if (processor_.IsFaceVisited(left_face_id)) {
+          corner_id = right_corner_id;
+       } else {
+          // Split the traversal.
+          corner_traversal_stack_.back() = left_corner_id;
+          corner_traversal_stack_.push_back(right_corner_id);
+          break; // Break from while(true) loop
+        }
+      }
+    }
+  }
+}
+
    +
    + +

    Mesh Traversal Sequencer

    + +

    GenerateSequenceInternal()

    + +
    GenerateSequenceInternal() {
+  traverser_.OnTraversalStart();
+   If (corner_order_) {
+    // TODO
+  } else {
+    int32_t num_faces = traverser_.corner_table()->num_faces();
+    for (i = 0; i < num_faces; ++i) {
+      ProcessCorner(3 * i)
+    }
+  }
+  traverser_.OnTraversalEnd();
+}
+
    +
    + +

    ProcessCorner()

    + +
    ProcessCorner(corner_id) {
+  traverser_.TraverseFromCorner(corner_id);
+}
+
    +
    + +

    UpdatePointToAttributeIndexMapping()

    + +
    UpdatePointToAttributeIndexMapping(PointAttribute *attribute) {
+  corner_table = traverser_.corner_table();
+  attribute->SetExplicitMapping(mesh_->num_points());
+  num_faces = mesh_->num_faces();
+  num_points = mesh_->num_points();
+  for (f = 0; f < num_faces; ++f) {
+    face = mesh_->face(f);
+    for (p = 0; p < 3; ++p) {
+      point_id = face[p];
+      vert_id = corner_table->Vertex(3 * f + p);
+      att_entry_id(
+            encoding_data_
+                ->vertex_to_encoded_attribute_value_index_map[vert_id]);
+      attribute->SetPointMapEntry(point_id, att_entry_id);
+    }
+  }
+}
+
    +
    + +

    PointsSequencer

    + +

    AddPointId()

    + +
    AddPointId(point_id) {
+  out_point_ids_->push_back(point_id);
+}
+
    +
    + +

    Corner Table

    + +

    Opposite()

    + +
    Opposite(corner) {
+  return opposite_corners_[corner];
+}
+
    +
    + +

    Next()

    + +
    Next(corner) {
+  return LocalIndex(++corner) ? corner : corner - 3;
+}
+
    +
    + +

    Previous()

    + +
    Previous(corner) {
+  return LocalIndex(corner) ? corner - 1 : corner + 2;
+}
+
    +
    + +

    Vertex()

    + +
    Vertex(corner) {
+  faces_[Face(corner)][LocalIndex(corner)];
+}
+
    +
    + +

    Face()

    + +
    Face(corner) {
+  return corner / 3;
+}
+
    +
    + +

    LocalIndex()

    + +
    LocalIndex(corner) {
+  return corner % 3;
+}
+
    +
    + +

    num_vertices()

    + +
    num_vertices() {
+  return vertex_corners_.size();
+}
+
    +
    + +

    num_corners()

    + +
    num_corners() {
+  return faces_.size() * 3;
+}
+
    +
    + +

    num_faces()

    + +
    num_faces() {
+  return faces_.size();
+}
+
    +
    + +

    bool IsOnBoundary()

    + +
    bool IsOnBoundary(vert) {
+  corner = LeftMostCorner(vert);
+  if (SwingLeft(corner) < 0)
+    return true;
+  return false;
+}
+
    +
    + +

    SwingRight()

    + +
    SwingRight(corner) {
+  return Previous(Opposite(Previous(corner)));
+}
+
    +
    + +

    SwingLeft()

    + +
    SwingLeft(corner) {
+  return Next(Opposite(Next(corner)));
+}
+
    +
    + +

    GetLeftCorner()

    + +
    GetLeftCorner(corner_id) {
+  if (corner_id < 0)
+     return kInvalidCornerIndex;
+  return Opposite(Previous(corner_id));
+}
+
    +
    + +

    GetRightCorner()

    + +
    GetRightCorner(corner_id) {
+  if (corner_id < 0)
+     return kInvalidCornerIndex;
+  return Opposite(Next(corner_id));
+}
+
    +
    + +

    SetOppositeCorner()

    + +
    SetOppositeCorner(corner_id, pp_corner_id) {
+  opposite_corners_[corner_id] = opp_corner_id;
+}
+
    +
    + +

    MapCornerToVertex()

    + +
    MapCornerToVertex(corner_id, vert_id) {
+  face = Face(corner_id);
+  faces_[face][LocalIndex(corner_id)] = vert_id;
+  if (vert_id >= 0) {
+    vertex_corners_[vert_id] = corner_id;
+  }
+}
+
    +
    + +

    UpdateVertexToCornerMap()

    + +
    UpdateVertexToCornerMap(vert) {
+  first_c = vertex_corners_[vert];
+  if (first_c < 0)
+    return;
+  act_c = SwingLeft(first_c);
+  c = first_c;
+  while (act_c >= 0 && act_c != first_c) {
+    c = act_c;
+    act_c = SwingLeft(act_c);
+  }
+  if (act_c != first_c) {
+    vertex_corners_[vert] = c;
+  }
+}
+
    +
    + +

    LeftMostCorner()

    + +
    LeftMostCorner(v) {
+  return vertex_corners_[v];
+}
+
    +
    + +

    MakeVertexIsolated()

    + +
    MakeVertexIsolated(vert) {
+  vertex_corners_[vert] = kInvalidCornerIndex;
+}
+
    +
    + +

    Mesh Attribute Corner Table

    + +

    bool IsCornerOnSeam()

    + +
    bool IsCornerOnSeam(corner) {
+  return is_vertex_on_seam_[corner_table_->Vertex(corner)];
+}
+
    +
    + +

    AddSeamEdge()

    + +
    AddSeamEdge(c) {
+  MarkSeam(c)
+  opp_corner = corner_table_->Opposite(c);
+  if (opp_corner >= 0) {
+    no_interior_seams_ = false;
+    MarkSeam(opp_corner)
+  }
+}
+
    +
    + +

    MarkSeam()

    + +
    MarkSeam(c) {
+  is_edge_on_seam_[c] = true;
+  is_vertex_on_seam_[corner_table_->Vertex(corner_table_->Next(c))] = true;
+  is_vertex_on_seam_[corner_table_->Vertex(corner_table_->Previous(c))
+                         ] = true;
+}
+
    +
    + +

    RecomputeVertices()

    + +
    RecomputeVertices() {
+  // in code RecomputeVerticesInternal<false>(nullptr, nullptr)
+  num_new_vertices = 0;
+  for (v = 0; v < corner_table_->num_vertices(); ++v) {
+    c = corner_table_->LeftMostCorner(v);
+    if (c < 0)
+      continue;
+    first_vert_id(num_new_vertices++);
+    vertex_to_attribute_entry_id_map_.push_back(first_vert_id);
+    first_c = c;
+    if (is_vertex_on_seam_[v]) {
+      act_c = SwingLeft(first_c);
+      while (act_c >= 0) {
+        first_c = act_c;
+        act_c = SwingLeft(act_c);
+      }
+    }
+    corner_to_vertex_map_[first_c] =first_vert_id;
+    vertex_to_left_most_corner_map_.push_back(first_c);
+    act_c = corner_table_->SwingRight(first_c);
+    while (act_c >= 0 && act_c != first_c) {
+      if (is_edge_on_seam_[corner_table_->Next(act_c)]) {
+        // in code IsCornerOppositeToSeamEdge()
+        first_vert_id = AttributeValueIndex(num_new_vertices++);
+        vertex_to_attribute_entry_id_map_.push_back(first_vert_id);
+        vertex_to_left_most_corner_map_.push_back(act_c);
+      }
+      corner_to_vertex_map_[act_c] = first_vert_id;
+      act_c = corner_table_->SwingRight(act_c);
+    }
+  }
+}
+
    +
    + +

    Symbol Decoding

    + +

    DecodeSymbols()

    + +
    DecodeSymbols(num_symbols, out_buffer, out_values) {
+  scheme                                                                     UI8
+  If (scheme == 0) {
+    DecodeTaggedSymbols<>(num_symbols, src_buffer, out_values)
+  } else if (scheme == 1) {
+    DecodeRawSymbols<>(num_symbols, src_buffer, out_values)
+  }
+}
+
    +
    + +

    DecodeTaggedSymbols()

    + +
    DecodeTaggedSymbols() {
+  FIXME
+}
+
    +
    + +

    DecodeRawSymbols()

    + +
    DecodeRawSymbols() {
+  max_bit_length                                                             UI8
+  DecodeRawSymbolsInternal(max_bit_length, out_values)
+  return symbols
+}
+
    +
    + +

    DecodeRawSymbolsInternal()

    + +
    DecodeRawSymbolsInternal(max_bit_length, out_values) {
+  decoder = CreateRansSymbolDecoder(max_bit_length)
+  decoder.StartDecoding()
+  // RansSymbolDecoder_StartDecoding
+  for (i = 0; i < num_values; ++i) {
+    out_values[i] = decoder.DecodeSymbol()
+    // RansSymbolDecoder_DecodeSymbol
+  }
+}
+
    +
    + +

    CreateRansSymbolDecoder()

    + +
    CreateRansSymbolDecoder(max_bit_length) {
+  rans_precision_bits  = (3 * max_bit_length) / 2;
+  rans_precision_bits = min(rans_precision_bits, 20)
+  rans_precision_bits = max(rans_precision_bits, 12)
+  rans_precision = 1 << rans_precision_bits_;
+  l_rans_base = rans_precision * 4;
+  num_symbols_                                                               UI32
+  for (i = 0; i < num_symbols_; ++i) {
+    prob_data                                                                UI8
+    if ((prob_data & 3) == 3) {
+      offset = prob_data >> 2
+      for (j = 0; j < offset + 1; ++j) {
+        probability_table_[i + j] = 0;
+      }
+      i += offset;
+    } else {
+      prob = prob_data >> 2
+      for (j = 0; j < token; ++j) {
+        eb                                                                   UI8
+        prob = prob | (eb << (8 * (j + 1) - 2)
+      }
+      probability_table_[i] = prob;
+    }
+  }
+  rans_build_look_up_table()
+}
+
    +
    + +

    RansSymbolDecoder_StartDecoding()

    + +
    RansSymbolDecoder_StartDecoding() {
+  bytes_encoded                                                              UI64
+  buffer                                                                     bytes_encoded * UI8
+  rans_read_init(buffer, bytes_encoded)
+}
+
    +
    + +

    RansSymbolDecoder_DecodeSymbol()

    + +
    RansSymbolDecoder_DecodeSymbol() {
+  ans_.rans_read()
+}
+
    +
    + +

    Rans Decoding

    + +

    ans_read_init()

    + +
    ans_read_init(struct AnsDecoder *const ans, const uint8_t *const buf,
+                       int offset) {
+  x = buf[offset - 1] >> 6
+  If (x == 0) {
+    ans->buf_offset = offset - 1;
+    ans->state = buf[offset - 1] & 0x3F;
+  } else if (x == 1) {
+    ans->buf_offset = offset - 2;
+    ans->state = mem_get_le16(buf + offset - 2) & 0x3FFF;
+  } else if (x == 2) {
+    ans->buf_offset = offset - 3;
+    ans->state = mem_get_le24(buf + offset - 3) & 0x3FFFFF;
+  } else if (x == 3) {
+   // x == 3 implies this byte is a superframe marker
+    return 1;
+  }
+  ans->state += l_base;
+}
+
    +
    + +

    int rabs_desc_read()

    + +
    int rabs_desc_read(struct AnsDecoder *ans, AnsP8 p0) {
+  AnsP8 p = ans_p8_precision - p0;
+  if (ans->state < l_base) {
+    ans->state = ans->state * io_base + ans->buf[--ans->buf_offset];
+  }
+  x = ans->state;
+  quot = x / ans_p8_precision;
+  rem = x % ans_p8_precision;
+  xn = quot * p;
+  val = rem < p;
+  if (val) {
+    ans->state = xn + rem;
+  } else {
+    ans->state = x - xn - p;
+  }
+  return val;
+}
+
    +
    + +

    rans_read_init()

    + +
    rans_read_init(UI8 *buf, int offset) {
+  ans_.buf = buf;
+  x = buf[offset - 1] >> 6
+  If (x == 0) {
+    ans_.buf_offset = offset - 1;
+    ans_.state = buf[offset - 1] & 0x3F;
+  } else if (x == 1) {
+    ans_.buf_offset = offset - 2;
+    ans_.state = mem_get_le16(buf + offset - 2) & 0x3FFF;
+  } else if (x == 2) {
+    ans_.buf_offset = offset - 3;
+    ans_.state = mem_get_le24(buf + offset - 3) & 0x3FFFFF;
+  } else if (x == 3) {
+    ans_.buf_offset = offset - 4;
+    ans_.state = mem_get_le32(buf + offset - 4) & 0x3FFFFFFF;
+  }
+  ans_.state += l_rans_base;
+}
+
    +
    + +

    rans_build_look_up_table()

    + +
    rans_build_look_up_table() {
+  cum_prob = 0
+  act_prob = 0
+  for (i = 0; i < num_symbols; ++i) {
+    probability_table_[i].prob = token_probs[i];
+    probability_table_[i].cum_prob = cum_prob;
+    cum_prob += token_probs[i];
+    for (j = act_prob; j < cum_prob; ++j) {
+      Lut_table_[j] = i
+    }
+    act_prob = cum_prob
+}
+
    +
    + +

    rans_read()

    + +
    rans_read() {
+  while (ans_.state < l_rans_base) {
+    ans_.state = ans_.state * io_base + ans_.buf[--ans_.buf_offset];
+  }
+  quo = ans_.state / rans_precision;
+  rem = ans_.state % rans_precision;
+  sym = fetch_sym()
+  ans_.state = quo * sym.prob + rem - sym.cum_prob;
+  return sym.val;
+}
+
    +
    + +

    fetch_sym()

    + +
    fetch_sym() {
+  symbol = lut_table[rem]
+  out->val = symbol
+  out->prob = probability_table_[symbol].prob;
+  out->cum_prob = probability_table_[symbol].cum_prob;
+}
+
    +
    + +

    Rans Bit Decoder

    + +

    RansBitDecoder_StartDecoding()

    + +
    RansBitDecoder_StartDecoding(DecoderBuffer *source_buffer) {
+  prob_zero_                                                                 UI8
+  size                                                                       UI32
+  buffer_                                                                    size * UI8
+  ans_read_init(&ans_decoder_, buffer_, size)
+}
+
    +
    + +

    DecodeNextBit()

    + +
    DecodeNextBit() {
+  uint8_t bit = rabs_desc_read(&ans_decoder_, prob_zero_);
+  return bit > 0;
+}
+
    +
    + +

    Core Functions

    + +

    DecodeVarint

    + +
    DecodeVarint<IT>() {
+  If (std::is_unsigned<IT>::value) {
+    in                                                                       UI8
+    If (in & (1 << 7)) {
+      out = DecodeVarint<IT>()
+      out = (out << 7) | (in & ((1 << 7) - 1))
+    } else {
+      typename std::make_unsigned<IT>::type UIT;
+      out = DecodeVarint<UIT>()
+      out = ConvertSymbolToSignedInt(out)
+    }
+    return out;
+}
+
    +
    + +

    ConvertSymbolToSignedInt()

    + +
    ConvertSymbolToSignedInt() {
+  abs_val = val >> 1
+  If (val & 1 == 0) {
+    return abs_val
+  } else {
+    signed_val = -abs_val - 1
+  }
+  return signed_val
+}
+
    +
    + +

    Sequential Decoder

    + +

    decode_connectivity()

    + +
    decode_connectivity() {
+  num_faces                                                       I32
+  num_points                                                      I32
+  connectivity _method                                            UI8
+  If (connectivity _method == 0) {
+    // TODO
+  } else {
+    loop num_faces {
+      If (num_points < 256) {
+        face[]                                                    UI8
+      } else if (num_points < (1 << 16)) {
+        face[]                                                    UI16
+      } else {
+        face[]                                                    UI32
+      }
+    }
+  }
+}
+
    +
    diff --git a/docs/_site/spec/edgebreaker.decoder.md b/docs/_site/spec/edgebreaker.decoder.md new file mode 100644 index 0000000..495901e --- /dev/null +++ b/docs/_site/spec/edgebreaker.decoder.md @@ -0,0 +1,1674 @@ +## EdgeBreaker Decoder + +### InitializeDecoder() + +
    +InitializeDecoder() { Type + edgebreaker_decoder_type UI8 +} + +
    + + +### DecodeConnectivity() + +
    +DecodeConnectivity() { Type + num_new_verts UI32 + num_encoded_vertices UI32 + num_faces UI32 + num_attribute_data I8 + num_encoded_symbols UI32 + num_encoded_split_symbols UI32 + encoded_connectivity_size UI32 + // file pointer must be set to current position + encoded_connectivity_size + hole_and_split_bytes = DecodeHoleAndTopologySplitEvents() + // file pointer must be set to old current position + EdgeBreakerTraversalValence_Start() + DecodeConnectivity(num_symbols) + if (attribute_data_.size() > 0) { + for (ci = 0; ci < corner_table_->num_corners(); ci += 3) { + DecodeAttributeConnectivitiesOnFace(ci) + } + } + for (i = 0; i < corner_table_->num_vertices(); ++i) { + if (is_vert_hole_[i]) { + corner_table_->UpdateVertexToCornerMap(i); + } + } + // Decode attribute connectivity. + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + attribute_data_[i].connectivity_data.InitEmpty(corner_table_.get()); + for (int32_t c : attribute_data_[i].attribute_seam_corners) { + attribute_data_[i].connectivity_data.AddSeamEdge(c); + } + attribute_data_[i].connectivity_data.RecomputeVertices(nullptr, nullptr); + } + // Preallocate vertex to value mapping + AssignPointsToCorners() +} + +
    + + +### AssignPointsToCorners() + +
    +AssignPointsToCorners() { Type + decoder_->mesh()->SetNumFaces(corner_table_->num_faces()); + if (attribute_data_.size() == 0) { + for (f = 0; f < decoder_->mesh()->num_faces(); ++f) { + for (c = 0; c < 3; ++c) { + vert_id = corner_table_->Vertex(3 * f + c); + if (point_id == -1) + point_id = num_points++; + face[c] = point_id; + } + decoder_->mesh()->SetFace(f, face); + } + decoder_->point_cloud()->set_num_points(num_points); + Return true; + } + for (v = 0; v < corner_table_->num_vertices(); ++v) { + c = corner_table_->LeftMostCorner(v); + if (c < 0) + continue; + deduplication_first_corner = c; + if (!is_vert_hole_[v]) { + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + if (!attribute_data_[i].connectivity_data.IsCornerOnSeam(c)) + continue; + vert_id = attribute_data_[i].connectivity_data.Vertex(c); + act_c = corner_table_->SwingRight(c); + seam_found = false; + while (act_c != c) { + if (attribute_data_[i].connectivity_data.Vertex(act_c) != vert_id) { + deduplication_first_corner = act_c; + seam_found = true; + break; + } + act_c = corner_table_->SwingRight(act_c); + } + if (seam_found) + break; + } + } + c = deduplication_first_corner; + corner_to_point_map[c] = point_to_corner_map.size(); + point_to_corner_map.push_back(c); + prev_c = c; + c = corner_table_->SwingRight(c); + while (c >= 0 && c != deduplication_first_corner) { + attribute_seam = false; + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + if (attribute_data_[i].connectivity_data.Vertex(c) != + attribute_data_[i].connectivity_data.Vertex(prev_c)) { + attribute_seam = true; + break; + } + } + if (attribute_seam) { + corner_to_point_map[c] = point_to_corner_map.size(); + point_to_corner_map.push_back(c); + } else { + corner_to_point_map[c] = corner_to_point_map[prev_c]; + } + prev_c = c; + c = corner_table_->SwingRight(c); + } + } + for (f = 0; f < decoder_->mesh()->num_faces(); ++f) { + for (c = 0; c < 3; ++c) { + face[c] = corner_to_point_map[3 * f + c]; + } + decoder_->mesh()->SetFace(f, face); + } + decoder_->point_cloud()->set_num_points(point_to_corner_map.size()); +} + +
    + + +### DecodeConnectivity() + +
    +DecodeConnectivity(num_symbols) { Type + for (i = 0; i < num_symbols; ++i) { + symbol = TraversalValence_DecodeSymbol() + corner = 3 * num_faces++ + if (symbol == TOPOLOGY_C) { + vertex_x = UpdateCornerTableForSymbolC() + is_vert_hole_[vertex_x] = false; + } else if (symbol == TOPOLOGY_R || symbol == TOPOLOGY_L) { + UpdateCornerTableForSymbolLR() + check_topology_split = true; + } else if (symbol == TOPOLOGY_S) { + HandleSymbolS() + } else if (symbol == TOPOLOGY_E) { + UpdateCornerTableForSymbolE() + check_topology_split = true; + } + active_corner_stack.back() = corner; + traversal_decoder_.NewActiveCornerReached(corner); + if (check_topology_split) { + encoder_symbol_id = num_symbols - symbol_id - 1; + while (true) { + split = IsTopologySplit(encoder_symbol_id, &split_edge, + &encoder_split_symbol_id); + if (!split) { + break; + } + act_top_corner = corner; + if (split_edge == RIGHT_FACE_EDGE) { + new_active_corner = corner_table_->Next(act_top_corner); + } else { + new_active_corner = corner_table_->Previous(act_top_corner); + } + decoder_split_symbol_id = num_symbols - encoder_split_symbol_id - 1; + topology_split_active_corners[decoder_split_symbol_id] = + new_active_corner; + } + } + } + while (active_corner_stack.size() > 0) { + corner = active_corner_stack.pop_back(); + interior_face = traversal_decoder_.DecodeStartFaceConfiguration(); + if (interior_face == true) { + UpdateCornerTableForInteriorFace() + for (ci = 0; ci < 3; ++ci) { + is_vert_hole_[corner_table_->Vertex(new_corner + ci)] = false; + } + init_face_configurations_.push_back(true); + init_corners_.push_back(new_corner); + } else { + init_face_configurations_.push_back(false); + init_corners_.push_back(corner); + } + } + Return num_vertices; +} + +
    + + +### UpdateCornerTableForSymbolC() + +
    +UpdateCornerTableForSymbolC(corner) { Type + corner_a = active_corner_stack.back(); + corner_b = corner_table_->Previous(corner_a); + while (corner_table_->Opposite(corner_b) >= 0) { + corner_b = corner_table_->Previous(corner_table_->Opposite(corner_b)); + } + SetOppositeCorners(corner_a, corner + 1); + SetOppositeCorners(corner_b, corner + 2); + vertex_x = corner_table_->Vertex(corner_table_->Next(corner_a)); + corner_table_->MapCornerToVertex(corner, vertex_x); + corner_table_->MapCornerToVertex( + corner + 1, corner_table_->Vertex(corner_table_->Next(corner_b))); + corner_table_->MapCornerToVertex( + corner + 2, corner_table_->Vertex(corner_table_->Previous(corner_a))); + return vertex_x; +} + +
    + + + +### UpdateCornerTableForSymbolLR() + +
    +UpdateCornerTableForSymbolLR(corner, symbol) { Type + if (symbol == TOPOLOGY_R) { + opp_corner = corner + 2; + } else { + opp_corner = corner + 1; + } + SetOppositeCorners(opp_corner, corner_a); + corner_table_->MapCornerToVertex(opp_corner,num_vertices++); + corner_table_->MapCornerToVertex( + corner_table_->Next(opp_corner), + corner_table_->Vertex(corner_table_->Previous(corner_a))); + corner_table_->MapCornerToVertex( + corner_table_->Previous(opp_corner), + corner_table_->Vertex(corner_table_->Next(corner_a))); +} + +
    + + +### HandleSymbolS() + +
    +HandleSymbolS(corner) { Type + corner_b = active_corner_stack.pop_back(); + it = topology_split_active_corners.find(symbol_id); + if (it != topology_split_active_corners.end()) { + active_corner_stack.push_back(it->second); + } + corner_a = active_corner_stack.back(); + SetOppositeCorners(corner_a, corner + 2); + SetOppositeCorners(corner_b, corner + 1); + vertex_p = corner_table_->Vertex(corner_table_->Previous(corner_a)); + corner_table_->MapCornerToVertex(corner, vertex_p); + corner_table_->MapCornerToVertex( + corner + 1, corner_table_->Vertex(corner_table_->Next(corner_a))); + corner_table_->MapCornerToVertex(corner + 2, + corner_table_->Vertex(corner_table_->Previous(corner_b))); + corner_n = corner_table_->Next(corner_b); + vertex_n = corner_table_->Vertex(corner_n); + traversal_decoder_.MergeVertices(vertex_p, vertex_n); + // TraversalValence_MergeVertices + while (corner_n >= 0) { + corner_table_->MapCornerToVertex(corner_n, vertex_p); + corner_n = corner_table_->SwingLeft(corner_n); + } + corner_table_->MakeVertexIsolated(vertex_n); +} + +
    + + +### UpdateCornerTableForSymbolE() + +
    +UpdateCornerTableForSymbolE() { Type + corner_table_->MapCornerToVertex(corner, num_vertices++); + corner_table_->MapCornerToVertex(corner + 1, num_vertices++); + corner_table_->MapCornerToVertex(corner + 2, num_vertices++); +} + +
    + + +### UpdateCornerTableForInteriorFace() + +
    +UpdateCornerTableForInteriorFace() { Type + corner_b = corner_table_->Previous(corner); + while (corner_table_->Opposite(corner_b) >= 0) { + corner_b = corner_table_->Previous(corner_table_->Opposite(corner_b)); + } + corner_c = corner_table_->Next(corner); + while (corner_table_->Opposite(corner_c) >= 0) { + corner_c = corner_table_->Next(corner_table_->Opposite(corner_c)); + } + face(num_faces++); + corner_table_->MapCornerToVertex( + new_corner, corner_table_->Vertex(corner_table_->Next(corner_b))); + corner_table_->MapCornerToVertex( + new_corner + 1, corner_table_->Vertex(corner_table_->Next(corner_c))); + corner_table_->MapCornerToVertex( + new_corner + 2, corner_table_->Vertex(corner_table_->Next(corner))); +} + +
    + + +### IsTopologySplit() + +
    +IsTopologySplit(encoder_symbol_id, *out_face_edge, Type + + *out_encoder_split_symbol_id) { + if (topology_split_data_.size() == 0) + return false; + if (topology_split_data_.back().source_symbol_id != encoder_symbol_id) + return false; + *out_face_edge = topology_split_data_.back().source_edge; + *out_encoder_split_symbol_id = + topology_split_data_.back().split_symbol_id; + topology_split_data_.pop_back(); + return true; +} + +
    + + +### DecodeAttributeConnectivitiesOnFace() + +
    +DecodeAttributeConnectivitiesOnFace(corner) { Type + corners[3] = {corner, corner_table_->Next(corner), + corner_table_->Previous(corner)} + for (c = 0; c < 3; ++c) { + opp_corner = corner_table_->Opposite(corners[c]); + if (opp_corner < 0) { + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + attribute_data_[i].attribute_seam_corners.push_back(corners[c]); + } + continue + } + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + bool is_seam = traversal_decoder_.DecodeAttributeSeam(i); + if (is_seam) { + attribute_data_[i].attribute_seam_corners.push_back(corners[c]); + } + } + } +} + +
    + + +### SetOppositeCorners() + +
    +SetOppositeCorners(corner_0, corner_1) { Type + corner_table_->SetOppositeCorner(corner_0, corner_1); + corner_table_->SetOppositeCorner(corner_1, corner_0); +} + +
    + + +## EdgeBreaker Hole and Topology Split Events + +### DecodeHoleAndTopologySplitEvents() + +FIXME: Escaping angle brackets + +
    +DecodeHoleAndTopologySplitEvents() { Type + num_topologoy_splits UI32 + source_symbol_id = 0 + for (i = 0; i < num_topologoy_splits; ++i) { + DecodeVarint\(&delta) + split_data[i].source_symbol_id = delta + source_symbol_id + DecodeVarint\(&delta) + split_data[i].split_symbol_id = source_symbol_id - delta + } + for (i = 0; i < num_topologoy_splits; ++i) { + split_data[i].split_edge bits1 + split_data[i].source_edge bits1 + } + num_hole_events UI32 + symbol_id = 0 + for (i = 0; i < num_hole_events; ++i) { + DecodeVarint\(&delta) + hole_data[i].symbol_id = delta + symbol_id + } + return bytes_decoded; +} + +
    + +### CreateAttributesDecoder + +FIXME: Escaping angle brackets + +
    +CreateAttributesDecoder() { Type + att_data_id I8 + decoder_type UI8 + if (att_data_id >= 0) { + attribute_data_[att_data_id].decoder_id = att_decoder_id; + } + traversal_method_encoded UI8 + if (decoder_type == MESH_VERTEX_ATTRIBUTE) { + if (att_data_id < 0) { + encoding_data = &pos_encoding_data_; + } else { + encoding_data = &attribute_data_[att_data_id].encoding_data; + attribute_data_[att_data_id].is_connectivity_used = false; + } + if (traversal_method == MESH_TRAVERSAL_DEPTH_FIRST) { + typedef EdgeBreakerTraverser\ AttTraverser; + sequencer = CreateVertexTraversalSequencer\(encoding_data); + } else if (traversal_method == MESH_TRAVERSAL_PREDICTION_DEGREE) { + typedef PredictionDegreeTraverser\ AttTraverser; + sequencer = CreateVertexTraversalSequencer\(encoding_data); + } + } else { + // TODO + } + att_controller(new SequentialAttributeDecodersController(std::move(sequencer))) + decoder_->SetAttributesDecoder(att_decoder_id, std::move(att_controller)); +} + +
    + + +## Edgebreaker Traversal Decoder + +### EdgebreakerTraversal_Start() + +
    +EdgebreakerTraversal_Start() { Type + size UI64 + symbol_buffer_ size * UI8 + size UI64 + start_face_buffer_ size * UI8 + if (num_attribute_data_ > 0) { + attribute_connectivity_decoders_ = std::unique_ptr( + new BinaryDecoder[num_attribute_data_]); + for (i = 0; i < num_attribute_data_; ++i) { + attribute_connectivity_decoders_[i].StartDecoding() + // RansBitDecoder_StartDecoding + } +} + +
    + + +### Traversal_DecodeSymbol() + +~~~~~ +Traversal_DecodeSymbol() { + symbol_buffer_.DecodeLeastSignificantBits32(1, &symbol); bits1 + if (symbol != TOPOLOGY_C) { + symbol_buffer_.DecodeLeastSignificantBits32(2, &symbol_suffix); bits2 + symbol |= (symbol_suffix << 1); + } + return symbol +} +~~~~~ + + +### DecodeAttributeSeam() + +~~~~~ +DecodeAttributeSeam(int attribute) { + return attribute_connectivity_decoders_[attribute].DecodeNextBit(); +} +~~~~~ + + +## EdgeBreaker Traversal Valence Decoder + +### EdgeBreakerTraversalValence_Start() + +~~~~~ +EdgeBreakerTraversalValence_Start(num_vertices, num_attribute_data) { + out_buffer = EdgebreakerTraversal_Start() + num_split_symbols I32 + mode == 0 I8 + num_vertices_ += num_split_symbols + vertex_valences_ init to 0 + vertex_valences_.resize(num_vertices_, 0); + min_valence_ = 2; + max_valence_ = 7; + num_unique_valences = 6 (max_valence_ - min_valence_ + 1) + for (i = 0; i < num_unique_valences; ++i) { + DecodeVarint(&num_symbols, out_buffer) + If (num_symbols > 0) { + DecodeSymbols(num_symbols, out_buffer, &context_symbols_[i]) + } + context_counters_[i] = num_symbols + } + return out_buffer; +} +~~~~~ + + + +### TraversalValence_DecodeSymbol() + +~~~~~ +TraversalValence_DecodeSymbol() { + if (active_context_ != -1) { + symbol_id = context_symbols_[active_context_] + [--context_counters_[active_context_]] + last_symbol_ = edge_breaker_symbol_to_topology_id[symbol_id] + } else { + last_symbol_ = Traversal_DecodeSymbol() + } + return last_symbol_ +} +~~~~~ + + + +### TraversalValence_NewActiveCornerReached() + +~~~~~ +TraversalValence_NewActiveCornerReached(corner) { + switch (last_symbol_) { + case TOPOLOGY_C: + case TOPOLOGY_S: + vertex_valences_[ct(next)] += 1; + vertex_valences_[ct(prev)] += 1; + break; + case TOPOLOGY_R: + vertex_valences_[corner] += 1; + vertex_valences_[ct(next)] += 1; + vertex_valences_[ct(prev)] += 2; + break; + case TOPOLOGY_L: + vertex_valences_[corner] += 1; + vertex_valences_[ct(next)] += 2; + vertex_valences_[ct(prev)] += 1; + break; + case TOPOLOGY_E: + vertex_valences_[corner] += 2; + vertex_valences_[ct(next)] += 2; + vertex_valences_[ct(prev)] += 2; + break; + } + valence = vertex_valences_[ct(next)] + valence = max(valence, min_valence_) + valence = min(valence, max_valence_) + active_context_ = (valence - min_valence_); +} +~~~~~ + + + +### TraversalValence_MergeVertices() + +~~~~~ +TraversalValence_MergeVertices(dest, source) { + vertex_valences_[dest] += vertex_valences_[source]; +} +~~~~~ + + +## Attributes Decoder + +### DecodeAttributesDecoderData() + +~~~~~ +DecodeAttributesDecoderData(buffer) { + num_attributes I32 + point_attribute_ids_.resize(num_attributes); + for (i = 0; i < num_attributes; ++i) { + att_type UI8 + data_type UI8 + components_count UI8 + normalized UI8 + custom_id UI16 + Initialize GeometryAttribute ga + att_id = pc->AddAttribute(new PointAttribute(ga)); + point_attribute_ids_[i] = att_id; +} +~~~~~ + + + +## Sequential Attributes Decoders Controller + +### DecodeAttributesDecoderData() + +~~~~~ +DecodeAttributesDecoderData(buffer) { + AttributesDecoder_DecodeAttributesDecoderData(buffer) + sequential_decoders_.resize(num_attributes()); + for (i = 0; i < num_attributes(); ++i) { + decoder_type UI8 + sequential_decoders_[i] = CreateSequentialDecoder(decoder_type); + sequential_decoders_[i]->Initialize(decoder(), GetAttributeId(i)) +} +~~~~~ + + +### DecodeAttributes() + +~~~~~ +DecodeAttributes(buffer) { + sequencer_->GenerateSequence(&point_ids_) + for (i = 0; i < num_attributes(); ++i) { + pa = decoder()->point_cloud()->attribute(GetAttributeId(i)); + sequencer_->UpdatePointToAttributeIndexMapping(pa) + } + for (i = 0; i < num_attributes(); ++i) { + sequential_decoders_[i]->Decode(point_ids_, buffer) + //SequentialAttributeDecoder_Decode() + } +} +~~~~~ + + + +### CreateSequentialDecoder() + +~~~~~ +CreateSequentialDecoder(type) { + switch (type) { + case SEQUENTIAL_ATTRIBUTE_ENCODER_GENERIC: + return new SequentialAttributeDecoder() + case SEQUENTIAL_ATTRIBUTE_ENCODER_INTEGER: + return new SequentialIntegerAttributeDecoder() + case SEQUENTIAL_ATTRIBUTE_ENCODER_QUANTIZATION: + return new SequentialQuantizationAttributeDecoder() + case SEQUENTIAL_ATTRIBUTE_ENCODER_NORMALS: + return new SequentialNormalAttributeDecoder() + } +} +~~~~~ + + +## Sequential Attribute Decoder + +~~~~~ +Initialize(...) { + // Init some members +} +~~~~~ + + +### DecodeValues() + +~~~~~ +DecodeValues(const std::vector &point_ids) { + num_values = point_ids.size(); + entry_size = attribute_->byte_stride(); + std::unique_ptr value_data_ptr(new uint8_t[entry_size]); + out_byte_pos = 0; + for (i = 0; i < num_values; ++i) { + value_data UI8 * entry_size + attribute_->buffer()->Write(out_byte_pos, value_data, entry_size); + out_byte_pos += entry_size; + } +} +~~~~~ + + +## Sequential Integer Attribute Decoder + +~~~~~ +Initialize(...) { + SequentialAttributeDecoder_Initialize() +} +~~~~~ + + +### DecodeValues() + +~~~~~ +DecodeValues(point_ids) { + prediction_scheme_method I8 + if (prediction_scheme_method != PREDICTION_NONE) { + prediction_transform_type I8 + prediction_scheme_ = CreateIntPredictionScheme(...) + } + if (prediction_scheme_) { + } + DecodeIntegerValues(point_ids) + //SequentialQuantizationAttributeDecoder_DecodeIntegerValues() + //StoreValues() + DequantizeValues(num_values) +} +~~~~~ + + +### DecodeIntegerValues() + +~~~~~ +DecodeIntegerValues(point_ids) { + compressed UI8 + if (compressed) { + DecodeSymbols(..., values_.data()) + } else { + // TODO + } + if (!prediction_scheme_->AreCorrectionsPositive()) { + ConvertSymbolsToSignedInts(...) + } + if (prediction_scheme_) { + prediction_scheme_->DecodePredictionData(buffer) + // DecodeTransformData(buffer) + if (!values_.empty()) { + prediction_scheme_->Decode(values_.data(), &values_[0], + values_.size(), num_components, point_ids.data()) + // MeshPredictionSchemeParallelogram_Decode() +} +~~~~~ + + + +## Sequential Quantization Attribute Decoder + +~~~~~ +Initialize(...) { + SequentialIntegerAttributeDecoder_Initialize() +} +~~~~~ + + +### DecodeIntegerValues() + +~~~~~ +DecodeIntegerValues(point_ids) { + // DecodeQuantizedDataInfo() + num_components = attribute()->components_count(); + for (i = 0; i < num_components; ++i) { + min_value_[i] F32 + } + max_value_dif_ F32 + quantization_bits_ UI8 + SequentialIntegerAttributeDecoder::DecodeIntegerValues() +} +~~~~~ + + +### DequantizeValues() + +~~~~~ +DequantizeValues(num_values) { + max_quantized_value = (1 << (quantization_bits_)) - 1; + num_components = attribute()->components_count(); + entry_size = sizeof(float) * num_components; + quant_val_id = 0; + out_byte_pos = 0; + for (i = 0; i < num_values; ++i) { + for (c = 0; c < num_components; ++c) { + value = dequantizer.DequantizeFloat(values()->at(quant_val_id++)); + value = value + min_value_[c]; + att_val[c] = value; + } + attribute()->buffer()->Write(out_byte_pos, att_val.get(), entry_size); + out_byte_pos += entry_size; + } +} +~~~~~ + + + +## Prediction Scheme Transform + +### ComputeOriginalValue() + +~~~~~ +ComputeOriginalValue(const DataTypeT *predicted_vals, + const CorrTypeT *corr_vals, + DataTypeT *out_original_vals, int val_id) { + for (i = 0; i < num_components_; ++i) { + out_original_vals[i] = predicted_vals[i] + corr_vals[val_id + i]; + } +} +~~~~~ + + + +## Prediction Scheme Wrap Transform + +### DecodeTransformData() + +~~~~~ +DecodeTransformData(buffer) { + min_value_ DT + max_value_ DT +} +~~~~~ + + +### ComputeOriginalValue() + +~~~~~ +ComputeOriginalValue(const DataTypeT *predicted_vals, + const CorrTypeT *corr_vals, + DataTypeT *out_original_vals, int val_id) { + clamped_vals = ClampPredictedValue(predicted_vals); + ComputeOriginalValue(clamped_vals, corr_vals, out_original_vals, val_id) + // PredictionSchemeTransform_ComputeOriginalValue() + for (i = 0; i < this->num_components(); ++i) { + if (out_original_vals[i] > max_value_) { + out_original_vals[i] -= max_dif_; + } else if (out_original_vals[i] < min_value_) { + out_original_vals[i] += max_dif_; + } +} +~~~~~ + + +### ClampPredictedValue() + +~~~~~ +ClampPredictedValue(const DataTypeT *predicted_val) { + for (i = 0; i < this->num_components(); ++i) { + clamped_value_[i] = min(predicted_val[i], max_value_) + clamped_value_[i] = max(predicted_val[i], min_value_) + } + return &clamped_value_[0]; +} +~~~~~ + + + +## Mesh Prediction Scheme Parallelogram + +### Decode() + +~~~~~ +Decode(...) { + this->transform().InitializeDecoding(num_components); + // restore the first value + this->transform().ComputeOriginalValue(pred_vals.get(), + in_corr, out_data, 0); + // PredictionSchemeWrapTransform_ComputeOriginalValue() + corner_map_size = this->mesh_data().data_to_corner_map()->size(); + for (p = 1; p < corner_map_size; ++p) { + corner_id = this->mesh_data().data_to_corner_map()->at(p); + dst_offset = p * num_components; + b= ComputeParallelogramPrediction(p, corner_id, table, + *vertex_to_data_map, out_data, + num_components, pred_vals.get()) + if (!b) { + src_offset = (p - 1) * num_components; + this->transform().ComputeOriginalValue(out_data + src_offset, in_corr, + out_data + dst_offset, dst_offset); + // PredictionSchemeWrapTransform_ComputeOriginalValue() + } else { + this->transform().ComputeOriginalValue(pred_vals.get(), in_corr, + out_data + dst_offset, dst_offset); + // PredictionSchemeWrapTransform_ComputeOriginalValue() + } + } +} +~~~~~ + + +MeshPredictionSchemeParallelogramShared + +### ComputeParallelogramPrediction() + +~~~~~ +ComputeParallelogramPrediction(...) { + oci = table->Opposite(ci); + vert_opp = vertex_to_data_map[table->Vertex(ci)]; + vert_next = vertex_to_data_map[table->Vertex(table->Next(ci))]; + vert_prev = vertex_to_data_map[table->Vertex(table->Previous(ci))]; + if (vert_opp < data_entry_id && vert_next < data_entry_id && + vert_prev < data_entry_id) { + v_opp_off = vert_opp * num_components; + v_next_off = vert_next * num_components; + v_prev_off = vert_prev * num_components; + for (c = 0; c < num_components; ++c) { + out_prediction[c] = (in_data[v_next_off + c] + in_data[v_prev_off + c]) - + in_data[v_opp_off + c]; + } + Return true; + } + return false; +} +~~~~~ + + + +## CornerTable Traversal Processor + + +### IsFaceVisited() + +~~~~~ +IsFaceVisited(corner_id) { + if (corner_id < 0) + return true + return is_face_visited_[corner_id / 3]; +} +~~~~~ + + +### MarkFaceVisited() + +~~~~~ +MarkFaceVisited(face_id) { + is_face_visited_[face_id] = true; +} +~~~~~ + + +### IsVertexVisited() + +~~~~~ +IsVertexVisited(vert_id) { + return is_vertex_visited_[vert_id]; +} +~~~~~ + + +### MarkVertexVisited() + +~~~~~ +MarkVertexVisited(vert_id) { + is_vertex_visited_[vert_id] = true; +} +~~~~~ + + +## Mesh Attribute Indices Encoding Observer + +### OnNewVertexVisited() + +~~~~~ +OnNewVertexVisited(vertex, corner) { + point_id = mesh_->face(corner / 3)[corner % 3]; + sequencer_->AddPointId(point_id); + // Keep track of visited corners. + encoding_data_->encoded_attribute_value_index_to_corner_map.push_back(corner); + encoding_data_ + ->vertex_to_encoded_attribute_value_index_map[vertex] = + encoding_data_->num_values; + encoding_data_->num_values++; +} +~~~~~ + + +## EdgeBreaker Traverser + +### TraverseFromCorner() + +~~~~~ +TraverseFromCorner(corner_id) { + if (processor_.IsFaceVisited(corner_id)) + return + corner_traversal_stack_.clear(); + corner_traversal_stack_.push_back(corner_id); + next_vert = corner_table_->Vertex(corner_table_->Next(corner_id)); + prev_vert = corner_table_->Vertex(corner_table_->Previous(corner_id)); + if (!processor_.IsVertexVisited(next_vert)) { + processor_.MarkVertexVisited(next_vert); + traversal_observer_.OnNewVertexVisited(next_vert, + corner_table_->Next(corner_id)); + } + if (!processor_.IsVertexVisited(prev_vert)) { + processor_.MarkVertexVisited(prev_vert); + traversal_observer_.OnNewVertexVisited(prev_vert, + corner_table_->Previous(corner_id)); + } + while (!corner_traversal_stack_.empty()) { + corner_id = corner_traversal_stack_.back(); + face_id =corner_id / 3; + if (processor_.IsFaceVisited(face_id)) { + corner_traversal_stack_.pop_back(); + continue + } + while(true) { + face_id = corner_id / 3; + processor_.MarkFaceVisited(face_id); + traversal_observer_.OnNewFaceVisited(face_id); + vert_id = corner_table_->Vertex(corner_id); + on_boundary = corner_table_->IsOnBoundary(vert_id); + if (!processor_.IsVertexVisited(vert_id)) { + processor_.MarkVertexVisited(vert_id); + traversal_observer_.OnNewVertexVisited(vert_id, corner_id); + if (!on_boundary) { + corner_id = corner_table_->GetRightCorner(corner_id); + continue; + } + } + // The current vertex has been already visited or it was on a boundary. + right_corner_id = corner_table_->GetRightCorner(corner_id); + left_corner_id = corner_table_->GetLeftCorner(corner_id); + right_face_id((right_corner_id < 0 ? -1 : right_corner_id / 3)); + left_face_id((left_corner_id < 0 ? -1 : left_corner_id / 3)); + if (processor_.IsFaceVisited(right_face_id)) { + if (processor_.IsFaceVisited(left_face_id)) { + corner_traversal_stack_.pop_back(); + break; // Break from while(true) loop + } else { + corner_id = left_corner_id; + } + } else { + if (processor_.IsFaceVisited(left_face_id)) { + corner_id = right_corner_id; + } else { + // Split the traversal. + corner_traversal_stack_.back() = left_corner_id; + corner_traversal_stack_.push_back(right_corner_id); + break; // Break from while(true) loop + } + } + } + } +} +~~~~~ + + +## Mesh Traversal Sequencer + +### GenerateSequenceInternal() + +~~~~~ +GenerateSequenceInternal() { + traverser_.OnTraversalStart(); + If (corner_order_) { + // TODO + } else { + int32_t num_faces = traverser_.corner_table()->num_faces(); + for (i = 0; i < num_faces; ++i) { + ProcessCorner(3 * i) + } + } + traverser_.OnTraversalEnd(); +} +~~~~~ + + +### ProcessCorner() + +~~~~~ +ProcessCorner(corner_id) { + traverser_.TraverseFromCorner(corner_id); +} +~~~~~ + + +### UpdatePointToAttributeIndexMapping() + +~~~~~ +UpdatePointToAttributeIndexMapping(PointAttribute *attribute) { + corner_table = traverser_.corner_table(); + attribute->SetExplicitMapping(mesh_->num_points()); + num_faces = mesh_->num_faces(); + num_points = mesh_->num_points(); + for (f = 0; f < num_faces; ++f) { + face = mesh_->face(f); + for (p = 0; p < 3; ++p) { + point_id = face[p]; + vert_id = corner_table->Vertex(3 * f + p); + att_entry_id( + encoding_data_ + ->vertex_to_encoded_attribute_value_index_map[vert_id]); + attribute->SetPointMapEntry(point_id, att_entry_id); + } + } +} +~~~~~ + + +PointsSequencer + +### AddPointId() + +~~~~~ +AddPointId(point_id) { + out_point_ids_->push_back(point_id); +} +~~~~~ + + + +## Corner Table + +### Opposite() + +~~~~~ +Opposite(corner) { + return opposite_corners_[corner]; +} +~~~~~ + + +### Next() + +~~~~~ +Next(corner) { + return LocalIndex(++corner) ? corner : corner - 3; +} +~~~~~ + + +### Previous() + +~~~~~ +Previous(corner) { + return LocalIndex(corner) ? corner - 1 : corner + 2; +} +~~~~~ + + +### Vertex() + +~~~~~ +Vertex(corner) { + faces_[Face(corner)][LocalIndex(corner)]; +} +~~~~~ + + +### Face() + +~~~~~ +Face(corner) { + return corner / 3; +} +~~~~~ + + +### LocalIndex() + +~~~~~ +LocalIndex(corner) { + return corner % 3; +} +~~~~~ + + +### num_vertices() + +~~~~~ +num_vertices() { + return vertex_corners_.size(); +} +~~~~~ + + +### num_corners() + +~~~~~ +num_corners() { + return faces_.size() * 3; +} +~~~~~ + + +### num_faces() + +~~~~~ +num_faces() { + return faces_.size(); +} +~~~~~ + + +### bool IsOnBoundary() + +~~~~~ +bool IsOnBoundary(vert) { + corner = LeftMostCorner(vert); + if (SwingLeft(corner) < 0) + return true; + return false; +} +~~~~~ + + + +### SwingRight() + +~~~~~ +SwingRight(corner) { + return Previous(Opposite(Previous(corner))); +} +~~~~~ + + +### SwingLeft() + +~~~~~ +SwingLeft(corner) { + return Next(Opposite(Next(corner))); +} +~~~~~ + + +### GetLeftCorner() + +~~~~~ +GetLeftCorner(corner_id) { + if (corner_id < 0) + return kInvalidCornerIndex; + return Opposite(Previous(corner_id)); +} +~~~~~ + + +### GetRightCorner() + +~~~~~ +GetRightCorner(corner_id) { + if (corner_id < 0) + return kInvalidCornerIndex; + return Opposite(Next(corner_id)); +} +~~~~~ + + +### SetOppositeCorner() + +~~~~~ +SetOppositeCorner(corner_id, pp_corner_id) { + opposite_corners_[corner_id] = opp_corner_id; +} +~~~~~ + + + +### MapCornerToVertex() + +~~~~~ +MapCornerToVertex(corner_id, vert_id) { + face = Face(corner_id); + faces_[face][LocalIndex(corner_id)] = vert_id; + if (vert_id >= 0) { + vertex_corners_[vert_id] = corner_id; + } +} +~~~~~ + + +### UpdateVertexToCornerMap() + +~~~~~ +UpdateVertexToCornerMap(vert) { + first_c = vertex_corners_[vert]; + if (first_c < 0) + return; + act_c = SwingLeft(first_c); + c = first_c; + while (act_c >= 0 && act_c != first_c) { + c = act_c; + act_c = SwingLeft(act_c); + } + if (act_c != first_c) { + vertex_corners_[vert] = c; + } +} +~~~~~ + + + +### LeftMostCorner() + +~~~~~ +LeftMostCorner(v) { + return vertex_corners_[v]; +} +~~~~~ + + +### MakeVertexIsolated() + +~~~~~ +MakeVertexIsolated(vert) { + vertex_corners_[vert] = kInvalidCornerIndex; +} +~~~~~ + + + +## Mesh Attribute Corner Table + +### bool IsCornerOnSeam() + +~~~~~ +bool IsCornerOnSeam(corner) { + return is_vertex_on_seam_[corner_table_->Vertex(corner)]; +} +~~~~~ + + +### AddSeamEdge() + +~~~~~ +AddSeamEdge(c) { + MarkSeam(c) + opp_corner = corner_table_->Opposite(c); + if (opp_corner >= 0) { + no_interior_seams_ = false; + MarkSeam(opp_corner) + } +} +~~~~~ + + +### MarkSeam() + +~~~~~ +MarkSeam(c) { + is_edge_on_seam_[c] = true; + is_vertex_on_seam_[corner_table_->Vertex(corner_table_->Next(c))] = true; + is_vertex_on_seam_[corner_table_->Vertex(corner_table_->Previous(c)) + ] = true; +} +~~~~~ + + +### RecomputeVertices() + +~~~~~ +RecomputeVertices() { + // in code RecomputeVerticesInternal(nullptr, nullptr) + num_new_vertices = 0; + for (v = 0; v < corner_table_->num_vertices(); ++v) { + c = corner_table_->LeftMostCorner(v); + if (c < 0) + continue; + first_vert_id(num_new_vertices++); + vertex_to_attribute_entry_id_map_.push_back(first_vert_id); + first_c = c; + if (is_vertex_on_seam_[v]) { + act_c = SwingLeft(first_c); + while (act_c >= 0) { + first_c = act_c; + act_c = SwingLeft(act_c); + } + } + corner_to_vertex_map_[first_c] =first_vert_id; + vertex_to_left_most_corner_map_.push_back(first_c); + act_c = corner_table_->SwingRight(first_c); + while (act_c >= 0 && act_c != first_c) { + if (is_edge_on_seam_[corner_table_->Next(act_c)]) { + // in code IsCornerOppositeToSeamEdge() + first_vert_id = AttributeValueIndex(num_new_vertices++); + vertex_to_attribute_entry_id_map_.push_back(first_vert_id); + vertex_to_left_most_corner_map_.push_back(act_c); + } + corner_to_vertex_map_[act_c] = first_vert_id; + act_c = corner_table_->SwingRight(act_c); + } + } +} +~~~~~ + + + + +## Symbol Decoding + +### DecodeSymbols() + +~~~~~ +DecodeSymbols(num_symbols, out_buffer, out_values) { + scheme UI8 + If (scheme == 0) { + DecodeTaggedSymbols<>(num_symbols, src_buffer, out_values) + } else if (scheme == 1) { + DecodeRawSymbols<>(num_symbols, src_buffer, out_values) + } +} +~~~~~ + + +### DecodeTaggedSymbols() + +~~~~~ +DecodeTaggedSymbols() { + FIXME +} +~~~~~ + + + +### DecodeRawSymbols() + +~~~~~ +DecodeRawSymbols() { + max_bit_length UI8 + DecodeRawSymbolsInternal(max_bit_length, out_values) + return symbols +} +~~~~~ + + + +### DecodeRawSymbolsInternal() + +~~~~~ +DecodeRawSymbolsInternal(max_bit_length, out_values) { + decoder = CreateRansSymbolDecoder(max_bit_length) + decoder.StartDecoding() + // RansSymbolDecoder_StartDecoding + for (i = 0; i < num_values; ++i) { + out_values[i] = decoder.DecodeSymbol() + // RansSymbolDecoder_DecodeSymbol + } +} +~~~~~ + + +### CreateRansSymbolDecoder() + +~~~~~ +CreateRansSymbolDecoder(max_bit_length) { + rans_precision_bits = (3 * max_bit_length) / 2; + rans_precision_bits = min(rans_precision_bits, 20) + rans_precision_bits = max(rans_precision_bits, 12) + rans_precision = 1 << rans_precision_bits_; + l_rans_base = rans_precision * 4; + num_symbols_ UI32 + for (i = 0; i < num_symbols_; ++i) { + prob_data UI8 + if ((prob_data & 3) == 3) { + offset = prob_data >> 2 + for (j = 0; j < offset + 1; ++j) { + probability_table_[i + j] = 0; + } + i += offset; + } else { + prob = prob_data >> 2 + for (j = 0; j < token; ++j) { + eb UI8 + prob = prob | (eb << (8 * (j + 1) - 2) + } + probability_table_[i] = prob; + } + } + rans_build_look_up_table() +} +~~~~~ + + +### RansSymbolDecoder_StartDecoding() + +~~~~~ +RansSymbolDecoder_StartDecoding() { + bytes_encoded UI64 + buffer bytes_encoded * UI8 + rans_read_init(buffer, bytes_encoded) +} +~~~~~ + + + +### RansSymbolDecoder_DecodeSymbol() + +~~~~~ +RansSymbolDecoder_DecodeSymbol() { + ans_.rans_read() +} +~~~~~ + + +## Rans Decoding + +### ans_read_init() + +~~~~~ +ans_read_init(struct AnsDecoder *const ans, const uint8_t *const buf, + int offset) { + x = buf[offset - 1] >> 6 + If (x == 0) { + ans->buf_offset = offset - 1; + ans->state = buf[offset - 1] & 0x3F; + } else if (x == 1) { + ans->buf_offset = offset - 2; + ans->state = mem_get_le16(buf + offset - 2) & 0x3FFF; + } else if (x == 2) { + ans->buf_offset = offset - 3; + ans->state = mem_get_le24(buf + offset - 3) & 0x3FFFFF; + } else if (x == 3) { + // x == 3 implies this byte is a superframe marker + return 1; + } + ans->state += l_base; +} +~~~~~ + + + +### int rabs_desc_read() + +~~~~~ +int rabs_desc_read(struct AnsDecoder *ans, AnsP8 p0) { + AnsP8 p = ans_p8_precision - p0; + if (ans->state < l_base) { + ans->state = ans->state * io_base + ans->buf[--ans->buf_offset]; + } + x = ans->state; + quot = x / ans_p8_precision; + rem = x % ans_p8_precision; + xn = quot * p; + val = rem < p; + if (val) { + ans->state = xn + rem; + } else { + ans->state = x - xn - p; + } + return val; +} +~~~~~ + + + +### rans_read_init() + +~~~~~ +rans_read_init(UI8 *buf, int offset) { + ans_.buf = buf; + x = buf[offset - 1] >> 6 + If (x == 0) { + ans_.buf_offset = offset - 1; + ans_.state = buf[offset - 1] & 0x3F; + } else if (x == 1) { + ans_.buf_offset = offset - 2; + ans_.state = mem_get_le16(buf + offset - 2) & 0x3FFF; + } else if (x == 2) { + ans_.buf_offset = offset - 3; + ans_.state = mem_get_le24(buf + offset - 3) & 0x3FFFFF; + } else if (x == 3) { + ans_.buf_offset = offset - 4; + ans_.state = mem_get_le32(buf + offset - 4) & 0x3FFFFFFF; + } + ans_.state += l_rans_base; +} +~~~~~ + + + + +### rans_build_look_up_table() + +~~~~~ +rans_build_look_up_table() { + cum_prob = 0 + act_prob = 0 + for (i = 0; i < num_symbols; ++i) { + probability_table_[i].prob = token_probs[i]; + probability_table_[i].cum_prob = cum_prob; + cum_prob += token_probs[i]; + for (j = act_prob; j < cum_prob; ++j) { + Lut_table_[j] = i + } + act_prob = cum_prob +} +~~~~~ + + + +### rans_read() + +~~~~~ +rans_read() { + while (ans_.state < l_rans_base) { + ans_.state = ans_.state * io_base + ans_.buf[--ans_.buf_offset]; + } + quo = ans_.state / rans_precision; + rem = ans_.state % rans_precision; + sym = fetch_sym() + ans_.state = quo * sym.prob + rem - sym.cum_prob; + return sym.val; +} +~~~~~ + + +### fetch_sym() + +~~~~~ +fetch_sym() { + symbol = lut_table[rem] + out->val = symbol + out->prob = probability_table_[symbol].prob; + out->cum_prob = probability_table_[symbol].cum_prob; +} +~~~~~ + + + +## Rans Bit Decoder + +### RansBitDecoder_StartDecoding() + +~~~~~ +RansBitDecoder_StartDecoding(DecoderBuffer *source_buffer) { + prob_zero_ UI8 + size UI32 + buffer_ size * UI8 + ans_read_init(&ans_decoder_, buffer_, size) +} +~~~~~ + + +### DecodeNextBit() + +~~~~~ +DecodeNextBit() { + uint8_t bit = rabs_desc_read(&ans_decoder_, prob_zero_); + return bit > 0; +} +~~~~~ + + +## Core Functions + +### DecodeVarint + +~~~~~ +DecodeVarint() { + If (std::is_unsigned::value) { + in UI8 + If (in & (1 << 7)) { + out = DecodeVarint() + out = (out << 7) | (in & ((1 << 7) - 1)) + } else { + typename std::make_unsigned::type UIT; + out = DecodeVarint() + out = ConvertSymbolToSignedInt(out) + } + return out; +} +~~~~~ + + + +### ConvertSymbolToSignedInt() + +~~~~~ +ConvertSymbolToSignedInt() { + abs_val = val >> 1 + If (val & 1 == 0) { + return abs_val + } else { + signed_val = -abs_val - 1 + } + return signed_val +} +~~~~~ + + + +Sequential Decoder + +### decode_connectivity() + +~~~~~ +decode_connectivity() { + num_faces I32 + num_points I32 + connectivity _method UI8 + If (connectivity _method == 0) { + // TODO + } else { + loop num_faces { + If (num_points < 256) { + face[] UI8 + } else if (num_points < (1 << 16)) { + face[] UI16 + } else { + face[] UI32 + } + } + } +} +~~~~~ diff --git a/docs/_site/spec/index.html b/docs/_site/spec/index.html new file mode 100644 index 0000000..05d03ed --- /dev/null +++ b/docs/_site/spec/index.html @@ -0,0 +1,1927 @@ + + + + + Draco Bitstream Specification (Draft) + + + + + + +

    Draco Bitstream Specification (Draft)

    + +

    Version 1,2
    +Released 2017-xx-xx

    + +

    Frank Galligan, Google
    +[author]
    +[author]

    + +

    Last modified: 2017-07-09 18:30:06 -0700

    + +

    Abstract

    + +

    This document defines the bitstream format and decoding process for the +Draco 3D Data Compression scheme.

    + +

    Contents

    + + + +

    Scope

    + +

    This document specifies the open-source Draco #D Data Compression bitstream +format and decoding process.

    + +

    Terms and Definitions

    + +

    For the purposes of this document, the following terms and definitions apply:

    + + + + + + + + + + + + + + +
    TermDefinition
      
    + +

    Symbols (and abbreviated terms)

    + +

    DCT: Discrete Cosine Transform

    + +

    FIXME

    + +

    The specification makes use of a number of constant integers. Constants that +relate to the semantics of a particular syntax element are defined in section +7.

    + +

    Additional constants are defined below:

    + + + + + + + + + + + + + + + + +
    Symbol nameValueDescription
    SYMBOL  
    + +

    Conventions

    + +
      +
    • +

      When bit reading is finished it will always pad the read to the current +byte.

      +
      • +
    • +

      Draco encoded mesh files are comprised of three main sections. This first +section is the header. The second section contains the connectivity data. +The third section contains the attribute data. The header must be decoded +first, then the connectivity section, and then the attribute section.

      +
      • +
    • +

      The Connectivity section is composed of the following sections in order:

      + +
        +
      • +

        Connectivity header

        +
        • +
      • +

        EdgeBreaker symbol buffer

        +
        • +
      • +

        Start face buffer

        +
        • +
      • +

        EdgeBreaker valence header

        +
        • +
      • +

        Context data for the valence prediction

        +
        • +
      • +

        Hole and Split data

        +
        • +
      +
      • +
    • +

      The hole and split data must be decoded before the EdgeBreaker symbols are +decoded.

      +
      • +
    + +

    Draco Decoder

    + +

    Decode()

    + +
    +Decode() { Type + DecodeHeader() + DecodeConnectivityData() + DecodeAttributeData()} + +
    + +

    DecodeHeader()

    + +
    +DecodeHeader() { Type + draco_string UI8[5] + major_version UI8 + minor_version UI8 + encoder_type UI8 + encoder_method UI8 + flags +} + +
    + +

    DecodeAttributeData()

    + +
    +DecodeAttributeData() { Type + num_attributes_decoders UI8 + for (i = 0; i < num_attributes_decoders; ++i) { + CreateAttributesDecoder(i); + } + for (auto &att_dec : attributes_decoders_) { + att_dec->Initialize(this, point_cloud_) + } + for (i = 0; i < num_attributes_decoders; ++i) { + attributes_decoders_[i]->DecodeAttributesDecoderData(buffer_) + } + DecodeAllAttributes() + OnAttributesDecoded() +
    + +

    Mesh Decoder

    + +

    DecodeConnectivityData()

    + +
    +DecodeConnectivityData() Type + InitializeDecoder() + DecodeConnectivity() +} + +
    + +

    EdgeBreaker Decoder

    + +

    InitializeDecoder()

    + +
    +InitializeDecoder() { Type + edgebreaker_decoder_type UI8 +} + +
    + +

    DecodeConnectivity()

    + +
    +DecodeConnectivity() { Type + num_new_verts UI32 + num_encoded_vertices UI32 + num_faces UI32 + num_attribute_data I8 + num_encoded_symbols UI32 + num_encoded_split_symbols UI32 + encoded_connectivity_size UI32 + // file pointer must be set to current position + encoded_connectivity_size + hole_and_split_bytes = DecodeHoleAndTopologySplitEvents() + // file pointer must be set to old current position + EdgeBreakerTraversalValence_Start() + DecodeConnectivity(num_symbols) + if (attribute_data_.size() > 0) { + for (ci = 0; ci < corner_table_->num_corners(); ci += 3) { + DecodeAttributeConnectivitiesOnFace(ci) + } + } + for (i = 0; i < corner_table_->num_vertices(); ++i) { + if (is_vert_hole_[i]) { + corner_table_->UpdateVertexToCornerMap(i); + } + } + // Decode attribute connectivity. + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + attribute_data_[i].connectivity_data.InitEmpty(corner_table_.get()); + for (int32_t c : attribute_data_[i].attribute_seam_corners) { + attribute_data_[i].connectivity_data.AddSeamEdge(c); + } + attribute_data_[i].connectivity_data.RecomputeVertices(nullptr, nullptr); + } + // Preallocate vertex to value mapping + AssignPointsToCorners() +} + +
    + +

    AssignPointsToCorners()

    + +
    +AssignPointsToCorners() { Type + decoder_->mesh()->SetNumFaces(corner_table_->num_faces()); + if (attribute_data_.size() == 0) { + for (f = 0; f < decoder_->mesh()->num_faces(); ++f) { + for (c = 0; c < 3; ++c) { + vert_id = corner_table_->Vertex(3 * f + c); + if (point_id == -1) + point_id = num_points++; + face[c] = point_id; + } + decoder_->mesh()->SetFace(f, face); + } + decoder_->point_cloud()->set_num_points(num_points); + Return true; + } + for (v = 0; v < corner_table_->num_vertices(); ++v) { + c = corner_table_->LeftMostCorner(v); + if (c < 0) + continue; + deduplication_first_corner = c; + if (!is_vert_hole_[v]) { + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + if (!attribute_data_[i].connectivity_data.IsCornerOnSeam(c)) + continue; + vert_id = attribute_data_[i].connectivity_data.Vertex(c); + act_c = corner_table_->SwingRight(c); + seam_found = false; + while (act_c != c) { + if (attribute_data_[i].connectivity_data.Vertex(act_c) != vert_id) { + deduplication_first_corner = act_c; + seam_found = true; + break; + } + act_c = corner_table_->SwingRight(act_c); + } + if (seam_found) + break; + } + } + c = deduplication_first_corner; + corner_to_point_map[c] = point_to_corner_map.size(); + point_to_corner_map.push_back(c); + prev_c = c; + c = corner_table_->SwingRight(c); + while (c >= 0 && c != deduplication_first_corner) { + attribute_seam = false; + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + if (attribute_data_[i].connectivity_data.Vertex(c) != + attribute_data_[i].connectivity_data.Vertex(prev_c)) { + attribute_seam = true; + break; + } + } + if (attribute_seam) { + corner_to_point_map[c] = point_to_corner_map.size(); + point_to_corner_map.push_back(c); + } else { + corner_to_point_map[c] = corner_to_point_map[prev_c]; + } + prev_c = c; + c = corner_table_->SwingRight(c); + } + } + for (f = 0; f < decoder_->mesh()->num_faces(); ++f) { + for (c = 0; c < 3; ++c) { + face[c] = corner_to_point_map[3 * f + c]; + } + decoder_->mesh()->SetFace(f, face); + } + decoder_->point_cloud()->set_num_points(point_to_corner_map.size()); +} + +
    + +

    DecodeConnectivity()

    + +
    +DecodeConnectivity(num_symbols) { Type + for (i = 0; i < num_symbols; ++i) { + symbol = TraversalValence_DecodeSymbol() + corner = 3 * num_faces++ + if (symbol == TOPOLOGY_C) { + vertex_x = UpdateCornerTableForSymbolC() + is_vert_hole_[vertex_x] = false; + } else if (symbol == TOPOLOGY_R || symbol == TOPOLOGY_L) { + UpdateCornerTableForSymbolLR() + check_topology_split = true; + } else if (symbol == TOPOLOGY_S) { + HandleSymbolS() + } else if (symbol == TOPOLOGY_E) { + UpdateCornerTableForSymbolE() + check_topology_split = true; + } + active_corner_stack.back() = corner; + traversal_decoder_.NewActiveCornerReached(corner); + if (check_topology_split) { + encoder_symbol_id = num_symbols - symbol_id - 1; + while (true) { + split = IsTopologySplit(encoder_symbol_id, &split_edge, + &encoder_split_symbol_id); + if (!split) { + break; + } + act_top_corner = corner; + if (split_edge == RIGHT_FACE_EDGE) { + new_active_corner = corner_table_->Next(act_top_corner); + } else { + new_active_corner = corner_table_->Previous(act_top_corner); + } + decoder_split_symbol_id = num_symbols - encoder_split_symbol_id - 1; + topology_split_active_corners[decoder_split_symbol_id] = + new_active_corner; + } + } + } + while (active_corner_stack.size() > 0) { + corner = active_corner_stack.pop_back(); + interior_face = traversal_decoder_.DecodeStartFaceConfiguration(); + if (interior_face == true) { + UpdateCornerTableForInteriorFace() + for (ci = 0; ci < 3; ++ci) { + is_vert_hole_[corner_table_->Vertex(new_corner + ci)] = false; + } + init_face_configurations_.push_back(true); + init_corners_.push_back(new_corner); + } else { + init_face_configurations_.push_back(false); + init_corners_.push_back(corner); + } + } + Return num_vertices; +} + +
    + +

    UpdateCornerTableForSymbolC()

    + +
    +UpdateCornerTableForSymbolC(corner) { Type + corner_a = active_corner_stack.back(); + corner_b = corner_table_->Previous(corner_a); + while (corner_table_->Opposite(corner_b) >= 0) { + corner_b = corner_table_->Previous(corner_table_->Opposite(corner_b)); + } + SetOppositeCorners(corner_a, corner + 1); + SetOppositeCorners(corner_b, corner + 2); + vertex_x = corner_table_->Vertex(corner_table_->Next(corner_a)); + corner_table_->MapCornerToVertex(corner, vertex_x); + corner_table_->MapCornerToVertex( + corner + 1, corner_table_->Vertex(corner_table_->Next(corner_b))); + corner_table_->MapCornerToVertex( + corner + 2, corner_table_->Vertex(corner_table_->Previous(corner_a))); + return vertex_x; +} + +
    + +

    UpdateCornerTableForSymbolLR()

    + +
    +UpdateCornerTableForSymbolLR(corner, symbol) { Type + if (symbol == TOPOLOGY_R) { + opp_corner = corner + 2; + } else { + opp_corner = corner + 1; + } + SetOppositeCorners(opp_corner, corner_a); + corner_table_->MapCornerToVertex(opp_corner,num_vertices++); + corner_table_->MapCornerToVertex( + corner_table_->Next(opp_corner), + corner_table_->Vertex(corner_table_->Previous(corner_a))); + corner_table_->MapCornerToVertex( + corner_table_->Previous(opp_corner), + corner_table_->Vertex(corner_table_->Next(corner_a))); +} + +
    + +

    HandleSymbolS()

    + +
    +HandleSymbolS(corner) { Type + corner_b = active_corner_stack.pop_back(); + it = topology_split_active_corners.find(symbol_id); + if (it != topology_split_active_corners.end()) { + active_corner_stack.push_back(it->second); + } + corner_a = active_corner_stack.back(); + SetOppositeCorners(corner_a, corner + 2); + SetOppositeCorners(corner_b, corner + 1); + vertex_p = corner_table_->Vertex(corner_table_->Previous(corner_a)); + corner_table_->MapCornerToVertex(corner, vertex_p); + corner_table_->MapCornerToVertex( + corner + 1, corner_table_->Vertex(corner_table_->Next(corner_a))); + corner_table_->MapCornerToVertex(corner + 2, + corner_table_->Vertex(corner_table_->Previous(corner_b))); + corner_n = corner_table_->Next(corner_b); + vertex_n = corner_table_->Vertex(corner_n); + traversal_decoder_.MergeVertices(vertex_p, vertex_n); + // TraversalValence_MergeVertices + while (corner_n >= 0) { + corner_table_->MapCornerToVertex(corner_n, vertex_p); + corner_n = corner_table_->SwingLeft(corner_n); + } + corner_table_->MakeVertexIsolated(vertex_n); +} + +
    + +

    UpdateCornerTableForSymbolE()

    + +
    +UpdateCornerTableForSymbolE() { Type + corner_table_->MapCornerToVertex(corner, num_vertices++); + corner_table_->MapCornerToVertex(corner + 1, num_vertices++); + corner_table_->MapCornerToVertex(corner + 2, num_vertices++); +} + +
    + +

    UpdateCornerTableForInteriorFace()

    + +
    +UpdateCornerTableForInteriorFace() { Type + corner_b = corner_table_->Previous(corner); + while (corner_table_->Opposite(corner_b) >= 0) { + corner_b = corner_table_->Previous(corner_table_->Opposite(corner_b)); + } + corner_c = corner_table_->Next(corner); + while (corner_table_->Opposite(corner_c) >= 0) { + corner_c = corner_table_->Next(corner_table_->Opposite(corner_c)); + } + face(num_faces++); + corner_table_->MapCornerToVertex( + new_corner, corner_table_->Vertex(corner_table_->Next(corner_b))); + corner_table_->MapCornerToVertex( + new_corner + 1, corner_table_->Vertex(corner_table_->Next(corner_c))); + corner_table_->MapCornerToVertex( + new_corner + 2, corner_table_->Vertex(corner_table_->Next(corner))); +} + +
    + +

    IsTopologySplit()

    + +
    +IsTopologySplit(encoder_symbol_id, *out_face_edge, Type + + *out_encoder_split_symbol_id) { + if (topology_split_data_.size() == 0) + return false; + if (topology_split_data_.back().source_symbol_id != encoder_symbol_id) + return false; + *out_face_edge = topology_split_data_.back().source_edge; + *out_encoder_split_symbol_id = + topology_split_data_.back().split_symbol_id; + topology_split_data_.pop_back(); + return true; +} + +
    + +

    DecodeAttributeConnectivitiesOnFace()

    + +
    +DecodeAttributeConnectivitiesOnFace(corner) { Type + corners[3] = {corner, corner_table_->Next(corner), + corner_table_->Previous(corner)} + for (c = 0; c < 3; ++c) { + opp_corner = corner_table_->Opposite(corners[c]); + if (opp_corner < 0) { + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + attribute_data_[i].attribute_seam_corners.push_back(corners[c]); + } + continue + } + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + bool is_seam = traversal_decoder_.DecodeAttributeSeam(i); + if (is_seam) { + attribute_data_[i].attribute_seam_corners.push_back(corners[c]); + } + } + } +} + +
    + +

    SetOppositeCorners()

    + +
    +SetOppositeCorners(corner_0, corner_1) { Type + corner_table_->SetOppositeCorner(corner_0, corner_1); + corner_table_->SetOppositeCorner(corner_1, corner_0); +} + +
    + +

    EdgeBreaker Hole and Topology Split Events

    + +

    DecodeHoleAndTopologySplitEvents()

    + +

    FIXME: Escaping angle brackets

    + +
    +DecodeHoleAndTopologySplitEvents() { Type + num_topologoy_splits UI32 + source_symbol_id = 0 + for (i = 0; i < num_topologoy_splits; ++i) { + DecodeVarint\<UI32\>(&delta) + split_data[i].source_symbol_id = delta + source_symbol_id + DecodeVarint\<UI32\>(&delta) + split_data[i].split_symbol_id = source_symbol_id - delta + } + for (i = 0; i < num_topologoy_splits; ++i) { + split_data[i].split_edge bits1 + split_data[i].source_edge bits1 + } + num_hole_events UI32 + symbol_id = 0 + for (i = 0; i < num_hole_events; ++i) { + DecodeVarint\<UI32\>(&delta) + hole_data[i].symbol_id = delta + symbol_id + } + return bytes_decoded; +} + +
    + +

    CreateAttributesDecoder

    + +

    FIXME: Escaping angle brackets

    + +
    +CreateAttributesDecoder() { Type + att_data_id I8 + decoder_type UI8 + if (att_data_id >= 0) { + attribute_data_[att_data_id].decoder_id = att_decoder_id; + } + traversal_method_encoded UI8 + if (decoder_type == MESH_VERTEX_ATTRIBUTE) { + if (att_data_id < 0) { + encoding_data = &pos_encoding_data_; + } else { + encoding_data = &attribute_data_[att_data_id].encoding_data; + attribute_data_[att_data_id].is_connectivity_used = false; + } + if (traversal_method == MESH_TRAVERSAL_DEPTH_FIRST) { + typedef EdgeBreakerTraverser\<AttProcessor, AttObserver\> AttTraverser; + sequencer = CreateVertexTraversalSequencer\<AttTraverser\>(encoding_data); + } else if (traversal_method == MESH_TRAVERSAL_PREDICTION_DEGREE) { + typedef PredictionDegreeTraverser\<AttProcessor, AttObserver\> AttTraverser; + sequencer = CreateVertexTraversalSequencer\<AttTraverser\>(encoding_data); + } + } else { + // TODO + } + att_controller(new SequentialAttributeDecodersController(std::move(sequencer))) + decoder_->SetAttributesDecoder(att_decoder_id, std::move(att_controller)); +} + +
    + +

    Edgebreaker Traversal Decoder

    + +

    EdgebreakerTraversal_Start()

    + +
    +EdgebreakerTraversal_Start() { Type + size UI64 + symbol_buffer_ size * UI8 + size UI64 + start_face_buffer_ size * UI8 + if (num_attribute_data_ > 0) { + attribute_connectivity_decoders_ = std::unique_ptr<BinaryDecoder[]>( + new BinaryDecoder[num_attribute_data_]); + for (i = 0; i < num_attribute_data_; ++i) { + attribute_connectivity_decoders_[i].StartDecoding() + // RansBitDecoder_StartDecoding + } +} + +
    + +

    Traversal_DecodeSymbol()

    + +
    Traversal_DecodeSymbol() {
+  symbol_buffer_.DecodeLeastSignificantBits32(1, &symbol);                   bits1
+  if (symbol != TOPOLOGY_C) {
+    symbol_buffer_.DecodeLeastSignificantBits32(2, &symbol_suffix);          bits2
+    symbol |= (symbol_suffix << 1);
+  }
+  return symbol
+}
+
    +
    + +

    DecodeAttributeSeam()

    + +
    DecodeAttributeSeam(int attribute) {
+  return attribute_connectivity_decoders_[attribute].DecodeNextBit();
+}
+
    +
    + +

    EdgeBreaker Traversal Valence Decoder

    + +

    EdgeBreakerTraversalValence_Start()

    + +
    EdgeBreakerTraversalValence_Start(num_vertices, num_attribute_data) {
+  out_buffer = EdgebreakerTraversal_Start()
+  num_split_symbols                                                          I32
+  mode == 0                                                                  I8
+  num_vertices_ += num_split_symbols
+  vertex_valences_ init to 0
+  vertex_valences_.resize(num_vertices_, 0);
+  min_valence_ = 2;
+  max_valence_ = 7;
+  num_unique_valences = 6 (max_valence_ - min_valence_ + 1)
+  for (i = 0; i < num_unique_valences; ++i) {
+    DecodeVarint<UI32>(&num_symbols, out_buffer)
+    If (num_symbols > 0) {
+      DecodeSymbols(num_symbols, out_buffer, &context_symbols_[i])
+    }
+    context_counters_[i] = num_symbols
+  }
+  return out_buffer;
+}
+
    +
    + +

    TraversalValence_DecodeSymbol()

    + +
    TraversalValence_DecodeSymbol() {
+  if (active_context_ != -1) {
+    symbol_id  = context_symbols_[active_context_]
+                                                      [--context_counters_[active_context_]]
+    last_symbol_ = edge_breaker_symbol_to_topology_id[symbol_id]
+  } else {
+    last_symbol_ = Traversal_DecodeSymbol()
+  }
+  return last_symbol_
+}
+
    +
    + +

    TraversalValence_NewActiveCornerReached()

    + +
    TraversalValence_NewActiveCornerReached(corner) {
+  switch (last_symbol_) {
+    case TOPOLOGY_C:
+    case TOPOLOGY_S:
+      vertex_valences_[ct(next)] += 1;
+      vertex_valences_[ct(prev)] += 1;
+      break;
+    case TOPOLOGY_R:
+      vertex_valences_[corner] += 1;
+      vertex_valences_[ct(next)] += 1;
+      vertex_valences_[ct(prev)] += 2;
+      break;
+    case TOPOLOGY_L:
+      vertex_valences_[corner] += 1;
+      vertex_valences_[ct(next)] += 2;
+      vertex_valences_[ct(prev)] += 1;
+      break;
+    case TOPOLOGY_E:
+      vertex_valences_[corner] += 2;
+      vertex_valences_[ct(next)] += 2;
+      vertex_valences_[ct(prev)] += 2;
+      break;
+  }
+  valence = vertex_valences_[ct(next)]
+  valence = max(valence, min_valence_)
+  valence = min(valence, max_valence_)
+  active_context_ = (valence - min_valence_);
+}
+
    +
    + +

    TraversalValence_MergeVertices()

    + +
    TraversalValence_MergeVertices(dest, source) {
+  vertex_valences_[dest] += vertex_valences_[source];
+}
+
    +
    + +

    Attributes Decoder

    + +

    DecodeAttributesDecoderData()

    + +
    DecodeAttributesDecoderData(buffer) {
+  num_attributes                                                             I32
+  point_attribute_ids_.resize(num_attributes);
+  for (i = 0; i < num_attributes; ++i) {
+    att_type                                                                 UI8
+    data_type                                                                UI8
+    components_count                                                         UI8
+    normalized                                                               UI8
+    custom_id                                                                UI16
+    Initialize GeometryAttribute ga
+    att_id = pc->AddAttribute(new PointAttribute(ga));
+    point_attribute_ids_[i] = att_id;
+}
+
    +
    + +

    Sequential Attributes Decoders Controller

    + +

    DecodeAttributesDecoderData()

    + +
    DecodeAttributesDecoderData(buffer) {
+  AttributesDecoder_DecodeAttributesDecoderData(buffer)
+  sequential_decoders_.resize(num_attributes());
+  for (i = 0; i < num_attributes(); ++i) {
+    decoder_type                                                             UI8
+    sequential_decoders_[i] = CreateSequentialDecoder(decoder_type);
+    sequential_decoders_[i]->Initialize(decoder(), GetAttributeId(i))
+}
+
    +
    + +

    DecodeAttributes()

    + +
    DecodeAttributes(buffer) {
+  sequencer_->GenerateSequence(&point_ids_)
+  for (i = 0; i < num_attributes(); ++i) {
+    pa = decoder()->point_cloud()->attribute(GetAttributeId(i));
+    sequencer_->UpdatePointToAttributeIndexMapping(pa)
+  }
+  for (i = 0; i < num_attributes(); ++i) {
+    sequential_decoders_[i]->Decode(point_ids_, buffer)
+    //SequentialAttributeDecoder_Decode()
+  }
+}
+
    +
    + +

    CreateSequentialDecoder()

    + +
    CreateSequentialDecoder(type) {
+  switch (type) {
+    case SEQUENTIAL_ATTRIBUTE_ENCODER_GENERIC:
+      return new SequentialAttributeDecoder()
+    case SEQUENTIAL_ATTRIBUTE_ENCODER_INTEGER:
+      return new SequentialIntegerAttributeDecoder()
+    case SEQUENTIAL_ATTRIBUTE_ENCODER_QUANTIZATION:
+      return new SequentialQuantizationAttributeDecoder()
+    case SEQUENTIAL_ATTRIBUTE_ENCODER_NORMALS:
+      return new SequentialNormalAttributeDecoder()
+  }
+}
+
    +
    + +

    Sequential Attribute Decoder

    + +
    Initialize(...) {
+  // Init some members
+}
+
    +
    + +

    DecodeValues()

    + +
    DecodeValues(const std::vector<PointIndex> &point_ids) {
+  num_values = point_ids.size();
+  entry_size = attribute_->byte_stride();
+  std::unique_ptr<uint8_t[]> value_data_ptr(new uint8_t[entry_size]);
+  out_byte_pos = 0;
+  for (i = 0; i < num_values; ++i) {
+   value_data                                                         UI8 * entry_size
+    attribute_->buffer()->Write(out_byte_pos, value_data, entry_size);
+    out_byte_pos += entry_size;
+  }
+}
+
    +
    + +

    Sequential Integer Attribute Decoder

    + +
    Initialize(...) {
+  SequentialAttributeDecoder_Initialize()
+}
+
    +
    + +

    DecodeValues()

    + +
    DecodeValues(point_ids) {
+  prediction_scheme_method                                                   I8
+  if (prediction_scheme_method != PREDICTION_NONE) {
+    prediction_transform_type                                                I8
+    prediction_scheme_ = CreateIntPredictionScheme(...)
+  }
+  if (prediction_scheme_) {
+  }
+  DecodeIntegerValues(point_ids)
+  //SequentialQuantizationAttributeDecoder_DecodeIntegerValues()
+  //StoreValues()
+  DequantizeValues(num_values)
+}
+
    +
    + +

    DecodeIntegerValues()

    + +
    DecodeIntegerValues(point_ids) {
+  compressed                                                                 UI8
+  if (compressed) {
+    DecodeSymbols(..., values_.data())
+  } else {
+  // TODO
+  }
+  if (!prediction_scheme_->AreCorrectionsPositive()) {
+    ConvertSymbolsToSignedInts(...)
+  }
+  if (prediction_scheme_) {
+    prediction_scheme_->DecodePredictionData(buffer)
+    // DecodeTransformData(buffer)
+    if (!values_.empty()) {
+      prediction_scheme_->Decode(values_.data(), &values_[0],
+                                      values_.size(), num_components, point_ids.data())
+      // MeshPredictionSchemeParallelogram_Decode()
+}
+
    +
    + +

    Sequential Quantization Attribute Decoder

    + +
    Initialize(...) {
+  SequentialIntegerAttributeDecoder_Initialize()
+}
+
    +
    + +

    DecodeIntegerValues()

    + +
    DecodeIntegerValues(point_ids) {
+  // DecodeQuantizedDataInfo()
+  num_components = attribute()->components_count();
+  for (i = 0; i < num_components; ++i) {
+    min_value_[i]                                                            F32
+  }
+  max_value_dif_                                                             F32
+  quantization_bits_                                                         UI8
+  SequentialIntegerAttributeDecoder::DecodeIntegerValues()
+}
+
    +
    + +

    DequantizeValues()

    + +
    DequantizeValues(num_values) {
+  max_quantized_value = (1 << (quantization_bits_)) - 1;
+  num_components = attribute()->components_count();
+  entry_size = sizeof(float) * num_components;
+  quant_val_id = 0;
+  out_byte_pos = 0;
+  for (i = 0; i < num_values; ++i) {
+    for (c = 0; c < num_components; ++c) {
+      value = dequantizer.DequantizeFloat(values()->at(quant_val_id++));
+      value = value + min_value_[c];
+      att_val[c] = value;
+    }
+    attribute()->buffer()->Write(out_byte_pos, att_val.get(), entry_size);
+    out_byte_pos += entry_size;
+  }
+}
+
    +
    + +

    Prediction Scheme Transform

    + +

    ComputeOriginalValue()

    + +
    ComputeOriginalValue(const DataTypeT *predicted_vals,
+                                   const CorrTypeT *corr_vals,
+                                   DataTypeT *out_original_vals, int val_id) {
+  for (i = 0; i < num_components_; ++i) {
+    out_original_vals[i] = predicted_vals[i] + corr_vals[val_id + i];
+  }
+}
+
    +
    + +

    Prediction Scheme Wrap Transform

    + +

    DecodeTransformData()

    + +
    DecodeTransformData(buffer) {
+  min_value_                                                                 DT
+  max_value_                                                                 DT
+}
+
    +
    + +

    ComputeOriginalValue()

    + +
    ComputeOriginalValue(const DataTypeT *predicted_vals,
+                                   const CorrTypeT *corr_vals,
+                                   DataTypeT *out_original_vals, int val_id) {
+  clamped_vals = ClampPredictedValue(predicted_vals);
+  ComputeOriginalValue(clamped_vals, corr_vals, out_original_vals, val_id)
+  // PredictionSchemeTransform_ComputeOriginalValue()
+  for (i = 0; i < this->num_components(); ++i) {
+    if (out_original_vals[i] > max_value_) {
+      out_original_vals[i] -= max_dif_;
+    } else if (out_original_vals[i] < min_value_) {
+      out_original_vals[i] += max_dif_;
+    }
+}
+
    +
    + +

    ClampPredictedValue()

    + +
    ClampPredictedValue(const DataTypeT *predicted_val) {
+  for (i = 0; i < this->num_components(); ++i) {
+    clamped_value_[i] = min(predicted_val[i], max_value_)
+    clamped_value_[i] = max(predicted_val[i], min_value_)
+  }
+  return &clamped_value_[0];
+}
+
    +
    + +

    Mesh Prediction Scheme Parallelogram

    + +

    Decode()

    + +
    Decode(...) {
+  this->transform().InitializeDecoding(num_components);
+  // restore the first value
+  this->transform().ComputeOriginalValue(pred_vals.get(),
+                                       in_corr, out_data, 0);
+  // PredictionSchemeWrapTransform_ComputeOriginalValue()
+  corner_map_size = this->mesh_data().data_to_corner_map()->size();
+  for (p = 1; p < corner_map_size; ++p) {
+    corner_id = this->mesh_data().data_to_corner_map()->at(p);
+    dst_offset = p * num_components;
+    b= ComputeParallelogramPrediction(p, corner_id, table,
+                                        *vertex_to_data_map, out_data,
+                                        num_components, pred_vals.get())
+    if (!b) {
+      src_offset = (p - 1) * num_components;
+      this->transform().ComputeOriginalValue(out_data + src_offset, in_corr,
+                                             out_data + dst_offset, dst_offset);
+      // PredictionSchemeWrapTransform_ComputeOriginalValue()
+    } else {
+      this->transform().ComputeOriginalValue(pred_vals.get(), in_corr,
+                                             out_data + dst_offset, dst_offset);
+      // PredictionSchemeWrapTransform_ComputeOriginalValue()
+    }
+  }
+}
+
    +
    + +

    MeshPredictionSchemeParallelogramShared

    + +

    ComputeParallelogramPrediction()

    + +
    ComputeParallelogramPrediction(...) {
+  oci = table->Opposite(ci);
+  vert_opp = vertex_to_data_map[table->Vertex(ci)];
+  vert_next = vertex_to_data_map[table->Vertex(table->Next(ci))];
+  vert_prev = vertex_to_data_map[table->Vertex(table->Previous(ci))];
+  if (vert_opp < data_entry_id && vert_next < data_entry_id &&
+      vert_prev < data_entry_id) {
+    v_opp_off = vert_opp * num_components;
+    v_next_off = vert_next * num_components;
+    v_prev_off = vert_prev * num_components;
+    for (c = 0; c < num_components; ++c) {
+      out_prediction[c] = (in_data[v_next_off + c] + in_data[v_prev_off + c]) -
+                          in_data[v_opp_off + c];
+    }
+    Return true;
+  }
+  return false;
+}
+
    +
    + +

    CornerTable Traversal Processor

    + +

    IsFaceVisited()

    + +
    IsFaceVisited(corner_id) {
+  if (corner_id < 0)
+    return true
+  return is_face_visited_[corner_id / 3];
+}
+
    +
    + +

    MarkFaceVisited()

    + +
    MarkFaceVisited(face_id) {
+  is_face_visited_[face_id] = true;
+}
+
    +
    + +

    IsVertexVisited()

    + +
    IsVertexVisited(vert_id) {
+  return is_vertex_visited_[vert_id];
+}
+
    +
    + +

    MarkVertexVisited()

    + +
    MarkVertexVisited(vert_id) {
+  is_vertex_visited_[vert_id] = true;
+}
+
    +
    + +

    Mesh Attribute Indices Encoding Observer

    + +

    OnNewVertexVisited()

    + +
    OnNewVertexVisited(vertex, corner) {
+  point_id = mesh_->face(corner / 3)[corner % 3];
+  sequencer_->AddPointId(point_id);
+  // Keep track of visited corners.
+  encoding_data_->encoded_attribute_value_index_to_corner_map.push_back(corner);
+  encoding_data_
+        ->vertex_to_encoded_attribute_value_index_map[vertex] =
+        encoding_data_->num_values;
+  encoding_data_->num_values++;
+}
+
    +
    + +

    EdgeBreaker Traverser

    + +

    TraverseFromCorner()

    + +
    TraverseFromCorner(corner_id) {
+  if (processor_.IsFaceVisited(corner_id))
+    return
+  corner_traversal_stack_.clear();
+  corner_traversal_stack_.push_back(corner_id);
+  next_vert = corner_table_->Vertex(corner_table_->Next(corner_id));
+  prev_vert = corner_table_->Vertex(corner_table_->Previous(corner_id));
+  if (!processor_.IsVertexVisited(next_vert)) {
+    processor_.MarkVertexVisited(next_vert);
+    traversal_observer_.OnNewVertexVisited(next_vert,
+                                        corner_table_->Next(corner_id));
+  }
+  if (!processor_.IsVertexVisited(prev_vert)) {
+    processor_.MarkVertexVisited(prev_vert);
+    traversal_observer_.OnNewVertexVisited(prev_vert,
+                                        corner_table_->Previous(corner_id));
+  }
+  while (!corner_traversal_stack_.empty()) {
+    corner_id = corner_traversal_stack_.back();
+    face_id =corner_id / 3;
+    if (processor_.IsFaceVisited(face_id)) {
+      corner_traversal_stack_.pop_back();
+      continue
+    }
+    while(true) {
+      face_id = corner_id / 3;
+      processor_.MarkFaceVisited(face_id);
+      traversal_observer_.OnNewFaceVisited(face_id);
+      vert_id = corner_table_->Vertex(corner_id);
+      on_boundary = corner_table_->IsOnBoundary(vert_id);
+      if (!processor_.IsVertexVisited(vert_id)) {
+        processor_.MarkVertexVisited(vert_id);
+        traversal_observer_.OnNewVertexVisited(vert_id, corner_id);
+        if (!on_boundary) {
+          corner_id = corner_table_->GetRightCorner(corner_id);
+          continue;
+        }
+      }
+      // The current vertex has been already visited or it was on a boundary.
+      right_corner_id = corner_table_->GetRightCorner(corner_id);
+      left_corner_id = corner_table_->GetLeftCorner(corner_id);
+      right_face_id((right_corner_id < 0 ? -1 : right_corner_id / 3));
+      left_face_id((left_corner_id < 0 ? -1 : left_corner_id / 3));
+      if (processor_.IsFaceVisited(right_face_id)) {
+        if (processor_.IsFaceVisited(left_face_id)) {
+          corner_traversal_stack_.pop_back();
+          break; // Break from while(true) loop
+        } else {
+          corner_id = left_corner_id;
+        }
+      } else {
+        if (processor_.IsFaceVisited(left_face_id)) {
+          corner_id = right_corner_id;
+       } else {
+          // Split the traversal.
+          corner_traversal_stack_.back() = left_corner_id;
+          corner_traversal_stack_.push_back(right_corner_id);
+          break; // Break from while(true) loop
+        }
+      }
+    }
+  }
+}
+
    +
    + +

    Mesh Traversal Sequencer

    + +

    GenerateSequenceInternal()

    + +
    GenerateSequenceInternal() {
+  traverser_.OnTraversalStart();
+   If (corner_order_) {
+    // TODO
+  } else {
+    int32_t num_faces = traverser_.corner_table()->num_faces();
+    for (i = 0; i < num_faces; ++i) {
+      ProcessCorner(3 * i)
+    }
+  }
+  traverser_.OnTraversalEnd();
+}
+
    +
    + +

    ProcessCorner()

    + +
    ProcessCorner(corner_id) {
+  traverser_.TraverseFromCorner(corner_id);
+}
+
    +
    + +

    UpdatePointToAttributeIndexMapping()

    + +
    UpdatePointToAttributeIndexMapping(PointAttribute *attribute) {
+  corner_table = traverser_.corner_table();
+  attribute->SetExplicitMapping(mesh_->num_points());
+  num_faces = mesh_->num_faces();
+  num_points = mesh_->num_points();
+  for (f = 0; f < num_faces; ++f) {
+    face = mesh_->face(f);
+    for (p = 0; p < 3; ++p) {
+      point_id = face[p];
+      vert_id = corner_table->Vertex(3 * f + p);
+      att_entry_id(
+            encoding_data_
+                ->vertex_to_encoded_attribute_value_index_map[vert_id]);
+      attribute->SetPointMapEntry(point_id, att_entry_id);
+    }
+  }
+}
+
    +
    + +

    PointsSequencer

    + +

    AddPointId()

    + +
    AddPointId(point_id) {
+  out_point_ids_->push_back(point_id);
+}
+
    +
    + +

    Corner Table

    + +

    Opposite()

    + +
    Opposite(corner) {
+  return opposite_corners_[corner];
+}
+
    +
    + +

    Next()

    + +
    Next(corner) {
+  return LocalIndex(++corner) ? corner : corner - 3;
+}
+
    +
    + +

    Previous()

    + +
    Previous(corner) {
+  return LocalIndex(corner) ? corner - 1 : corner + 2;
+}
+
    +
    + +

    Vertex()

    + +
    Vertex(corner) {
+  faces_[Face(corner)][LocalIndex(corner)];
+}
+
    +
    + +

    Face()

    + +
    Face(corner) {
+  return corner / 3;
+}
+
    +
    + +

    LocalIndex()

    + +
    LocalIndex(corner) {
+  return corner % 3;
+}
+
    +
    + +

    num_vertices()

    + +
    num_vertices() {
+  return vertex_corners_.size();
+}
+
    +
    + +

    num_corners()

    + +
    num_corners() {
+  return faces_.size() * 3;
+}
+
    +
    + +

    num_faces()

    + +
    num_faces() {
+  return faces_.size();
+}
+
    +
    + +

    bool IsOnBoundary()

    + +
    bool IsOnBoundary(vert) {
+  corner = LeftMostCorner(vert);
+  if (SwingLeft(corner) < 0)
+    return true;
+  return false;
+}
+
    +
    + +

    SwingRight()

    + +
    SwingRight(corner) {
+  return Previous(Opposite(Previous(corner)));
+}
+
    +
    + +

    SwingLeft()

    + +
    SwingLeft(corner) {
+  return Next(Opposite(Next(corner)));
+}
+
    +
    + +

    GetLeftCorner()

    + +
    GetLeftCorner(corner_id) {
+  if (corner_id < 0)
+     return kInvalidCornerIndex;
+  return Opposite(Previous(corner_id));
+}
+
    +
    + +

    GetRightCorner()

    + +
    GetRightCorner(corner_id) {
+  if (corner_id < 0)
+     return kInvalidCornerIndex;
+  return Opposite(Next(corner_id));
+}
+
    +
    + +

    SetOppositeCorner()

    + +
    SetOppositeCorner(corner_id, pp_corner_id) {
+  opposite_corners_[corner_id] = opp_corner_id;
+}
+
    +
    + +

    MapCornerToVertex()

    + +
    MapCornerToVertex(corner_id, vert_id) {
+  face = Face(corner_id);
+  faces_[face][LocalIndex(corner_id)] = vert_id;
+  if (vert_id >= 0) {
+    vertex_corners_[vert_id] = corner_id;
+  }
+}
+
    +
    + +

    UpdateVertexToCornerMap()

    + +
    UpdateVertexToCornerMap(vert) {
+  first_c = vertex_corners_[vert];
+  if (first_c < 0)
+    return;
+  act_c = SwingLeft(first_c);
+  c = first_c;
+  while (act_c >= 0 && act_c != first_c) {
+    c = act_c;
+    act_c = SwingLeft(act_c);
+  }
+  if (act_c != first_c) {
+    vertex_corners_[vert] = c;
+  }
+}
+
    +
    + +

    LeftMostCorner()

    + +
    LeftMostCorner(v) {
+  return vertex_corners_[v];
+}
+
    +
    + +

    MakeVertexIsolated()

    + +
    MakeVertexIsolated(vert) {
+  vertex_corners_[vert] = kInvalidCornerIndex;
+}
+
    +
    + +

    Mesh Attribute Corner Table

    + +

    bool IsCornerOnSeam()

    + +
    bool IsCornerOnSeam(corner) {
+  return is_vertex_on_seam_[corner_table_->Vertex(corner)];
+}
+
    +
    + +

    AddSeamEdge()

    + +
    AddSeamEdge(c) {
+  MarkSeam(c)
+  opp_corner = corner_table_->Opposite(c);
+  if (opp_corner >= 0) {
+    no_interior_seams_ = false;
+    MarkSeam(opp_corner)
+  }
+}
+
    +
    + +

    MarkSeam()

    + +
    MarkSeam(c) {
+  is_edge_on_seam_[c] = true;
+  is_vertex_on_seam_[corner_table_->Vertex(corner_table_->Next(c))] = true;
+  is_vertex_on_seam_[corner_table_->Vertex(corner_table_->Previous(c))
+                         ] = true;
+}
+
    +
    + +

    RecomputeVertices()

    + +
    RecomputeVertices() {
+  // in code RecomputeVerticesInternal<false>(nullptr, nullptr)
+  num_new_vertices = 0;
+  for (v = 0; v < corner_table_->num_vertices(); ++v) {
+    c = corner_table_->LeftMostCorner(v);
+    if (c < 0)
+      continue;
+    first_vert_id(num_new_vertices++);
+    vertex_to_attribute_entry_id_map_.push_back(first_vert_id);
+    first_c = c;
+    if (is_vertex_on_seam_[v]) {
+      act_c = SwingLeft(first_c);
+      while (act_c >= 0) {
+        first_c = act_c;
+        act_c = SwingLeft(act_c);
+      }
+    }
+    corner_to_vertex_map_[first_c] =first_vert_id;
+    vertex_to_left_most_corner_map_.push_back(first_c);
+    act_c = corner_table_->SwingRight(first_c);
+    while (act_c >= 0 && act_c != first_c) {
+      if (is_edge_on_seam_[corner_table_->Next(act_c)]) {
+        // in code IsCornerOppositeToSeamEdge()
+        first_vert_id = AttributeValueIndex(num_new_vertices++);
+        vertex_to_attribute_entry_id_map_.push_back(first_vert_id);
+        vertex_to_left_most_corner_map_.push_back(act_c);
+      }
+      corner_to_vertex_map_[act_c] = first_vert_id;
+      act_c = corner_table_->SwingRight(act_c);
+    }
+  }
+}
+
    +
    + +

    Symbol Decoding

    + +

    DecodeSymbols()

    + +
    DecodeSymbols(num_symbols, out_buffer, out_values) {
+  scheme                                                                     UI8
+  If (scheme == 0) {
+    DecodeTaggedSymbols<>(num_symbols, src_buffer, out_values)
+  } else if (scheme == 1) {
+    DecodeRawSymbols<>(num_symbols, src_buffer, out_values)
+  }
+}
+
    +
    + +

    DecodeTaggedSymbols()

    + +
    DecodeTaggedSymbols() {
+  FIXME
+}
+
    +
    + +

    DecodeRawSymbols()

    + +
    DecodeRawSymbols() {
+  max_bit_length                                                             UI8
+  DecodeRawSymbolsInternal(max_bit_length, out_values)
+  return symbols
+}
+
    +
    + +

    DecodeRawSymbolsInternal()

    + +
    DecodeRawSymbolsInternal(max_bit_length, out_values) {
+  decoder = CreateRansSymbolDecoder(max_bit_length)
+  decoder.StartDecoding()
+  // RansSymbolDecoder_StartDecoding
+  for (i = 0; i < num_values; ++i) {
+    out_values[i] = decoder.DecodeSymbol()
+    // RansSymbolDecoder_DecodeSymbol
+  }
+}
+
    +
    + +

    CreateRansSymbolDecoder()

    + +
    CreateRansSymbolDecoder(max_bit_length) {
+  rans_precision_bits  = (3 * max_bit_length) / 2;
+  rans_precision_bits = min(rans_precision_bits, 20)
+  rans_precision_bits = max(rans_precision_bits, 12)
+  rans_precision = 1 << rans_precision_bits_;
+  l_rans_base = rans_precision * 4;
+  num_symbols_                                                               UI32
+  for (i = 0; i < num_symbols_; ++i) {
+    prob_data                                                                UI8
+    if ((prob_data & 3) == 3) {
+      offset = prob_data >> 2
+      for (j = 0; j < offset + 1; ++j) {
+        probability_table_[i + j] = 0;
+      }
+      i += offset;
+    } else {
+      prob = prob_data >> 2
+      for (j = 0; j < token; ++j) {
+        eb                                                                   UI8
+        prob = prob | (eb << (8 * (j + 1) - 2)
+      }
+      probability_table_[i] = prob;
+    }
+  }
+  rans_build_look_up_table()
+}
+
    +
    + +

    RansSymbolDecoder_StartDecoding()

    + +
    RansSymbolDecoder_StartDecoding() {
+  bytes_encoded                                                              UI64
+  buffer                                                                     bytes_encoded * UI8
+  rans_read_init(buffer, bytes_encoded)
+}
+
    +
    + +

    RansSymbolDecoder_DecodeSymbol()

    + +
    RansSymbolDecoder_DecodeSymbol() {
+  ans_.rans_read()
+}
+
    +
    + +

    Rans Decoding

    + +

    ans_read_init()

    + +
    ans_read_init(struct AnsDecoder *const ans, const uint8_t *const buf,
+                       int offset) {
+  x = buf[offset - 1] >> 6
+  If (x == 0) {
+    ans->buf_offset = offset - 1;
+    ans->state = buf[offset - 1] & 0x3F;
+  } else if (x == 1) {
+    ans->buf_offset = offset - 2;
+    ans->state = mem_get_le16(buf + offset - 2) & 0x3FFF;
+  } else if (x == 2) {
+    ans->buf_offset = offset - 3;
+    ans->state = mem_get_le24(buf + offset - 3) & 0x3FFFFF;
+  } else if (x == 3) {
+   // x == 3 implies this byte is a superframe marker
+    return 1;
+  }
+  ans->state += l_base;
+}
+
    +
    + +

    int rabs_desc_read()

    + +
    int rabs_desc_read(struct AnsDecoder *ans, AnsP8 p0) {
+  AnsP8 p = ans_p8_precision - p0;
+  if (ans->state < l_base) {
+    ans->state = ans->state * io_base + ans->buf[--ans->buf_offset];
+  }
+  x = ans->state;
+  quot = x / ans_p8_precision;
+  rem = x % ans_p8_precision;
+  xn = quot * p;
+  val = rem < p;
+  if (val) {
+    ans->state = xn + rem;
+  } else {
+    ans->state = x - xn - p;
+  }
+  return val;
+}
+
    +
    + +

    rans_read_init()

    + +
    rans_read_init(UI8 *buf, int offset) {
+  ans_.buf = buf;
+  x = buf[offset - 1] >> 6
+  If (x == 0) {
+    ans_.buf_offset = offset - 1;
+    ans_.state = buf[offset - 1] & 0x3F;
+  } else if (x == 1) {
+    ans_.buf_offset = offset - 2;
+    ans_.state = mem_get_le16(buf + offset - 2) & 0x3FFF;
+  } else if (x == 2) {
+    ans_.buf_offset = offset - 3;
+    ans_.state = mem_get_le24(buf + offset - 3) & 0x3FFFFF;
+  } else if (x == 3) {
+    ans_.buf_offset = offset - 4;
+    ans_.state = mem_get_le32(buf + offset - 4) & 0x3FFFFFFF;
+  }
+  ans_.state += l_rans_base;
+}
+
    +
    + +

    rans_build_look_up_table()

    + +
    rans_build_look_up_table() {
+  cum_prob = 0
+  act_prob = 0
+  for (i = 0; i < num_symbols; ++i) {
+    probability_table_[i].prob = token_probs[i];
+    probability_table_[i].cum_prob = cum_prob;
+    cum_prob += token_probs[i];
+    for (j = act_prob; j < cum_prob; ++j) {
+      Lut_table_[j] = i
+    }
+    act_prob = cum_prob
+}
+
    +
    + +

    rans_read()

    + +
    rans_read() {
+  while (ans_.state < l_rans_base) {
+    ans_.state = ans_.state * io_base + ans_.buf[--ans_.buf_offset];
+  }
+  quo = ans_.state / rans_precision;
+  rem = ans_.state % rans_precision;
+  sym = fetch_sym()
+  ans_.state = quo * sym.prob + rem - sym.cum_prob;
+  return sym.val;
+}
+
    +
    + +

    fetch_sym()

    + +
    fetch_sym() {
+  symbol = lut_table[rem]
+  out->val = symbol
+  out->prob = probability_table_[symbol].prob;
+  out->cum_prob = probability_table_[symbol].cum_prob;
+}
+
    +
    + +

    Rans Bit Decoder

    + +

    RansBitDecoder_StartDecoding()

    + +
    RansBitDecoder_StartDecoding(DecoderBuffer *source_buffer) {
+  prob_zero_                                                                 UI8
+  size                                                                       UI32
+  buffer_                                                                    size * UI8
+  ans_read_init(&ans_decoder_, buffer_, size)
+}
+
    +
    + +

    DecodeNextBit()

    + +
    DecodeNextBit() {
+  uint8_t bit = rabs_desc_read(&ans_decoder_, prob_zero_);
+  return bit > 0;
+}
+
    +
    + +

    Core Functions

    + +

    DecodeVarint

    + +
    DecodeVarint<IT>() {
+  If (std::is_unsigned<IT>::value) {
+    in                                                                       UI8
+    If (in & (1 << 7)) {
+      out = DecodeVarint<IT>()
+      out = (out << 7) | (in & ((1 << 7) - 1))
+    } else {
+      typename std::make_unsigned<IT>::type UIT;
+      out = DecodeVarint<UIT>()
+      out = ConvertSymbolToSignedInt(out)
+    }
+    return out;
+}
+
    +
    + +

    ConvertSymbolToSignedInt()

    + +
    ConvertSymbolToSignedInt() {
+  abs_val = val >> 1
+  If (val & 1 == 0) {
+    return abs_val
+  } else {
+    signed_val = -abs_val - 1
+  }
+  return signed_val
+}
+
    +
    + +

    Sequential Decoder

    + +

    decode_connectivity()

    + +
    decode_connectivity() {
+  num_faces                                                       I32
+  num_points                                                      I32
+  connectivity _method                                            UI8
+  If (connectivity _method == 0) {
+    // TODO
+  } else {
+    loop num_faces {
+      If (num_points < 256) {
+        face[]                                                    UI8
+      } else if (num_points < (1 << 16)) {
+        face[]                                                    UI16
+      } else {
+        face[]                                                    UI32
+      }
+    }
+  }
+}
+
    +
    + + + + + + diff --git a/docs/_site/spec/mesh.decoder.html b/docs/_site/spec/mesh.decoder.html new file mode 100644 index 0000000..d4d0d2a --- /dev/null +++ b/docs/_site/spec/mesh.decoder.html @@ -0,0 +1,11 @@ +

    Mesh Decoder

    + +

    DecodeConnectivityData()

    + +
    +DecodeConnectivityData() Type + InitializeDecoder() + DecodeConnectivity() +} + +
    diff --git a/docs/_site/spec/mesh.decoder.md b/docs/_site/spec/mesh.decoder.md new file mode 100644 index 0000000..c283bea --- /dev/null +++ b/docs/_site/spec/mesh.decoder.md @@ -0,0 +1,11 @@ +## Mesh Decoder + +### DecodeConnectivityData() + +
    +DecodeConnectivityData() Type + InitializeDecoder() + DecodeConnectivity() +} + +
    diff --git a/docs/assets/css/pygments/README.md b/docs/assets/css/pygments/README.md new file mode 100644 index 0000000..83c205a --- /dev/null +++ b/docs/assets/css/pygments/README.md @@ -0,0 +1,23 @@ +# jekyll-pygments-themes + +A set of CSS theme files for Pygments (Python-based code highlighting tool) +created from the original built-in Pygments styles, ready for use with Jekyll. + +## Theme Previews and Custom Theme Builder +- + +## Using Themes Without Jekyll +If you want to use the themes with something other than Jekyll, you may need to +remove or change the CSS style prefix of `.highlight`. + +## Links + +- [Jekyll](http://jekyllrb.com/) ([direct link to code highlighting documentation](http://jekyllrb.com/docs/templates/#code-snippet-highlighting)) +- [Pygments](http://pygments.org) + +## Hacking + +If you want to hack on the site, check out the [gh-pages](https://github.com/jwarby/jekyll-pygments-themes/tree/gh-pages) branch. + +## Acknowledgements +Forked from [richleland/pygments-css](https://github.com/richleland/pygments-css). diff --git a/docs/assets/css/pygments/UNLICENSE.txt b/docs/assets/css/pygments/UNLICENSE.txt new file mode 100644 index 0000000..cf1ab25 --- /dev/null +++ b/docs/assets/css/pygments/UNLICENSE.txt @@ -0,0 +1,24 @@ +This is free and unencumbered software released into the public domain. + +Anyone is free to copy, modify, publish, use, compile, sell, or +distribute this software, either in source code form or as a compiled +binary, for any purpose, commercial or non-commercial, and by any +means. + +In jurisdictions that recognize copyright laws, the author or authors +of this software dedicate any and all copyright interest in the +software to the public domain. We make this dedication for the benefit +of the public at large and to the detriment of our heirs and +successors. We intend this dedication to be an overt act of +relinquishment in perpetuity of all present and future rights to this +software under copyright law. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, +EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF +MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. +IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR +OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, +ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR +OTHER DEALINGS IN THE SOFTWARE. + +For more information, please refer to diff --git a/docs/assets/css/pygments/autumn.css b/docs/assets/css/pygments/autumn.css new file mode 100644 index 0000000..a5f3d4c --- /dev/null +++ b/docs/assets/css/pygments/autumn.css @@ -0,0 +1,58 @@ +.highlight .hll { background-color: #ffffcc } +.highlight .c { color: #aaaaaa; font-style: italic } /* Comment */ +.highlight .err { color: #F00000; background-color: #F0A0A0 } /* Error */ +.highlight .k { color: #0000aa } /* Keyword */ +.highlight .cm { color: #aaaaaa; 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The conversion is done while the +HTML page loads, and should work with Firefox and other browsers that can +render MathML. + +Just add the next line to your HTML page with this file in the same folder: + + + +Version 2.2 Mar 3, 2014. +Latest version at https://github.com/mathjax/asciimathml +If you use it on a webpage, please send the URL to jipsen@chapman.edu + +Copyright (c) 2014 Peter Jipsen and other ASCIIMathML.js contributors + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ +var asciimath = {}; + +(function(){ +var mathcolor = "blue"; // change it to "" (to inherit) or another color +var mathfontsize = "1em"; // change to e.g. 1.2em for larger math +var mathfontfamily = "serif"; // change to "" to inherit (works in IE) + // or another family (e.g. "arial") +var automathrecognize = false; // writing "amath" on page makes this true +var checkForMathML = true; // check if browser can display MathML +var notifyIfNoMathML = true; // display note at top if no MathML capability +var alertIfNoMathML = false; // show alert box if no MathML capability +var translateOnLoad = true; // set to false to do call translators from js +var translateASCIIMath = true; // false to preserve `..` +var displaystyle = true; // puts limits above and below large operators +var showasciiformulaonhover = true; // helps students learn ASCIIMath +var decimalsign = "."; // change to "," if you like, beware of `(1,2)`! +var AMdelimiter1 = "`", AMescape1 = "\\\\`"; // can use other characters +var AMdocumentId = "wikitext" // PmWiki element containing math (default=body) +var fixphi = true; //false to return to legacy phi/varphi mapping + +/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++*/ + +var isIE = (navigator.appName.slice(0,9)=="Microsoft"); +var noMathML = false, translated = false; + +if (isIE) { // add MathPlayer info to IE webpages + document.write(""); + document.write(""); +} + +// Add a stylesheet, replacing any previous custom stylesheet (adapted from TW) +function setStylesheet(s) { + var id = "AMMLcustomStyleSheet"; + var n = document.getElementById(id); + if(document.createStyleSheet) { + // Test for IE's non-standard createStyleSheet method + if(n) + n.parentNode.removeChild(n); + // This failed without the   + document.getElementsByTagName("head")[0].insertAdjacentHTML("beforeEnd"," "); + } else { + if(n) { + n.replaceChild(document.createTextNode(s),n.firstChild); + } else { + n = document.createElement("style"); + n.type = "text/css"; + n.id = id; + n.appendChild(document.createTextNode(s)); + document.getElementsByTagName("head")[0].appendChild(n); + } + } +} + +setStylesheet("#AMMLcloseDiv \{font-size:0.8em; padding-top:1em; color:#014\}\n#AMMLwarningBox \{position:absolute; width:100%; top:0; left:0; z-index:200; text-align:center; font-size:1em; font-weight:bold; padding:0.5em 0 0.5em 0; color:#ffc; background:#c30\}"); + +function init(){ + var msg, warnings = new Array(); + if (document.getElementById==null){ + alert("This webpage requires a recent browser such as Mozilla Firefox"); + return null; + } + if (checkForMathML && (msg = checkMathML())) warnings.push(msg); + if (warnings.length>0) displayWarnings(warnings); + if (!noMathML) initSymbols(); + return true; +} + +function checkMathML(){ + if (navigator.appName.slice(0,8)=="Netscape") + if (navigator.appVersion.slice(0,1)>="5") noMathML = null; + else noMathML = true; + else if (navigator.appName.slice(0,9)=="Microsoft") + try { + var ActiveX = new ActiveXObject("MathPlayer.Factory.1"); + noMathML = null; + } catch (e) { + noMathML = true; + } + else if (navigator.appName.slice(0,5)=="Opera") + if (navigator.appVersion.slice(0,3)>="9.5") noMathML = null; + else noMathML = true; +//noMathML = true; //uncomment to check + if (noMathML && notifyIfNoMathML) { + var msg = "To view the ASCIIMathML notation use Internet Explorer + MathPlayer or Mozilla Firefox 2.0 or later."; + if (alertIfNoMathML) + alert(msg); + else return msg; + } +} + +function hideWarning(){ + var body = document.getElementsByTagName("body")[0]; + body.removeChild(document.getElementById('AMMLwarningBox')); + body.onclick = null; +} + +function displayWarnings(warnings) { + var i, frag, nd = createElementXHTML("div"); + var body = document.getElementsByTagName("body")[0]; + body.onclick=hideWarning; + nd.id = 'AMMLwarningBox'; + for (i=0; i<", tag:"mo", output:"\u22C9", tex:"ltimes", ttype:CONST}, +{input:"><|", tag:"mo", output:"\u22CA", tex:"rtimes", ttype:CONST}, +{input:"|><|", tag:"mo", output:"\u22C8", tex:"bowtie", ttype:CONST}, +{input:"-:", tag:"mo", output:"\u00F7", tex:"div", ttype:CONST}, +{input:"divide", tag:"mo", output:"-:", tex:null, ttype:DEFINITION}, +{input:"@", tag:"mo", output:"\u2218", tex:"circ", ttype:CONST}, +{input:"o+", tag:"mo", output:"\u2295", tex:"oplus", ttype:CONST}, +{input:"ox", tag:"mo", output:"\u2297", tex:"otimes", ttype:CONST}, +{input:"o.", tag:"mo", output:"\u2299", tex:"odot", ttype:CONST}, +{input:"sum", tag:"mo", output:"\u2211", tex:null, ttype:UNDEROVER}, +{input:"prod", tag:"mo", output:"\u220F", tex:null, ttype:UNDEROVER}, +{input:"^^", tag:"mo", output:"\u2227", tex:"wedge", ttype:CONST}, +{input:"^^^", tag:"mo", output:"\u22C0", tex:"bigwedge", ttype:UNDEROVER}, +{input:"vv", tag:"mo", output:"\u2228", tex:"vee", ttype:CONST}, +{input:"vvv", tag:"mo", output:"\u22C1", tex:"bigvee", ttype:UNDEROVER}, +{input:"nn", tag:"mo", output:"\u2229", tex:"cap", ttype:CONST}, +{input:"nnn", tag:"mo", output:"\u22C2", tex:"bigcap", ttype:UNDEROVER}, +{input:"uu", tag:"mo", output:"\u222A", tex:"cup", ttype:CONST}, +{input:"uuu", tag:"mo", output:"\u22C3", tex:"bigcup", ttype:UNDEROVER}, + +//binary relation symbols +{input:"!=", tag:"mo", output:"\u2260", tex:"ne", ttype:CONST}, +{input:":=", tag:"mo", output:":=", tex:null, ttype:CONST}, +{input:"lt", tag:"mo", output:"<", tex:null, ttype:CONST}, +{input:"<=", tag:"mo", output:"\u2264", tex:"le", ttype:CONST}, +{input:"lt=", tag:"mo", output:"\u2264", tex:"leq", ttype:CONST}, +{input:"gt", tag:"mo", output:">", tex:null, ttype:CONST}, +{input:">=", tag:"mo", output:"\u2265", tex:"ge", ttype:CONST}, +{input:"gt=", tag:"mo", output:"\u2265", tex:"geq", ttype:CONST}, +{input:"-<", tag:"mo", output:"\u227A", tex:"prec", ttype:CONST}, +{input:"-lt", tag:"mo", output:"\u227A", tex:null, ttype:CONST}, +{input:">-", tag:"mo", output:"\u227B", tex:"succ", ttype:CONST}, +{input:"-<=", tag:"mo", output:"\u2AAF", tex:"preceq", ttype:CONST}, +{input:">-=", tag:"mo", output:"\u2AB0", tex:"succeq", ttype:CONST}, +{input:"in", tag:"mo", output:"\u2208", tex:null, ttype:CONST}, +{input:"!in", tag:"mo", output:"\u2209", tex:"notin", ttype:CONST}, +{input:"sub", tag:"mo", output:"\u2282", tex:"subset", ttype:CONST}, +{input:"sup", tag:"mo", output:"\u2283", tex:"supset", ttype:CONST}, +{input:"sube", tag:"mo", output:"\u2286", tex:"subseteq", ttype:CONST}, +{input:"supe", tag:"mo", output:"\u2287", tex:"supseteq", ttype:CONST}, +{input:"-=", tag:"mo", output:"\u2261", tex:"equiv", ttype:CONST}, +{input:"~=", tag:"mo", output:"\u2245", tex:"cong", ttype:CONST}, +{input:"~~", tag:"mo", output:"\u2248", tex:"approx", ttype:CONST}, +{input:"prop", tag:"mo", output:"\u221D", tex:"propto", ttype:CONST}, + +//logical symbols +{input:"and", tag:"mtext", output:"and", tex:null, ttype:SPACE}, +{input:"or", tag:"mtext", output:"or", tex:null, ttype:SPACE}, +{input:"not", tag:"mo", output:"\u00AC", tex:"neg", ttype:CONST}, +{input:"=>", tag:"mo", output:"\u21D2", tex:"implies", ttype:CONST}, +{input:"if", tag:"mo", output:"if", tex:null, ttype:SPACE}, +{input:"<=>", tag:"mo", output:"\u21D4", tex:"iff", ttype:CONST}, +{input:"AA", tag:"mo", output:"\u2200", tex:"forall", ttype:CONST}, +{input:"EE", tag:"mo", output:"\u2203", tex:"exists", ttype:CONST}, +{input:"_|_", tag:"mo", output:"\u22A5", tex:"bot", ttype:CONST}, +{input:"TT", tag:"mo", output:"\u22A4", tex:"top", ttype:CONST}, +{input:"|--", tag:"mo", output:"\u22A2", tex:"vdash", ttype:CONST}, +{input:"|==", tag:"mo", output:"\u22A8", tex:"models", ttype:CONST}, + +//grouping brackets +{input:"(", tag:"mo", output:"(", tex:null, ttype:LEFTBRACKET}, +{input:")", tag:"mo", output:")", tex:null, ttype:RIGHTBRACKET}, +{input:"[", tag:"mo", output:"[", tex:null, ttype:LEFTBRACKET}, +{input:"]", tag:"mo", output:"]", tex:null, ttype:RIGHTBRACKET}, +{input:"{", tag:"mo", output:"{", tex:null, ttype:LEFTBRACKET}, +{input:"}", tag:"mo", output:"}", tex:null, ttype:RIGHTBRACKET}, +{input:"|", tag:"mo", output:"|", tex:null, ttype:LEFTRIGHT}, +//{input:"||", tag:"mo", output:"||", tex:null, ttype:LEFTRIGHT}, +{input:"(:", tag:"mo", output:"\u2329", tex:"langle", ttype:LEFTBRACKET}, +{input:":)", tag:"mo", output:"\u232A", tex:"rangle", ttype:RIGHTBRACKET}, +{input:"<<", tag:"mo", output:"\u2329", tex:null, ttype:LEFTBRACKET}, +{input:">>", tag:"mo", output:"\u232A", tex:null, ttype:RIGHTBRACKET}, +{input:"{:", tag:"mo", output:"{:", tex:null, ttype:LEFTBRACKET, invisible:true}, +{input:":}", tag:"mo", output:":}", tex:null, ttype:RIGHTBRACKET, invisible:true}, + +//miscellaneous symbols +{input:"int", tag:"mo", output:"\u222B", tex:null, ttype:CONST}, +{input:"dx", tag:"mi", output:"{:d x:}", tex:null, ttype:DEFINITION}, +{input:"dy", tag:"mi", output:"{:d y:}", tex:null, ttype:DEFINITION}, +{input:"dz", tag:"mi", output:"{:d z:}", tex:null, ttype:DEFINITION}, +{input:"dt", tag:"mi", output:"{:d t:}", tex:null, ttype:DEFINITION}, +{input:"oint", tag:"mo", output:"\u222E", tex:null, ttype:CONST}, +{input:"del", tag:"mo", output:"\u2202", tex:"partial", ttype:CONST}, +{input:"grad", tag:"mo", output:"\u2207", tex:"nabla", ttype:CONST}, +{input:"+-", tag:"mo", output:"\u00B1", tex:"pm", ttype:CONST}, +{input:"O/", tag:"mo", output:"\u2205", tex:"emptyset", ttype:CONST}, +{input:"oo", tag:"mo", output:"\u221E", tex:"infty", ttype:CONST}, +{input:"aleph", tag:"mo", output:"\u2135", tex:null, ttype:CONST}, +{input:"...", tag:"mo", output:"...", tex:"ldots", ttype:CONST}, +{input:":.", tag:"mo", output:"\u2234", tex:"therefore", ttype:CONST}, +{input:":'", tag:"mo", output:"\u2235", tex:"because", ttype:CONST}, +{input:"/_", tag:"mo", output:"\u2220", tex:"angle", ttype:CONST}, +{input:"/_\\", tag:"mo", output:"\u25B3", tex:"triangle", ttype:CONST}, +{input:"'", tag:"mo", output:"\u2032", tex:"prime", ttype:CONST}, +{input:"tilde", tag:"mover", output:"~", tex:null, ttype:UNARY, acc:true}, +{input:"\\ ", tag:"mo", output:"\u00A0", tex:null, ttype:CONST}, +{input:"frown", tag:"mo", output:"\u2322", tex:null, ttype:CONST}, +{input:"quad", tag:"mo", output:"\u00A0\u00A0", tex:null, ttype:CONST}, +{input:"qquad", tag:"mo", output:"\u00A0\u00A0\u00A0\u00A0", tex:null, ttype:CONST}, +{input:"cdots", tag:"mo", output:"\u22EF", tex:null, ttype:CONST}, +{input:"vdots", tag:"mo", output:"\u22EE", tex:null, ttype:CONST}, +{input:"ddots", tag:"mo", output:"\u22F1", tex:null, ttype:CONST}, +{input:"diamond", tag:"mo", output:"\u22C4", tex:null, ttype:CONST}, +{input:"square", tag:"mo", output:"\u25A1", tex:null, ttype:CONST}, +{input:"|__", tag:"mo", output:"\u230A", tex:"lfloor", ttype:CONST}, +{input:"__|", tag:"mo", output:"\u230B", tex:"rfloor", ttype:CONST}, +{input:"|~", tag:"mo", output:"\u2308", tex:"lceiling", ttype:CONST}, +{input:"~|", tag:"mo", output:"\u2309", tex:"rceiling", ttype:CONST}, +{input:"CC", tag:"mo", output:"\u2102", tex:null, ttype:CONST}, +{input:"NN", tag:"mo", output:"\u2115", tex:null, ttype:CONST}, +{input:"QQ", tag:"mo", output:"\u211A", tex:null, ttype:CONST}, +{input:"RR", tag:"mo", output:"\u211D", tex:null, ttype:CONST}, +{input:"ZZ", tag:"mo", output:"\u2124", tex:null, ttype:CONST}, +{input:"f", tag:"mi", output:"f", tex:null, ttype:UNARY, func:true}, +{input:"g", tag:"mi", output:"g", tex:null, ttype:UNARY, func:true}, + +//standard functions +{input:"lim", tag:"mo", output:"lim", tex:null, ttype:UNDEROVER}, +{input:"Lim", tag:"mo", output:"Lim", tex:null, ttype:UNDEROVER}, +{input:"sin", tag:"mo", output:"sin", tex:null, ttype:UNARY, func:true}, +{input:"cos", tag:"mo", output:"cos", tex:null, ttype:UNARY, func:true}, +{input:"tan", tag:"mo", output:"tan", tex:null, ttype:UNARY, func:true}, +{input:"sinh", tag:"mo", output:"sinh", tex:null, ttype:UNARY, func:true}, +{input:"cosh", tag:"mo", output:"cosh", tex:null, ttype:UNARY, func:true}, +{input:"tanh", tag:"mo", output:"tanh", tex:null, ttype:UNARY, func:true}, +{input:"cot", tag:"mo", output:"cot", tex:null, ttype:UNARY, func:true}, +{input:"sec", tag:"mo", output:"sec", tex:null, ttype:UNARY, func:true}, +{input:"csc", tag:"mo", output:"csc", tex:null, ttype:UNARY, func:true}, +{input:"arcsin", tag:"mo", output:"arcsin", tex:null, ttype:UNARY, func:true}, +{input:"arccos", tag:"mo", output:"arccos", tex:null, ttype:UNARY, func:true}, +{input:"arctan", tag:"mo", output:"arctan", tex:null, ttype:UNARY, func:true}, +{input:"coth", tag:"mo", output:"coth", tex:null, ttype:UNARY, func:true}, +{input:"sech", tag:"mo", output:"sech", tex:null, ttype:UNARY, func:true}, +{input:"csch", tag:"mo", output:"csch", tex:null, ttype:UNARY, func:true}, +{input:"exp", tag:"mo", output:"exp", tex:null, ttype:UNARY, func:true}, +{input:"abs", tag:"mo", output:"abs", tex:null, ttype:UNARY, rewriteleftright:["|","|"]}, +{input:"norm", tag:"mo", output:"norm", tex:null, ttype:UNARY, rewriteleftright:["\u2225","\u2225"]}, +{input:"floor", tag:"mo", output:"floor", tex:null, ttype:UNARY, rewriteleftright:["\u230A","\u230B"]}, +{input:"ceil", tag:"mo", output:"ceil", tex:null, ttype:UNARY, rewriteleftright:["\u2308","\u2309"]}, +{input:"log", tag:"mo", output:"log", tex:null, ttype:UNARY, func:true}, +{input:"ln", tag:"mo", output:"ln", tex:null, ttype:UNARY, func:true}, +{input:"det", tag:"mo", output:"det", tex:null, ttype:UNARY, func:true}, +{input:"dim", tag:"mo", output:"dim", tex:null, ttype:CONST}, +{input:"mod", tag:"mo", output:"mod", tex:null, ttype:CONST}, +{input:"gcd", tag:"mo", output:"gcd", tex:null, ttype:UNARY, func:true}, +{input:"lcm", tag:"mo", output:"lcm", tex:null, ttype:UNARY, func:true}, +{input:"lub", tag:"mo", output:"lub", tex:null, ttype:CONST}, +{input:"glb", tag:"mo", output:"glb", tex:null, ttype:CONST}, +{input:"min", tag:"mo", output:"min", tex:null, ttype:UNDEROVER}, +{input:"max", tag:"mo", output:"max", tex:null, ttype:UNDEROVER}, + +//arrows +{input:"uarr", tag:"mo", output:"\u2191", tex:"uparrow", ttype:CONST}, +{input:"darr", tag:"mo", output:"\u2193", tex:"downarrow", ttype:CONST}, +{input:"rarr", tag:"mo", output:"\u2192", tex:"rightarrow", ttype:CONST}, +{input:"->", tag:"mo", output:"\u2192", tex:"to", ttype:CONST}, +{input:">->", tag:"mo", output:"\u21A3", tex:"rightarrowtail", ttype:CONST}, +{input:"->>", tag:"mo", output:"\u21A0", tex:"twoheadrightarrow", ttype:CONST}, +{input:">->>", tag:"mo", output:"\u2916", tex:"twoheadrightarrowtail", ttype:CONST}, +{input:"|->", tag:"mo", output:"\u21A6", tex:"mapsto", ttype:CONST}, +{input:"larr", tag:"mo", output:"\u2190", tex:"leftarrow", ttype:CONST}, +{input:"harr", tag:"mo", output:"\u2194", tex:"leftrightarrow", ttype:CONST}, +{input:"rArr", tag:"mo", output:"\u21D2", tex:"Rightarrow", ttype:CONST}, +{input:"lArr", tag:"mo", output:"\u21D0", tex:"Leftarrow", ttype:CONST}, +{input:"hArr", tag:"mo", output:"\u21D4", tex:"Leftrightarrow", ttype:CONST}, +//commands with argument +{input:"sqrt", tag:"msqrt", output:"sqrt", tex:null, ttype:UNARY}, +{input:"root", tag:"mroot", output:"root", tex:null, ttype:BINARY}, +{input:"frac", tag:"mfrac", output:"/", tex:null, ttype:BINARY}, +{input:"/", tag:"mfrac", output:"/", tex:null, ttype:INFIX}, +{input:"stackrel", tag:"mover", output:"stackrel", tex:null, ttype:BINARY}, +{input:"overset", tag:"mover", output:"stackrel", tex:null, ttype:BINARY}, +{input:"underset", tag:"munder", output:"stackrel", tex:null, ttype:BINARY}, +{input:"_", tag:"msub", output:"_", tex:null, ttype:INFIX}, +{input:"^", tag:"msup", output:"^", tex:null, ttype:INFIX}, +{input:"hat", tag:"mover", output:"\u005E", tex:null, ttype:UNARY, acc:true}, +{input:"bar", tag:"mover", output:"\u00AF", tex:"overline", ttype:UNARY, acc:true}, +{input:"vec", tag:"mover", output:"\u2192", tex:null, ttype:UNARY, acc:true}, +{input:"dot", tag:"mover", output:".", tex:null, ttype:UNARY, acc:true}, +{input:"ddot", tag:"mover", output:"..", tex:null, ttype:UNARY, acc:true}, +{input:"ul", tag:"munder", output:"\u0332", tex:"underline", ttype:UNARY, acc:true}, +{input:"ubrace", tag:"munder", output:"\u23DF", tex:"underbrace", ttype:UNARYUNDEROVER, acc:true}, +{input:"obrace", tag:"mover", output:"\u23DE", tex:"overbrace", ttype:UNARYUNDEROVER, acc:true}, +{input:"text", tag:"mtext", output:"text", tex:null, ttype:TEXT}, +{input:"mbox", tag:"mtext", output:"mbox", tex:null, ttype:TEXT}, +{input:"color", tag:"mstyle", ttype:BINARY}, +{input:"cancel", tag:"menclose", output:"cancel", tex:null, ttype:UNARY}, +AMquote, +{input:"bb", tag:"mstyle", atname:"mathvariant", atval:"bold", output:"bb", tex:null, ttype:UNARY}, +{input:"mathbf", tag:"mstyle", atname:"mathvariant", atval:"bold", output:"mathbf", tex:null, ttype:UNARY}, +{input:"sf", tag:"mstyle", atname:"mathvariant", atval:"sans-serif", output:"sf", tex:null, ttype:UNARY}, +{input:"mathsf", tag:"mstyle", atname:"mathvariant", atval:"sans-serif", output:"mathsf", tex:null, ttype:UNARY}, +{input:"bbb", tag:"mstyle", atname:"mathvariant", atval:"double-struck", output:"bbb", tex:null, ttype:UNARY, codes:AMbbb}, +{input:"mathbb", tag:"mstyle", atname:"mathvariant", atval:"double-struck", output:"mathbb", tex:null, ttype:UNARY, codes:AMbbb}, +{input:"cc", tag:"mstyle", atname:"mathvariant", atval:"script", output:"cc", tex:null, ttype:UNARY, codes:AMcal}, +{input:"mathcal", tag:"mstyle", atname:"mathvariant", atval:"script", output:"mathcal", tex:null, ttype:UNARY, codes:AMcal}, +{input:"tt", tag:"mstyle", atname:"mathvariant", atval:"monospace", output:"tt", tex:null, ttype:UNARY}, +{input:"mathtt", tag:"mstyle", atname:"mathvariant", atval:"monospace", output:"mathtt", tex:null, ttype:UNARY}, +{input:"fr", tag:"mstyle", atname:"mathvariant", atval:"fraktur", output:"fr", tex:null, ttype:UNARY, codes:AMfrk}, +{input:"mathfrak", tag:"mstyle", atname:"mathvariant", atval:"fraktur", output:"mathfrak", tex:null, ttype:UNARY, codes:AMfrk} +]; + +function compareNames(s1,s2) { + if (s1.input > s2.input) return 1 + else return -1; +} + +var AMnames = []; //list of input symbols + +function initSymbols() { + var i; + var symlen = AMsymbols.length; + for (i=0; i=n where str appears or would be inserted +// assumes arr is sorted + if (n==0) { + var h,m; + n = -1; + h = arr.length; + while (n+1> 1; + if (arr[m]=str +} + +function AMgetSymbol(str) { +//return maximal initial substring of str that appears in names +//return null if there is none + var k = 0; //new pos + var j = 0; //old pos + var mk; //match pos + var st; + var tagst; + var match = ""; + var more = true; + for (var i=1; i<=str.length && more; i++) { + st = str.slice(0,i); //initial substring of length i + j = k; + k = position(AMnames, st, j); + if (k=AMnames[k]; + } + AMpreviousSymbol=AMcurrentSymbol; + if (match!=""){ + AMcurrentSymbol=AMsymbols[mk].ttype; + return AMsymbols[mk]; + } +// if str[0] is a digit or - return maxsubstring of digits.digits + AMcurrentSymbol=CONST; + k = 1; + st = str.slice(0,1); + var integ = true; + while ("0"<=st && st<="9" && k<=str.length) { + st = str.slice(k,k+1); + k++; + } + if (st == decimalsign) { + st = str.slice(k,k+1); + if ("0"<=st && st<="9") { + integ = false; + k++; + while ("0"<=st && st<="9" && k<=str.length) { + st = str.slice(k,k+1); + k++; + } + } + } + if ((integ && k>1) || k>2) { + st = str.slice(0,k-1); + tagst = "mn"; + } else { + k = 2; + st = str.slice(0,1); //take 1 character + tagst = (("A">st || st>"Z") && ("a">st || st>"z")?"mo":"mi"); + } + if (st=="-" && AMpreviousSymbol==INFIX) { + AMcurrentSymbol = INFIX; //trick "/" into recognizing "-" on second parse + return {input:st, tag:tagst, output:st, ttype:UNARY, func:true}; + } + return {input:st, tag:tagst, output:st, ttype:CONST}; +} + +function AMremoveBrackets(node) { + var st; + if (!node.hasChildNodes()) { return; } + if (node.firstChild.hasChildNodes() && (node.nodeName=="mrow" || node.nodeName=="M:MROW")) { + st = node.firstChild.firstChild.nodeValue; + if (st=="(" || st=="[" || st=="{") node.removeChild(node.firstChild); + } + if (node.lastChild.hasChildNodes() && (node.nodeName=="mrow" || node.nodeName=="M:MROW")) { + st = node.lastChild.firstChild.nodeValue; + if (st==")" || st=="]" || st=="}") node.removeChild(node.lastChild); + } +} + +/*Parsing ASCII math expressions with the following grammar +v ::= [A-Za-z] | greek letters | numbers | other constant symbols +u ::= sqrt | text | bb | other unary symbols for font commands +b ::= frac | root | stackrel binary symbols +l ::= ( | [ | { | (: | {: left brackets +r ::= ) | ] | } | :) | :} right brackets +S ::= v | lEr | uS | bSS Simple expression +I ::= S_S | S^S | S_S^S | S Intermediate expression +E ::= IE | I/I Expression +Each terminal symbol is translated into a corresponding mathml node.*/ + +var AMnestingDepth,AMpreviousSymbol,AMcurrentSymbol; + +function AMparseSexpr(str) { //parses str and returns [node,tailstr] + var symbol, node, result, i, st,// rightvert = false, + newFrag = document.createDocumentFragment(); + str = AMremoveCharsAndBlanks(str,0); + symbol = AMgetSymbol(str); //either a token or a bracket or empty + if (symbol == null || symbol.ttype == RIGHTBRACKET && AMnestingDepth > 0) { + return [null,str]; + } + if (symbol.ttype == DEFINITION) { + str = symbol.output+AMremoveCharsAndBlanks(str,symbol.input.length); + symbol = AMgetSymbol(str); + } + switch (symbol.ttype) { case UNDEROVER: + case CONST: + str = AMremoveCharsAndBlanks(str,symbol.input.length); + return [createMmlNode(symbol.tag, //its a constant + document.createTextNode(symbol.output)),str]; + case LEFTBRACKET: //read (expr+) + AMnestingDepth++; + str = AMremoveCharsAndBlanks(str,symbol.input.length); + result = AMparseExpr(str,true); + AMnestingDepth--; + if (typeof symbol.invisible == "boolean" && symbol.invisible) + node = createMmlNode("mrow",result[0]); + else { + node = createMmlNode("mo",document.createTextNode(symbol.output)); + node = createMmlNode("mrow",node); + node.appendChild(result[0]); + } + return [node,result[1]]; + case TEXT: + if (symbol!=AMquote) str = AMremoveCharsAndBlanks(str,symbol.input.length); + if (str.charAt(0)=="{") i=str.indexOf("}"); + else if (str.charAt(0)=="(") i=str.indexOf(")"); + else if (str.charAt(0)=="[") i=str.indexOf("]"); + else if (symbol==AMquote) i=str.slice(1).indexOf("\"")+1; + else i = 0; + if (i==-1) i = str.length; + st = str.slice(1,i); + if (st.charAt(0) == " ") { + node = createMmlNode("mspace"); + node.setAttribute("width","1ex"); + newFrag.appendChild(node); + } + newFrag.appendChild( + createMmlNode(symbol.tag,document.createTextNode(st))); + if (st.charAt(st.length-1) == " ") { + node = createMmlNode("mspace"); + node.setAttribute("width","1ex"); + newFrag.appendChild(node); + } + str = AMremoveCharsAndBlanks(str,i+1); + return [createMmlNode("mrow",newFrag),str]; + case UNARYUNDEROVER: + case UNARY: + str = AMremoveCharsAndBlanks(str,symbol.input.length); + result = AMparseSexpr(str); + if (result[0]==null) return [createMmlNode(symbol.tag, + document.createTextNode(symbol.output)),str]; + if (typeof symbol.func == "boolean" && symbol.func) { // functions hack + st = str.charAt(0); + if (st=="^" || st=="_" || st=="/" || st=="|" || st=="," || + (symbol.input.length==1 && symbol.input.match(/\w/) && st!="(")) { + return [createMmlNode(symbol.tag, + document.createTextNode(symbol.output)),str]; + } else { + node = createMmlNode("mrow", + createMmlNode(symbol.tag,document.createTextNode(symbol.output))); + node.appendChild(result[0]); + return [node,result[1]]; + } + } + AMremoveBrackets(result[0]); + if (symbol.input == "sqrt") { // sqrt + return [createMmlNode(symbol.tag,result[0]),result[1]]; + } else if (typeof symbol.rewriteleftright != "undefined") { // abs, floor, ceil + node = createMmlNode("mrow", createMmlNode("mo",document.createTextNode(symbol.rewriteleftright[0]))); + node.appendChild(result[0]); + node.appendChild(createMmlNode("mo",document.createTextNode(symbol.rewriteleftright[1]))); + return [node,result[1]]; + } else if (symbol.input == "cancel") { // cancel + node = createMmlNode(symbol.tag,result[0]); + node.setAttribute("notation","updiagonalstrike"); + return [node,result[1]]; + } else if (typeof symbol.acc == "boolean" && symbol.acc) { // accent + node = createMmlNode(symbol.tag,result[0]); + node.appendChild(createMmlNode("mo",document.createTextNode(symbol.output))); + return [node,result[1]]; + } else { // font change command + if (!isIE && typeof symbol.codes != "undefined") { + for (i=0; i64 && st.charCodeAt(j)<91) + newst = newst + symbol.codes[st.charCodeAt(j)-65]; + else if (st.charCodeAt(j)>96 && st.charCodeAt(j)<123) + newst = newst + symbol.codes[st.charCodeAt(j)-71]; + else newst = newst + st.charAt(j); + if (result[0].nodeName=="mi") + result[0]=createMmlNode("mo"). + appendChild(document.createTextNode(newst)); + else result[0].replaceChild(createMmlNode("mo"). + appendChild(document.createTextNode(newst)), + result[0].childNodes[i]); + } + } + node = createMmlNode(symbol.tag,result[0]); + node.setAttribute(symbol.atname,symbol.atval); + return [node,result[1]]; + } + case BINARY: + str = AMremoveCharsAndBlanks(str,symbol.input.length); + result = AMparseSexpr(str); + if (result[0]==null) return [createMmlNode("mo", + document.createTextNode(symbol.input)),str]; + AMremoveBrackets(result[0]); + var result2 = AMparseSexpr(result[1]); + if (result2[0]==null) return [createMmlNode("mo", + document.createTextNode(symbol.input)),str]; + AMremoveBrackets(result2[0]); + if (symbol.input=="color") { + if (str.charAt(0)=="{") i=str.indexOf("}"); + else if (str.charAt(0)=="(") i=str.indexOf(")"); + else if (str.charAt(0)=="[") i=str.indexOf("]"); + st = str.slice(1,i); + node = createMmlNode(symbol.tag,result2[0]); + node.setAttribute("mathcolor",st); + return [node,result2[1]]; + } + if (symbol.input=="root" || symbol.output=="stackrel") + newFrag.appendChild(result2[0]); + newFrag.appendChild(result[0]); + if (symbol.input=="frac") newFrag.appendChild(result2[0]); + return [createMmlNode(symbol.tag,newFrag),result2[1]]; + case INFIX: + str = AMremoveCharsAndBlanks(str,symbol.input.length); + return [createMmlNode("mo",document.createTextNode(symbol.output)),str]; + case SPACE: + str = AMremoveCharsAndBlanks(str,symbol.input.length); + node = createMmlNode("mspace"); + node.setAttribute("width","1ex"); + newFrag.appendChild(node); + newFrag.appendChild( + createMmlNode(symbol.tag,document.createTextNode(symbol.output))); + node = createMmlNode("mspace"); + node.setAttribute("width","1ex"); + newFrag.appendChild(node); + return [createMmlNode("mrow",newFrag),str]; + case LEFTRIGHT: +// if (rightvert) return [null,str]; else rightvert = true; + AMnestingDepth++; + str = AMremoveCharsAndBlanks(str,symbol.input.length); + result = AMparseExpr(str,false); + AMnestingDepth--; + st = ""; + if (result[0].lastChild!=null) + st = result[0].lastChild.firstChild.nodeValue; + if (st == "|") { // its an absolute value subterm + node = createMmlNode("mo",document.createTextNode(symbol.output)); + node = createMmlNode("mrow",node); + node.appendChild(result[0]); + return [node,result[1]]; + } else { // the "|" is a \mid so use unicode 2223 (divides) for spacing + node = createMmlNode("mo",document.createTextNode("\u2223")); + node = createMmlNode("mrow",node); + return [node,str]; + } + default: +//alert("default"); + str = AMremoveCharsAndBlanks(str,symbol.input.length); + return [createMmlNode(symbol.tag, //its a constant + document.createTextNode(symbol.output)),str]; + } +} + +function AMparseIexpr(str) { + var symbol, sym1, sym2, node, result, underover; + str = AMremoveCharsAndBlanks(str,0); + sym1 = AMgetSymbol(str); + result = AMparseSexpr(str); + node = result[0]; + str = result[1]; + symbol = AMgetSymbol(str); + if (symbol.ttype == INFIX && symbol.input != "/") { + str = AMremoveCharsAndBlanks(str,symbol.input.length); +// if (symbol.input == "/") result = AMparseIexpr(str); else ... + result = AMparseSexpr(str); + if (result[0] == null) // show box in place of missing argument + result[0] = createMmlNode("mo",document.createTextNode("\u25A1")); + else AMremoveBrackets(result[0]); + str = result[1]; +// if (symbol.input == "/") AMremoveBrackets(node); + underover = (sym1.ttype == UNDEROVER || sym1.ttype == UNARYUNDEROVER); + if (symbol.input == "_") { + sym2 = AMgetSymbol(str); + if (sym2.input == "^") { + str = AMremoveCharsAndBlanks(str,sym2.input.length); + var res2 = AMparseSexpr(str); + AMremoveBrackets(res2[0]); + str = res2[1]; + node = createMmlNode((underover?"munderover":"msubsup"),node); + node.appendChild(result[0]); + node.appendChild(res2[0]); + node = createMmlNode("mrow",node); // so sum does not stretch + } else { + node = createMmlNode((underover?"munder":"msub"),node); + node.appendChild(result[0]); + } + } else if (symbol.input == "^" && underover) { + node = createMmlNode("mover",node); + node.appendChild(result[0]); + } else { + node = createMmlNode(symbol.tag,node); + node.appendChild(result[0]); + } + if (typeof sym1.func != 'undefined' && sym1.func) { + sym2 = AMgetSymbol(str); + if (sym2.ttype != INFIX && sym2.ttype != RIGHTBRACKET) { + result = AMparseIexpr(str); + node = createMmlNode("mrow",node); + node.appendChild(result[0]); + str = result[1]; + } + } + } + return [node,str]; +} + +function AMparseExpr(str,rightbracket) { + var symbol, node, result, i, + newFrag = document.createDocumentFragment(); + do { + str = AMremoveCharsAndBlanks(str,0); + result = AMparseIexpr(str); + node = result[0]; + str = result[1]; + symbol = AMgetSymbol(str); + if (symbol.ttype == INFIX && symbol.input == "/") { + str = AMremoveCharsAndBlanks(str,symbol.input.length); + result = AMparseIexpr(str); + if (result[0] == null) // show box in place of missing argument + result[0] = createMmlNode("mo",document.createTextNode("\u25A1")); + else AMremoveBrackets(result[0]); + str = result[1]; + AMremoveBrackets(node); + node = createMmlNode(symbol.tag,node); + node.appendChild(result[0]); + newFrag.appendChild(node); + symbol = AMgetSymbol(str); + } + else if (node!=undefined) newFrag.appendChild(node); + } while ((symbol.ttype != RIGHTBRACKET && + (symbol.ttype != LEFTRIGHT || rightbracket) + || AMnestingDepth == 0) && symbol!=null && symbol.output!=""); + if (symbol.ttype == RIGHTBRACKET || symbol.ttype == LEFTRIGHT) { +// if (AMnestingDepth > 0) AMnestingDepth--; + var len = newFrag.childNodes.length; + if (len>0 && newFrag.childNodes[len-1].nodeName == "mrow" + && newFrag.childNodes[len-1].lastChild + && newFrag.childNodes[len-1].lastChild.firstChild ) { //matrix + //removed to allow row vectors: //&& len>1 && + //newFrag.childNodes[len-2].nodeName == "mo" && + //newFrag.childNodes[len-2].firstChild.nodeValue == "," + var right = newFrag.childNodes[len-1].lastChild.firstChild.nodeValue; + if (right==")" || right=="]") { + var left = newFrag.childNodes[len-1].firstChild.firstChild.nodeValue; + if (left=="(" && right==")" && symbol.output != "}" || + left=="[" && right=="]") { + var pos = []; // positions of commas + var matrix = true; + var m = newFrag.childNodes.length; + for (i=0; matrix && i1) matrix = pos[i].length == pos[i-2].length; + } + matrix = matrix && (pos.length>1 || pos[0].length>0); + if (matrix) { + var row, frag, n, k, table = document.createDocumentFragment(); + for (i=0; i(-,-,...,-,-) + n = node.childNodes.length; + k = 0; + node.removeChild(node.firstChild); //remove ( + for (j=1; j2) { + newFrag.removeChild(newFrag.firstChild); //remove ) + newFrag.removeChild(newFrag.firstChild); //remove , + } + table.appendChild(createMmlNode("mtr",row)); + } + node = createMmlNode("mtable",table); + if (typeof symbol.invisible == "boolean" && symbol.invisible) node.setAttribute("columnalign","left"); + newFrag.replaceChild(node,newFrag.firstChild); + } + } + } + } + str = AMremoveCharsAndBlanks(str,symbol.input.length); + if (typeof symbol.invisible != "boolean" || !symbol.invisible) { + node = createMmlNode("mo",document.createTextNode(symbol.output)); + newFrag.appendChild(node); + } + } + return [newFrag,str]; +} + +function parseMath(str,latex) { + var frag, node; + AMnestingDepth = 0; + //some basic cleanup for dealing with stuff editors like TinyMCE adds + str = str.replace(/ /g,""); + str = str.replace(/>/g,">"); + str = str.replace(/</g,"<"); + str = str.replace(/(Sin|Cos|Tan|Arcsin|Arccos|Arctan|Sinh|Cosh|Tanh|Cot|Sec|Csc|Log|Ln|Abs)/g, function(v) { return v.toLowerCase(); }); + frag = AMparseExpr(str.replace(/^\s+/g,""),false)[0]; + node = createMmlNode("mstyle",frag); + if (mathcolor != "") node.setAttribute("mathcolor",mathcolor); + if (mathfontfamily != "") node.setAttribute("fontfamily",mathfontfamily); + if (displaystyle) node.setAttribute("displaystyle","true"); + node = createMmlNode("math",node); + if (showasciiformulaonhover) //fixed by djhsu so newline + node.setAttribute("title",str.replace(/\s+/g," "));//does not show in Gecko + return node; +} + +function strarr2docFrag(arr, linebreaks, latex) { + var newFrag=document.createDocumentFragment(); + var expr = false; + for (var i=0; i,\\|!:;'~]|\\.(?!(?:\x20|$))|"+ambigAMtoken+englishAMtoken+simpleAMtoken; + var re = new RegExp("(^|\\s)((("+token+")\\s?)(("+token+secondenglishAMtoken+")\\s?)+)([,.?]?(?=\\s|$))","g"); + str = str.replace(re," `$2`$7"); + var arr = str.split(AMdelimiter1); + var re1 = new RegExp("(^|\\s)([b-zB-HJ-Z+*<>]|"+texcommand+ambigAMtoken+simpleAMtoken+")(\\s|\\n|$)","g"); + var re2 = new RegExp("(^|\\s)([a-z]|"+texcommand+ambigAMtoken+simpleAMtoken+")([,.])","g"); // removed |\d+ for now + for (i=0; i1 || mtch) { + if (!noMathML) { + frg = strarr2docFrag(arr,n.nodeType==8,latex); + var len = frg.childNodes.length; + n.parentNode.replaceChild(frg,n); + return len-1; + } else return 0; + } + } + } else return 0; + } else if (n.nodeName!="math") { + for (i=0; igCniQG(FtL6Gs5B_neCZ(TfY`b|RTNM52 zdiKpdwZcQ~7mEsDhn76cy7!~&2WOp&^AfZB;V%MNme!?Y#60boeXX>=A@{HZV z0THs_c~1!Xgxlj1Apy_dBrv!67o(n=Xs9wQgAJ43f3eNqEZYZS4nNr@Ra$a1`!9jB zYm`O%Y+3mB?+O{p59!y)+WC!I_z#Kt-#@-1JOEsLHq3fg9pYX*hOy|@4bSv(tb3oZ z+@G+dmTO#FQ?rM?yOtu6;^Qz&p&(K9jG({?Ri0UCQMjj9j(i-X0G849v_~6d!W^ovkkFtV#d)W2HRr2@g)8NhK;gA zGtpLkbX;oh3Z|{kX4*Gu5BgBaQiVTuhN+tr!h_AKaRVhLkv}%^CZorF&Nm{yqxTTW z>v^?NN9&!~Z8}_6ej+Q5wj0TvbvamJ($;qgEHBJI`(@?jn8U|`4McLBBy3{a2bIh! zR?_}*fU3Gt>3-mG`q_u`jwmVNLw`I4BK3wsQE+2a%eZ4W?uZjU4}TaWSdCTP<=xcL}_qFkD}ccU9MXX_7hQm^a*Cz zNxm)VVXT2H@65I3-2OdRrjOaAG;U2EZD!r}BG9cF&N!Z@rv=8OBhR?@qlkR@)K0Ch z$7Fg~;*mlpjs3P=m+?w>u~}9UC%5u8K{HP`15?%9+rIb>LS!lez%(VpauK5<9}I%c z^sxo6Xe+o)j@Nc?_n-3(eL1+)lI`HZ5_6bW2bY`{YVs^Q8{_LBxs`^_`B2xf&%i;$CL 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Cocca + +jQuery.fn.extend({ + autoTOC: function(options) { + + var monitoredDOMElements = new Array(); + var windowHeight = $(window).height(); + + // Make sure we keep tabs on the window height as the user changes the browser window dimensions + $(window).on("resize", function() { + windowHeight = $(window).height(); + }); + + // Bind monitor to scroll event to keep an eye which heading element is in the top quarter of the page + $(window).on("scroll",function() { + topOfWindow = $(window).scrollTop(); + bottomOfWindow = $(window).scrollTop() + (windowHeight * .25); + for(element in monitoredDOMElements) { + if( monitoredDOMElements[element].offset > topOfWindow && + monitoredDOMElements[element].offset < bottomOfWindow) { + $(monitoredDOMElements[element].anchor).addClass("selected"); + $(".autotoc li").not(monitoredDOMElements[element].anchor).removeClass("selected"); + break; + } + } + }); + + + // Default settings + var settings = $.extend({ + toc: "#toc" + },options); + + var toc = $('
      '); + + $(settings.toc).append(toc); + + return this.each(function() { + tocEntry = $('
    • ' + $(this).html() + '
      • '); + tocEntry.data("parentHeading",this); + tocEntry.on("click", function() { + $('html, body').animate({ + scrollTop: $($(this).data("parentHeading")).offset().top - (windowHeight * .2) + }, 750 ); + }); + + $(".autotoc").append(tocEntry); + + monitoredDOMElements.push({ + offset: $(this).offset().top, + anchor: tocEntry + }); + }); + } +}); \ No newline at end of file diff --git a/docs/spec/00.00.00.title.md b/docs/spec/00.00.00.title.md new file mode 100644 index 0000000..fffa716 --- /dev/null +++ b/docs/spec/00.00.00.title.md @@ -0,0 +1,3 @@ + +# {{ page.title }} +{:.no_toc} diff --git a/docs/spec/00.00.01.version.md b/docs/spec/00.00.01.version.md new file mode 100644 index 0000000..1796d22 --- /dev/null +++ b/docs/spec/00.00.01.version.md @@ -0,0 +1,3 @@ + +_{{ page.version }}_ +_{{ page.version_date }}_ diff --git a/docs/spec/00.00.02.authors.md b/docs/spec/00.00.02.authors.md new file mode 100644 index 0000000..2cf7726 --- /dev/null +++ b/docs/spec/00.00.02.authors.md @@ -0,0 +1,4 @@ + +_Frank Galligan, Google +\[author] +\[author]_ diff --git a/docs/spec/00.00.03.last.modified.md b/docs/spec/00.00.03.last.modified.md new file mode 100644 index 0000000..092b08c --- /dev/null +++ b/docs/spec/00.00.03.last.modified.md @@ -0,0 +1,2 @@ + +_Last modified: {{ site.time }}_ diff --git a/docs/spec/00.00.04.abstract.md b/docs/spec/00.00.04.abstract.md new file mode 100644 index 0000000..2fc4a46 --- /dev/null +++ b/docs/spec/00.00.04.abstract.md @@ -0,0 +1,6 @@ + +## Abstract +{:.no_toc .nocount} + +This document defines the bitstream format and decoding process for the +Draco 3D Data Compression scheme. diff --git a/docs/spec/00.00.05.toc.md b/docs/spec/00.00.05.toc.md new file mode 100644 index 0000000..9ce6baf --- /dev/null +++ b/docs/spec/00.00.05.toc.md @@ -0,0 +1,5 @@ + +**Contents** + +* TOC +{:toc} diff --git a/docs/spec/01.00.00.scope.md b/docs/spec/01.00.00.scope.md new file mode 100644 index 0000000..d17eff9 --- /dev/null +++ b/docs/spec/01.00.00.scope.md @@ -0,0 +1,5 @@ + +## Scope + +This document specifies the open-source Draco #D Data Compression bitstream +format and decoding process. diff --git a/docs/spec/02.00.00.terms.md b/docs/spec/02.00.00.terms.md new file mode 100644 index 0000000..cfca0dd --- /dev/null +++ b/docs/spec/02.00.00.terms.md @@ -0,0 +1,8 @@ + +## Terms and Definitions + +For the purposes of this document, the following terms and definitions apply: + +| Term | Definition | +| ------- | ---------------- | +| | | diff --git a/docs/spec/03.00.00.symbols.md b/docs/spec/03.00.00.symbols.md new file mode 100644 index 0000000..58b42cf --- /dev/null +++ b/docs/spec/03.00.00.symbols.md @@ -0,0 +1,18 @@ + +## Symbols (and abbreviated terms) + +**DCT:** Discrete Cosine Transform + +FIXME + +The specification makes use of a number of constant integers. Constants that +relate to the semantics of a particular syntax element are defined in section +7. + +Additional constants are defined below: + + +| Symbol name | Value | Description | +| ------------------------ |:-----:| ----------- | +| `SYMBOL` | | + diff --git a/docs/spec/04.00.00.conventions.md b/docs/spec/04.00.00.conventions.md new file mode 100644 index 0000000..767de7c --- /dev/null +++ b/docs/spec/04.00.00.conventions.md @@ -0,0 +1,26 @@ +## Conventions + + * When bit reading is finished it will always pad the read to the current + byte. + + * Draco encoded mesh files are comprised of three main sections. This first + section is the header. The second section contains the connectivity data. + The third section contains the attribute data. The header must be decoded + first, then the connectivity section, and then the attribute section. + + * The Connectivity section is composed of the following sections in order: + + * Connectivity header + + * EdgeBreaker symbol buffer + + * Start face buffer + + * EdgeBreaker valence header + + * Context data for the valence prediction + + * Hole and Split data + + * The hole and split data must be decoded before the EdgeBreaker symbols are + decoded. diff --git a/docs/spec/draco.decoder.md b/docs/spec/draco.decoder.md new file mode 100644 index 0000000..99c8096 --- /dev/null +++ b/docs/spec/draco.decoder.md @@ -0,0 +1,45 @@ +## Draco Decoder + +### Decode() + +
      +Decode() { Type + DecodeHeader() + DecodeConnectivityData() + DecodeAttributeData()} + +
      + + +### DecodeHeader() + +
      +DecodeHeader() { Type + draco_string UI8[5] + major_version UI8 + minor_version UI8 + encoder_type UI8 + encoder_method UI8 + flags +} + +
      + + +### DecodeAttributeData() + +
      +DecodeAttributeData() { Type + num_attributes_decoders UI8 + for (i = 0; i < num_attributes_decoders; ++i) { + CreateAttributesDecoder(i); + } + for (auto &att_dec : attributes_decoders_) { + att_dec->Initialize(this, point_cloud_) + } + for (i = 0; i < num_attributes_decoders; ++i) { + attributes_decoders_[i]->DecodeAttributesDecoderData(buffer_) + } + DecodeAllAttributes() + OnAttributesDecoded() +
      diff --git a/docs/spec/edgebreaker.decoder.md b/docs/spec/edgebreaker.decoder.md new file mode 100644 index 0000000..495901e --- /dev/null +++ b/docs/spec/edgebreaker.decoder.md @@ -0,0 +1,1674 @@ +## EdgeBreaker Decoder + +### InitializeDecoder() + +
      +InitializeDecoder() { Type + edgebreaker_decoder_type UI8 +} + +
      + + +### DecodeConnectivity() + +
      +DecodeConnectivity() { Type + num_new_verts UI32 + num_encoded_vertices UI32 + num_faces UI32 + num_attribute_data I8 + num_encoded_symbols UI32 + num_encoded_split_symbols UI32 + encoded_connectivity_size UI32 + // file pointer must be set to current position + encoded_connectivity_size + hole_and_split_bytes = DecodeHoleAndTopologySplitEvents() + // file pointer must be set to old current position + EdgeBreakerTraversalValence_Start() + DecodeConnectivity(num_symbols) + if (attribute_data_.size() > 0) { + for (ci = 0; ci < corner_table_->num_corners(); ci += 3) { + DecodeAttributeConnectivitiesOnFace(ci) + } + } + for (i = 0; i < corner_table_->num_vertices(); ++i) { + if (is_vert_hole_[i]) { + corner_table_->UpdateVertexToCornerMap(i); + } + } + // Decode attribute connectivity. + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + attribute_data_[i].connectivity_data.InitEmpty(corner_table_.get()); + for (int32_t c : attribute_data_[i].attribute_seam_corners) { + attribute_data_[i].connectivity_data.AddSeamEdge(c); + } + attribute_data_[i].connectivity_data.RecomputeVertices(nullptr, nullptr); + } + // Preallocate vertex to value mapping + AssignPointsToCorners() +} + +
      + + +### AssignPointsToCorners() + +
      +AssignPointsToCorners() { Type + decoder_->mesh()->SetNumFaces(corner_table_->num_faces()); + if (attribute_data_.size() == 0) { + for (f = 0; f < decoder_->mesh()->num_faces(); ++f) { + for (c = 0; c < 3; ++c) { + vert_id = corner_table_->Vertex(3 * f + c); + if (point_id == -1) + point_id = num_points++; + face[c] = point_id; + } + decoder_->mesh()->SetFace(f, face); + } + decoder_->point_cloud()->set_num_points(num_points); + Return true; + } + for (v = 0; v < corner_table_->num_vertices(); ++v) { + c = corner_table_->LeftMostCorner(v); + if (c < 0) + continue; + deduplication_first_corner = c; + if (!is_vert_hole_[v]) { + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + if (!attribute_data_[i].connectivity_data.IsCornerOnSeam(c)) + continue; + vert_id = attribute_data_[i].connectivity_data.Vertex(c); + act_c = corner_table_->SwingRight(c); + seam_found = false; + while (act_c != c) { + if (attribute_data_[i].connectivity_data.Vertex(act_c) != vert_id) { + deduplication_first_corner = act_c; + seam_found = true; + break; + } + act_c = corner_table_->SwingRight(act_c); + } + if (seam_found) + break; + } + } + c = deduplication_first_corner; + corner_to_point_map[c] = point_to_corner_map.size(); + point_to_corner_map.push_back(c); + prev_c = c; + c = corner_table_->SwingRight(c); + while (c >= 0 && c != deduplication_first_corner) { + attribute_seam = false; + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + if (attribute_data_[i].connectivity_data.Vertex(c) != + attribute_data_[i].connectivity_data.Vertex(prev_c)) { + attribute_seam = true; + break; + } + } + if (attribute_seam) { + corner_to_point_map[c] = point_to_corner_map.size(); + point_to_corner_map.push_back(c); + } else { + corner_to_point_map[c] = corner_to_point_map[prev_c]; + } + prev_c = c; + c = corner_table_->SwingRight(c); + } + } + for (f = 0; f < decoder_->mesh()->num_faces(); ++f) { + for (c = 0; c < 3; ++c) { + face[c] = corner_to_point_map[3 * f + c]; + } + decoder_->mesh()->SetFace(f, face); + } + decoder_->point_cloud()->set_num_points(point_to_corner_map.size()); +} + +
      + + +### DecodeConnectivity() + +
      +DecodeConnectivity(num_symbols) { Type + for (i = 0; i < num_symbols; ++i) { + symbol = TraversalValence_DecodeSymbol() + corner = 3 * num_faces++ + if (symbol == TOPOLOGY_C) { + vertex_x = UpdateCornerTableForSymbolC() + is_vert_hole_[vertex_x] = false; + } else if (symbol == TOPOLOGY_R || symbol == TOPOLOGY_L) { + UpdateCornerTableForSymbolLR() + check_topology_split = true; + } else if (symbol == TOPOLOGY_S) { + HandleSymbolS() + } else if (symbol == TOPOLOGY_E) { + UpdateCornerTableForSymbolE() + check_topology_split = true; + } + active_corner_stack.back() = corner; + traversal_decoder_.NewActiveCornerReached(corner); + if (check_topology_split) { + encoder_symbol_id = num_symbols - symbol_id - 1; + while (true) { + split = IsTopologySplit(encoder_symbol_id, &split_edge, + &encoder_split_symbol_id); + if (!split) { + break; + } + act_top_corner = corner; + if (split_edge == RIGHT_FACE_EDGE) { + new_active_corner = corner_table_->Next(act_top_corner); + } else { + new_active_corner = corner_table_->Previous(act_top_corner); + } + decoder_split_symbol_id = num_symbols - encoder_split_symbol_id - 1; + topology_split_active_corners[decoder_split_symbol_id] = + new_active_corner; + } + } + } + while (active_corner_stack.size() > 0) { + corner = active_corner_stack.pop_back(); + interior_face = traversal_decoder_.DecodeStartFaceConfiguration(); + if (interior_face == true) { + UpdateCornerTableForInteriorFace() + for (ci = 0; ci < 3; ++ci) { + is_vert_hole_[corner_table_->Vertex(new_corner + ci)] = false; + } + init_face_configurations_.push_back(true); + init_corners_.push_back(new_corner); + } else { + init_face_configurations_.push_back(false); + init_corners_.push_back(corner); + } + } + Return num_vertices; +} + +
      + + +### UpdateCornerTableForSymbolC() + +
      +UpdateCornerTableForSymbolC(corner) { Type + corner_a = active_corner_stack.back(); + corner_b = corner_table_->Previous(corner_a); + while (corner_table_->Opposite(corner_b) >= 0) { + corner_b = corner_table_->Previous(corner_table_->Opposite(corner_b)); + } + SetOppositeCorners(corner_a, corner + 1); + SetOppositeCorners(corner_b, corner + 2); + vertex_x = corner_table_->Vertex(corner_table_->Next(corner_a)); + corner_table_->MapCornerToVertex(corner, vertex_x); + corner_table_->MapCornerToVertex( + corner + 1, corner_table_->Vertex(corner_table_->Next(corner_b))); + corner_table_->MapCornerToVertex( + corner + 2, corner_table_->Vertex(corner_table_->Previous(corner_a))); + return vertex_x; +} + +
      + + + +### UpdateCornerTableForSymbolLR() + +
      +UpdateCornerTableForSymbolLR(corner, symbol) { Type + if (symbol == TOPOLOGY_R) { + opp_corner = corner + 2; + } else { + opp_corner = corner + 1; + } + SetOppositeCorners(opp_corner, corner_a); + corner_table_->MapCornerToVertex(opp_corner,num_vertices++); + corner_table_->MapCornerToVertex( + corner_table_->Next(opp_corner), + corner_table_->Vertex(corner_table_->Previous(corner_a))); + corner_table_->MapCornerToVertex( + corner_table_->Previous(opp_corner), + corner_table_->Vertex(corner_table_->Next(corner_a))); +} + +
      + + +### HandleSymbolS() + +
      +HandleSymbolS(corner) { Type + corner_b = active_corner_stack.pop_back(); + it = topology_split_active_corners.find(symbol_id); + if (it != topology_split_active_corners.end()) { + active_corner_stack.push_back(it->second); + } + corner_a = active_corner_stack.back(); + SetOppositeCorners(corner_a, corner + 2); + SetOppositeCorners(corner_b, corner + 1); + vertex_p = corner_table_->Vertex(corner_table_->Previous(corner_a)); + corner_table_->MapCornerToVertex(corner, vertex_p); + corner_table_->MapCornerToVertex( + corner + 1, corner_table_->Vertex(corner_table_->Next(corner_a))); + corner_table_->MapCornerToVertex(corner + 2, + corner_table_->Vertex(corner_table_->Previous(corner_b))); + corner_n = corner_table_->Next(corner_b); + vertex_n = corner_table_->Vertex(corner_n); + traversal_decoder_.MergeVertices(vertex_p, vertex_n); + // TraversalValence_MergeVertices + while (corner_n >= 0) { + corner_table_->MapCornerToVertex(corner_n, vertex_p); + corner_n = corner_table_->SwingLeft(corner_n); + } + corner_table_->MakeVertexIsolated(vertex_n); +} + +
      + + +### UpdateCornerTableForSymbolE() + +
      +UpdateCornerTableForSymbolE() { Type + corner_table_->MapCornerToVertex(corner, num_vertices++); + corner_table_->MapCornerToVertex(corner + 1, num_vertices++); + corner_table_->MapCornerToVertex(corner + 2, num_vertices++); +} + +
      + + +### UpdateCornerTableForInteriorFace() + +
      +UpdateCornerTableForInteriorFace() { Type + corner_b = corner_table_->Previous(corner); + while (corner_table_->Opposite(corner_b) >= 0) { + corner_b = corner_table_->Previous(corner_table_->Opposite(corner_b)); + } + corner_c = corner_table_->Next(corner); + while (corner_table_->Opposite(corner_c) >= 0) { + corner_c = corner_table_->Next(corner_table_->Opposite(corner_c)); + } + face(num_faces++); + corner_table_->MapCornerToVertex( + new_corner, corner_table_->Vertex(corner_table_->Next(corner_b))); + corner_table_->MapCornerToVertex( + new_corner + 1, corner_table_->Vertex(corner_table_->Next(corner_c))); + corner_table_->MapCornerToVertex( + new_corner + 2, corner_table_->Vertex(corner_table_->Next(corner))); +} + +
      + + +### IsTopologySplit() + +
      +IsTopologySplit(encoder_symbol_id, *out_face_edge, Type + + *out_encoder_split_symbol_id) { + if (topology_split_data_.size() == 0) + return false; + if (topology_split_data_.back().source_symbol_id != encoder_symbol_id) + return false; + *out_face_edge = topology_split_data_.back().source_edge; + *out_encoder_split_symbol_id = + topology_split_data_.back().split_symbol_id; + topology_split_data_.pop_back(); + return true; +} + +
      + + +### DecodeAttributeConnectivitiesOnFace() + +
      +DecodeAttributeConnectivitiesOnFace(corner) { Type + corners[3] = {corner, corner_table_->Next(corner), + corner_table_->Previous(corner)} + for (c = 0; c < 3; ++c) { + opp_corner = corner_table_->Opposite(corners[c]); + if (opp_corner < 0) { + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + attribute_data_[i].attribute_seam_corners.push_back(corners[c]); + } + continue + } + for (uint32_t i = 0; i < attribute_data_.size(); ++i) { + bool is_seam = traversal_decoder_.DecodeAttributeSeam(i); + if (is_seam) { + attribute_data_[i].attribute_seam_corners.push_back(corners[c]); + } + } + } +} + +
      + + +### SetOppositeCorners() + +
      +SetOppositeCorners(corner_0, corner_1) { Type + corner_table_->SetOppositeCorner(corner_0, corner_1); + corner_table_->SetOppositeCorner(corner_1, corner_0); +} + +
      + + +## EdgeBreaker Hole and Topology Split Events + +### DecodeHoleAndTopologySplitEvents() + +FIXME: Escaping angle brackets + +
      +DecodeHoleAndTopologySplitEvents() { Type + num_topologoy_splits UI32 + source_symbol_id = 0 + for (i = 0; i < num_topologoy_splits; ++i) { + DecodeVarint\(&delta) + split_data[i].source_symbol_id = delta + source_symbol_id + DecodeVarint\(&delta) + split_data[i].split_symbol_id = source_symbol_id - delta + } + for (i = 0; i < num_topologoy_splits; ++i) { + split_data[i].split_edge bits1 + split_data[i].source_edge bits1 + } + num_hole_events UI32 + symbol_id = 0 + for (i = 0; i < num_hole_events; ++i) { + DecodeVarint\(&delta) + hole_data[i].symbol_id = delta + symbol_id + } + return bytes_decoded; +} + +
      + +### CreateAttributesDecoder + +FIXME: Escaping angle brackets + +
      +CreateAttributesDecoder() { Type + att_data_id I8 + decoder_type UI8 + if (att_data_id >= 0) { + attribute_data_[att_data_id].decoder_id = att_decoder_id; + } + traversal_method_encoded UI8 + if (decoder_type == MESH_VERTEX_ATTRIBUTE) { + if (att_data_id < 0) { + encoding_data = &pos_encoding_data_; + } else { + encoding_data = &attribute_data_[att_data_id].encoding_data; + attribute_data_[att_data_id].is_connectivity_used = false; + } + if (traversal_method == MESH_TRAVERSAL_DEPTH_FIRST) { + typedef EdgeBreakerTraverser\ AttTraverser; + sequencer = CreateVertexTraversalSequencer\(encoding_data); + } else if (traversal_method == MESH_TRAVERSAL_PREDICTION_DEGREE) { + typedef PredictionDegreeTraverser\ AttTraverser; + sequencer = CreateVertexTraversalSequencer\(encoding_data); + } + } else { + // TODO + } + att_controller(new SequentialAttributeDecodersController(std::move(sequencer))) + decoder_->SetAttributesDecoder(att_decoder_id, std::move(att_controller)); +} + +
      + + +## Edgebreaker Traversal Decoder + +### EdgebreakerTraversal_Start() + +
      +EdgebreakerTraversal_Start() { Type + size UI64 + symbol_buffer_ size * UI8 + size UI64 + start_face_buffer_ size * UI8 + if (num_attribute_data_ > 0) { + attribute_connectivity_decoders_ = std::unique_ptr( + new BinaryDecoder[num_attribute_data_]); + for (i = 0; i < num_attribute_data_; ++i) { + attribute_connectivity_decoders_[i].StartDecoding() + // RansBitDecoder_StartDecoding + } +} + +
      + + +### Traversal_DecodeSymbol() + +~~~~~ +Traversal_DecodeSymbol() { + symbol_buffer_.DecodeLeastSignificantBits32(1, &symbol); bits1 + if (symbol != TOPOLOGY_C) { + symbol_buffer_.DecodeLeastSignificantBits32(2, &symbol_suffix); bits2 + symbol |= (symbol_suffix << 1); + } + return symbol +} +~~~~~ + + +### DecodeAttributeSeam() + +~~~~~ +DecodeAttributeSeam(int attribute) { + return attribute_connectivity_decoders_[attribute].DecodeNextBit(); +} +~~~~~ + + +## EdgeBreaker Traversal Valence Decoder + +### EdgeBreakerTraversalValence_Start() + +~~~~~ +EdgeBreakerTraversalValence_Start(num_vertices, num_attribute_data) { + out_buffer = EdgebreakerTraversal_Start() + num_split_symbols I32 + mode == 0 I8 + num_vertices_ += num_split_symbols + vertex_valences_ init to 0 + vertex_valences_.resize(num_vertices_, 0); + min_valence_ = 2; + max_valence_ = 7; + num_unique_valences = 6 (max_valence_ - min_valence_ + 1) + for (i = 0; i < num_unique_valences; ++i) { + DecodeVarint(&num_symbols, out_buffer) + If (num_symbols > 0) { + DecodeSymbols(num_symbols, out_buffer, &context_symbols_[i]) + } + context_counters_[i] = num_symbols + } + return out_buffer; +} +~~~~~ + + + +### TraversalValence_DecodeSymbol() + +~~~~~ +TraversalValence_DecodeSymbol() { + if (active_context_ != -1) { + symbol_id = context_symbols_[active_context_] + [--context_counters_[active_context_]] + last_symbol_ = edge_breaker_symbol_to_topology_id[symbol_id] + } else { + last_symbol_ = Traversal_DecodeSymbol() + } + return last_symbol_ +} +~~~~~ + + + +### TraversalValence_NewActiveCornerReached() + +~~~~~ +TraversalValence_NewActiveCornerReached(corner) { + switch (last_symbol_) { + case TOPOLOGY_C: + case TOPOLOGY_S: + vertex_valences_[ct(next)] += 1; + vertex_valences_[ct(prev)] += 1; + break; + case TOPOLOGY_R: + vertex_valences_[corner] += 1; + vertex_valences_[ct(next)] += 1; + vertex_valences_[ct(prev)] += 2; + break; + case TOPOLOGY_L: + vertex_valences_[corner] += 1; + vertex_valences_[ct(next)] += 2; + vertex_valences_[ct(prev)] += 1; + break; + case TOPOLOGY_E: + vertex_valences_[corner] += 2; + vertex_valences_[ct(next)] += 2; + vertex_valences_[ct(prev)] += 2; + break; + } + valence = vertex_valences_[ct(next)] + valence = max(valence, min_valence_) + valence = min(valence, max_valence_) + active_context_ = (valence - min_valence_); +} +~~~~~ + + + +### TraversalValence_MergeVertices() + +~~~~~ +TraversalValence_MergeVertices(dest, source) { + vertex_valences_[dest] += vertex_valences_[source]; +} +~~~~~ + + +## Attributes Decoder + +### DecodeAttributesDecoderData() + +~~~~~ +DecodeAttributesDecoderData(buffer) { + num_attributes I32 + point_attribute_ids_.resize(num_attributes); + for (i = 0; i < num_attributes; ++i) { + att_type UI8 + data_type UI8 + components_count UI8 + normalized UI8 + custom_id UI16 + Initialize GeometryAttribute ga + att_id = pc->AddAttribute(new PointAttribute(ga)); + point_attribute_ids_[i] = att_id; +} +~~~~~ + + + +## Sequential Attributes Decoders Controller + +### DecodeAttributesDecoderData() + +~~~~~ +DecodeAttributesDecoderData(buffer) { + AttributesDecoder_DecodeAttributesDecoderData(buffer) + sequential_decoders_.resize(num_attributes()); + for (i = 0; i < num_attributes(); ++i) { + decoder_type UI8 + sequential_decoders_[i] = CreateSequentialDecoder(decoder_type); + sequential_decoders_[i]->Initialize(decoder(), GetAttributeId(i)) +} +~~~~~ + + +### DecodeAttributes() + +~~~~~ +DecodeAttributes(buffer) { + sequencer_->GenerateSequence(&point_ids_) + for (i = 0; i < num_attributes(); ++i) { + pa = decoder()->point_cloud()->attribute(GetAttributeId(i)); + sequencer_->UpdatePointToAttributeIndexMapping(pa) + } + for (i = 0; i < num_attributes(); ++i) { + sequential_decoders_[i]->Decode(point_ids_, buffer) + //SequentialAttributeDecoder_Decode() + } +} +~~~~~ + + + +### CreateSequentialDecoder() + +~~~~~ +CreateSequentialDecoder(type) { + switch (type) { + case SEQUENTIAL_ATTRIBUTE_ENCODER_GENERIC: + return new SequentialAttributeDecoder() + case SEQUENTIAL_ATTRIBUTE_ENCODER_INTEGER: + return new SequentialIntegerAttributeDecoder() + case SEQUENTIAL_ATTRIBUTE_ENCODER_QUANTIZATION: + return new SequentialQuantizationAttributeDecoder() + case SEQUENTIAL_ATTRIBUTE_ENCODER_NORMALS: + return new SequentialNormalAttributeDecoder() + } +} +~~~~~ + + +## Sequential Attribute Decoder + +~~~~~ +Initialize(...) { + // Init some members +} +~~~~~ + + +### DecodeValues() + +~~~~~ +DecodeValues(const std::vector &point_ids) { + num_values = point_ids.size(); + entry_size = attribute_->byte_stride(); + std::unique_ptr value_data_ptr(new uint8_t[entry_size]); + out_byte_pos = 0; + for (i = 0; i < num_values; ++i) { + value_data UI8 * entry_size + attribute_->buffer()->Write(out_byte_pos, value_data, entry_size); + out_byte_pos += entry_size; + } +} +~~~~~ + + +## Sequential Integer Attribute Decoder + +~~~~~ +Initialize(...) { + SequentialAttributeDecoder_Initialize() +} +~~~~~ + + +### DecodeValues() + +~~~~~ +DecodeValues(point_ids) { + prediction_scheme_method I8 + if (prediction_scheme_method != PREDICTION_NONE) { + prediction_transform_type I8 + prediction_scheme_ = CreateIntPredictionScheme(...) + } + if (prediction_scheme_) { + } + DecodeIntegerValues(point_ids) + //SequentialQuantizationAttributeDecoder_DecodeIntegerValues() + //StoreValues() + DequantizeValues(num_values) +} +~~~~~ + + +### DecodeIntegerValues() + +~~~~~ +DecodeIntegerValues(point_ids) { + compressed UI8 + if (compressed) { + DecodeSymbols(..., values_.data()) + } else { + // TODO + } + if (!prediction_scheme_->AreCorrectionsPositive()) { + ConvertSymbolsToSignedInts(...) + } + if (prediction_scheme_) { + prediction_scheme_->DecodePredictionData(buffer) + // DecodeTransformData(buffer) + if (!values_.empty()) { + prediction_scheme_->Decode(values_.data(), &values_[0], + values_.size(), num_components, point_ids.data()) + // MeshPredictionSchemeParallelogram_Decode() +} +~~~~~ + + + +## Sequential Quantization Attribute Decoder + +~~~~~ +Initialize(...) { + SequentialIntegerAttributeDecoder_Initialize() +} +~~~~~ + + +### DecodeIntegerValues() + +~~~~~ +DecodeIntegerValues(point_ids) { + // DecodeQuantizedDataInfo() + num_components = attribute()->components_count(); + for (i = 0; i < num_components; ++i) { + min_value_[i] F32 + } + max_value_dif_ F32 + quantization_bits_ UI8 + SequentialIntegerAttributeDecoder::DecodeIntegerValues() +} +~~~~~ + + +### DequantizeValues() + +~~~~~ +DequantizeValues(num_values) { + max_quantized_value = (1 << (quantization_bits_)) - 1; + num_components = attribute()->components_count(); + entry_size = sizeof(float) * num_components; + quant_val_id = 0; + out_byte_pos = 0; + for (i = 0; i < num_values; ++i) { + for (c = 0; c < num_components; ++c) { + value = dequantizer.DequantizeFloat(values()->at(quant_val_id++)); + value = value + min_value_[c]; + att_val[c] = value; + } + attribute()->buffer()->Write(out_byte_pos, att_val.get(), entry_size); + out_byte_pos += entry_size; + } +} +~~~~~ + + + +## Prediction Scheme Transform + +### ComputeOriginalValue() + +~~~~~ +ComputeOriginalValue(const DataTypeT *predicted_vals, + const CorrTypeT *corr_vals, + DataTypeT *out_original_vals, int val_id) { + for (i = 0; i < num_components_; ++i) { + out_original_vals[i] = predicted_vals[i] + corr_vals[val_id + i]; + } +} +~~~~~ + + + +## Prediction Scheme Wrap Transform + +### DecodeTransformData() + +~~~~~ +DecodeTransformData(buffer) { + min_value_ DT + max_value_ DT +} +~~~~~ + + +### ComputeOriginalValue() + +~~~~~ +ComputeOriginalValue(const DataTypeT *predicted_vals, + const CorrTypeT *corr_vals, + DataTypeT *out_original_vals, int val_id) { + clamped_vals = ClampPredictedValue(predicted_vals); + ComputeOriginalValue(clamped_vals, corr_vals, out_original_vals, val_id) + // PredictionSchemeTransform_ComputeOriginalValue() + for (i = 0; i < this->num_components(); ++i) { + if (out_original_vals[i] > max_value_) { + out_original_vals[i] -= max_dif_; + } else if (out_original_vals[i] < min_value_) { + out_original_vals[i] += max_dif_; + } +} +~~~~~ + + +### ClampPredictedValue() + +~~~~~ +ClampPredictedValue(const DataTypeT *predicted_val) { + for (i = 0; i < this->num_components(); ++i) { + clamped_value_[i] = min(predicted_val[i], max_value_) + clamped_value_[i] = max(predicted_val[i], min_value_) + } + return &clamped_value_[0]; +} +~~~~~ + + + +## Mesh Prediction Scheme Parallelogram + +### Decode() + +~~~~~ +Decode(...) { + this->transform().InitializeDecoding(num_components); + // restore the first value + this->transform().ComputeOriginalValue(pred_vals.get(), + in_corr, out_data, 0); + // PredictionSchemeWrapTransform_ComputeOriginalValue() + corner_map_size = this->mesh_data().data_to_corner_map()->size(); + for (p = 1; p < corner_map_size; ++p) { + corner_id = this->mesh_data().data_to_corner_map()->at(p); + dst_offset = p * num_components; + b= ComputeParallelogramPrediction(p, corner_id, table, + *vertex_to_data_map, out_data, + num_components, pred_vals.get()) + if (!b) { + src_offset = (p - 1) * num_components; + this->transform().ComputeOriginalValue(out_data + src_offset, in_corr, + out_data + dst_offset, dst_offset); + // PredictionSchemeWrapTransform_ComputeOriginalValue() + } else { + this->transform().ComputeOriginalValue(pred_vals.get(), in_corr, + out_data + dst_offset, dst_offset); + // PredictionSchemeWrapTransform_ComputeOriginalValue() + } + } +} +~~~~~ + + +MeshPredictionSchemeParallelogramShared + +### ComputeParallelogramPrediction() + +~~~~~ +ComputeParallelogramPrediction(...) { + oci = table->Opposite(ci); + vert_opp = vertex_to_data_map[table->Vertex(ci)]; + vert_next = vertex_to_data_map[table->Vertex(table->Next(ci))]; + vert_prev = vertex_to_data_map[table->Vertex(table->Previous(ci))]; + if (vert_opp < data_entry_id && vert_next < data_entry_id && + vert_prev < data_entry_id) { + v_opp_off = vert_opp * num_components; + v_next_off = vert_next * num_components; + v_prev_off = vert_prev * num_components; + for (c = 0; c < num_components; ++c) { + out_prediction[c] = (in_data[v_next_off + c] + in_data[v_prev_off + c]) - + in_data[v_opp_off + c]; + } + Return true; + } + return false; +} +~~~~~ + + + +## CornerTable Traversal Processor + + +### IsFaceVisited() + +~~~~~ +IsFaceVisited(corner_id) { + if (corner_id < 0) + return true + return is_face_visited_[corner_id / 3]; +} +~~~~~ + + +### MarkFaceVisited() + +~~~~~ +MarkFaceVisited(face_id) { + is_face_visited_[face_id] = true; +} +~~~~~ + + +### IsVertexVisited() + +~~~~~ +IsVertexVisited(vert_id) { + return is_vertex_visited_[vert_id]; +} +~~~~~ + + +### MarkVertexVisited() + +~~~~~ +MarkVertexVisited(vert_id) { + is_vertex_visited_[vert_id] = true; +} +~~~~~ + + +## Mesh Attribute Indices Encoding Observer + +### OnNewVertexVisited() + +~~~~~ +OnNewVertexVisited(vertex, corner) { + point_id = mesh_->face(corner / 3)[corner % 3]; + sequencer_->AddPointId(point_id); + // Keep track of visited corners. + encoding_data_->encoded_attribute_value_index_to_corner_map.push_back(corner); + encoding_data_ + ->vertex_to_encoded_attribute_value_index_map[vertex] = + encoding_data_->num_values; + encoding_data_->num_values++; +} +~~~~~ + + +## EdgeBreaker Traverser + +### TraverseFromCorner() + +~~~~~ +TraverseFromCorner(corner_id) { + if (processor_.IsFaceVisited(corner_id)) + return + corner_traversal_stack_.clear(); + corner_traversal_stack_.push_back(corner_id); + next_vert = corner_table_->Vertex(corner_table_->Next(corner_id)); + prev_vert = corner_table_->Vertex(corner_table_->Previous(corner_id)); + if (!processor_.IsVertexVisited(next_vert)) { + processor_.MarkVertexVisited(next_vert); + traversal_observer_.OnNewVertexVisited(next_vert, + corner_table_->Next(corner_id)); + } + if (!processor_.IsVertexVisited(prev_vert)) { + processor_.MarkVertexVisited(prev_vert); + traversal_observer_.OnNewVertexVisited(prev_vert, + corner_table_->Previous(corner_id)); + } + while (!corner_traversal_stack_.empty()) { + corner_id = corner_traversal_stack_.back(); + face_id =corner_id / 3; + if (processor_.IsFaceVisited(face_id)) { + corner_traversal_stack_.pop_back(); + continue + } + while(true) { + face_id = corner_id / 3; + processor_.MarkFaceVisited(face_id); + traversal_observer_.OnNewFaceVisited(face_id); + vert_id = corner_table_->Vertex(corner_id); + on_boundary = corner_table_->IsOnBoundary(vert_id); + if (!processor_.IsVertexVisited(vert_id)) { + processor_.MarkVertexVisited(vert_id); + traversal_observer_.OnNewVertexVisited(vert_id, corner_id); + if (!on_boundary) { + corner_id = corner_table_->GetRightCorner(corner_id); + continue; + } + } + // The current vertex has been already visited or it was on a boundary. + right_corner_id = corner_table_->GetRightCorner(corner_id); + left_corner_id = corner_table_->GetLeftCorner(corner_id); + right_face_id((right_corner_id < 0 ? -1 : right_corner_id / 3)); + left_face_id((left_corner_id < 0 ? -1 : left_corner_id / 3)); + if (processor_.IsFaceVisited(right_face_id)) { + if (processor_.IsFaceVisited(left_face_id)) { + corner_traversal_stack_.pop_back(); + break; // Break from while(true) loop + } else { + corner_id = left_corner_id; + } + } else { + if (processor_.IsFaceVisited(left_face_id)) { + corner_id = right_corner_id; + } else { + // Split the traversal. + corner_traversal_stack_.back() = left_corner_id; + corner_traversal_stack_.push_back(right_corner_id); + break; // Break from while(true) loop + } + } + } + } +} +~~~~~ + + +## Mesh Traversal Sequencer + +### GenerateSequenceInternal() + +~~~~~ +GenerateSequenceInternal() { + traverser_.OnTraversalStart(); + If (corner_order_) { + // TODO + } else { + int32_t num_faces = traverser_.corner_table()->num_faces(); + for (i = 0; i < num_faces; ++i) { + ProcessCorner(3 * i) + } + } + traverser_.OnTraversalEnd(); +} +~~~~~ + + +### ProcessCorner() + +~~~~~ +ProcessCorner(corner_id) { + traverser_.TraverseFromCorner(corner_id); +} +~~~~~ + + +### UpdatePointToAttributeIndexMapping() + +~~~~~ +UpdatePointToAttributeIndexMapping(PointAttribute *attribute) { + corner_table = traverser_.corner_table(); + attribute->SetExplicitMapping(mesh_->num_points()); + num_faces = mesh_->num_faces(); + num_points = mesh_->num_points(); + for (f = 0; f < num_faces; ++f) { + face = mesh_->face(f); + for (p = 0; p < 3; ++p) { + point_id = face[p]; + vert_id = corner_table->Vertex(3 * f + p); + att_entry_id( + encoding_data_ + ->vertex_to_encoded_attribute_value_index_map[vert_id]); + attribute->SetPointMapEntry(point_id, att_entry_id); + } + } +} +~~~~~ + + +PointsSequencer + +### AddPointId() + +~~~~~ +AddPointId(point_id) { + out_point_ids_->push_back(point_id); +} +~~~~~ + + + +## Corner Table + +### Opposite() + +~~~~~ +Opposite(corner) { + return opposite_corners_[corner]; +} +~~~~~ + + +### Next() + +~~~~~ +Next(corner) { + return LocalIndex(++corner) ? corner : corner - 3; +} +~~~~~ + + +### Previous() + +~~~~~ +Previous(corner) { + return LocalIndex(corner) ? corner - 1 : corner + 2; +} +~~~~~ + + +### Vertex() + +~~~~~ +Vertex(corner) { + faces_[Face(corner)][LocalIndex(corner)]; +} +~~~~~ + + +### Face() + +~~~~~ +Face(corner) { + return corner / 3; +} +~~~~~ + + +### LocalIndex() + +~~~~~ +LocalIndex(corner) { + return corner % 3; +} +~~~~~ + + +### num_vertices() + +~~~~~ +num_vertices() { + return vertex_corners_.size(); +} +~~~~~ + + +### num_corners() + +~~~~~ +num_corners() { + return faces_.size() * 3; +} +~~~~~ + + +### num_faces() + +~~~~~ +num_faces() { + return faces_.size(); +} +~~~~~ + + +### bool IsOnBoundary() + +~~~~~ +bool IsOnBoundary(vert) { + corner = LeftMostCorner(vert); + if (SwingLeft(corner) < 0) + return true; + return false; +} +~~~~~ + + + +### SwingRight() + +~~~~~ +SwingRight(corner) { + return Previous(Opposite(Previous(corner))); +} +~~~~~ + + +### SwingLeft() + +~~~~~ +SwingLeft(corner) { + return Next(Opposite(Next(corner))); +} +~~~~~ + + +### GetLeftCorner() + +~~~~~ +GetLeftCorner(corner_id) { + if (corner_id < 0) + return kInvalidCornerIndex; + return Opposite(Previous(corner_id)); +} +~~~~~ + + +### GetRightCorner() + +~~~~~ +GetRightCorner(corner_id) { + if (corner_id < 0) + return kInvalidCornerIndex; + return Opposite(Next(corner_id)); +} +~~~~~ + + +### SetOppositeCorner() + +~~~~~ +SetOppositeCorner(corner_id, pp_corner_id) { + opposite_corners_[corner_id] = opp_corner_id; +} +~~~~~ + + + +### MapCornerToVertex() + +~~~~~ +MapCornerToVertex(corner_id, vert_id) { + face = Face(corner_id); + faces_[face][LocalIndex(corner_id)] = vert_id; + if (vert_id >= 0) { + vertex_corners_[vert_id] = corner_id; + } +} +~~~~~ + + +### UpdateVertexToCornerMap() + +~~~~~ +UpdateVertexToCornerMap(vert) { + first_c = vertex_corners_[vert]; + if (first_c < 0) + return; + act_c = SwingLeft(first_c); + c = first_c; + while (act_c >= 0 && act_c != first_c) { + c = act_c; + act_c = SwingLeft(act_c); + } + if (act_c != first_c) { + vertex_corners_[vert] = c; + } +} +~~~~~ + + + +### LeftMostCorner() + +~~~~~ +LeftMostCorner(v) { + return vertex_corners_[v]; +} +~~~~~ + + +### MakeVertexIsolated() + +~~~~~ +MakeVertexIsolated(vert) { + vertex_corners_[vert] = kInvalidCornerIndex; +} +~~~~~ + + + +## Mesh Attribute Corner Table + +### bool IsCornerOnSeam() + +~~~~~ +bool IsCornerOnSeam(corner) { + return is_vertex_on_seam_[corner_table_->Vertex(corner)]; +} +~~~~~ + + +### AddSeamEdge() + +~~~~~ +AddSeamEdge(c) { + MarkSeam(c) + opp_corner = corner_table_->Opposite(c); + if (opp_corner >= 0) { + no_interior_seams_ = false; + MarkSeam(opp_corner) + } +} +~~~~~ + + +### MarkSeam() + +~~~~~ +MarkSeam(c) { + is_edge_on_seam_[c] = true; + is_vertex_on_seam_[corner_table_->Vertex(corner_table_->Next(c))] = true; + is_vertex_on_seam_[corner_table_->Vertex(corner_table_->Previous(c)) + ] = true; +} +~~~~~ + + +### RecomputeVertices() + +~~~~~ +RecomputeVertices() { + // in code RecomputeVerticesInternal(nullptr, nullptr) + num_new_vertices = 0; + for (v = 0; v < corner_table_->num_vertices(); ++v) { + c = corner_table_->LeftMostCorner(v); + if (c < 0) + continue; + first_vert_id(num_new_vertices++); + vertex_to_attribute_entry_id_map_.push_back(first_vert_id); + first_c = c; + if (is_vertex_on_seam_[v]) { + act_c = SwingLeft(first_c); + while (act_c >= 0) { + first_c = act_c; + act_c = SwingLeft(act_c); + } + } + corner_to_vertex_map_[first_c] =first_vert_id; + vertex_to_left_most_corner_map_.push_back(first_c); + act_c = corner_table_->SwingRight(first_c); + while (act_c >= 0 && act_c != first_c) { + if (is_edge_on_seam_[corner_table_->Next(act_c)]) { + // in code IsCornerOppositeToSeamEdge() + first_vert_id = AttributeValueIndex(num_new_vertices++); + vertex_to_attribute_entry_id_map_.push_back(first_vert_id); + vertex_to_left_most_corner_map_.push_back(act_c); + } + corner_to_vertex_map_[act_c] = first_vert_id; + act_c = corner_table_->SwingRight(act_c); + } + } +} +~~~~~ + + + + +## Symbol Decoding + +### DecodeSymbols() + +~~~~~ +DecodeSymbols(num_symbols, out_buffer, out_values) { + scheme UI8 + If (scheme == 0) { + DecodeTaggedSymbols<>(num_symbols, src_buffer, out_values) + } else if (scheme == 1) { + DecodeRawSymbols<>(num_symbols, src_buffer, out_values) + } +} +~~~~~ + + +### DecodeTaggedSymbols() + +~~~~~ +DecodeTaggedSymbols() { + FIXME +} +~~~~~ + + + +### DecodeRawSymbols() + +~~~~~ +DecodeRawSymbols() { + max_bit_length UI8 + DecodeRawSymbolsInternal(max_bit_length, out_values) + return symbols +} +~~~~~ + + + +### DecodeRawSymbolsInternal() + +~~~~~ +DecodeRawSymbolsInternal(max_bit_length, out_values) { + decoder = CreateRansSymbolDecoder(max_bit_length) + decoder.StartDecoding() + // RansSymbolDecoder_StartDecoding + for (i = 0; i < num_values; ++i) { + out_values[i] = decoder.DecodeSymbol() + // RansSymbolDecoder_DecodeSymbol + } +} +~~~~~ + + +### CreateRansSymbolDecoder() + +~~~~~ +CreateRansSymbolDecoder(max_bit_length) { + rans_precision_bits = (3 * max_bit_length) / 2; + rans_precision_bits = min(rans_precision_bits, 20) + rans_precision_bits = max(rans_precision_bits, 12) + rans_precision = 1 << rans_precision_bits_; + l_rans_base = rans_precision * 4; + num_symbols_ UI32 + for (i = 0; i < num_symbols_; ++i) { + prob_data UI8 + if ((prob_data & 3) == 3) { + offset = prob_data >> 2 + for (j = 0; j < offset + 1; ++j) { + probability_table_[i + j] = 0; + } + i += offset; + } else { + prob = prob_data >> 2 + for (j = 0; j < token; ++j) { + eb UI8 + prob = prob | (eb << (8 * (j + 1) - 2) + } + probability_table_[i] = prob; + } + } + rans_build_look_up_table() +} +~~~~~ + + +### RansSymbolDecoder_StartDecoding() + +~~~~~ +RansSymbolDecoder_StartDecoding() { + bytes_encoded UI64 + buffer bytes_encoded * UI8 + rans_read_init(buffer, bytes_encoded) +} +~~~~~ + + + +### RansSymbolDecoder_DecodeSymbol() + +~~~~~ +RansSymbolDecoder_DecodeSymbol() { + ans_.rans_read() +} +~~~~~ + + +## Rans Decoding + +### ans_read_init() + +~~~~~ +ans_read_init(struct AnsDecoder *const ans, const uint8_t *const buf, + int offset) { + x = buf[offset - 1] >> 6 + If (x == 0) { + ans->buf_offset = offset - 1; + ans->state = buf[offset - 1] & 0x3F; + } else if (x == 1) { + ans->buf_offset = offset - 2; + ans->state = mem_get_le16(buf + offset - 2) & 0x3FFF; + } else if (x == 2) { + ans->buf_offset = offset - 3; + ans->state = mem_get_le24(buf + offset - 3) & 0x3FFFFF; + } else if (x == 3) { + // x == 3 implies this byte is a superframe marker + return 1; + } + ans->state += l_base; +} +~~~~~ + + + +### int rabs_desc_read() + +~~~~~ +int rabs_desc_read(struct AnsDecoder *ans, AnsP8 p0) { + AnsP8 p = ans_p8_precision - p0; + if (ans->state < l_base) { + ans->state = ans->state * io_base + ans->buf[--ans->buf_offset]; + } + x = ans->state; + quot = x / ans_p8_precision; + rem = x % ans_p8_precision; + xn = quot * p; + val = rem < p; + if (val) { + ans->state = xn + rem; + } else { + ans->state = x - xn - p; + } + return val; +} +~~~~~ + + + +### rans_read_init() + +~~~~~ +rans_read_init(UI8 *buf, int offset) { + ans_.buf = buf; + x = buf[offset - 1] >> 6 + If (x == 0) { + ans_.buf_offset = offset - 1; + ans_.state = buf[offset - 1] & 0x3F; + } else if (x == 1) { + ans_.buf_offset = offset - 2; + ans_.state = mem_get_le16(buf + offset - 2) & 0x3FFF; + } else if (x == 2) { + ans_.buf_offset = offset - 3; + ans_.state = mem_get_le24(buf + offset - 3) & 0x3FFFFF; + } else if (x == 3) { + ans_.buf_offset = offset - 4; + ans_.state = mem_get_le32(buf + offset - 4) & 0x3FFFFFFF; + } + ans_.state += l_rans_base; +} +~~~~~ + + + + +### rans_build_look_up_table() + +~~~~~ +rans_build_look_up_table() { + cum_prob = 0 + act_prob = 0 + for (i = 0; i < num_symbols; ++i) { + probability_table_[i].prob = token_probs[i]; + probability_table_[i].cum_prob = cum_prob; + cum_prob += token_probs[i]; + for (j = act_prob; j < cum_prob; ++j) { + Lut_table_[j] = i + } + act_prob = cum_prob +} +~~~~~ + + + +### rans_read() + +~~~~~ +rans_read() { + while (ans_.state < l_rans_base) { + ans_.state = ans_.state * io_base + ans_.buf[--ans_.buf_offset]; + } + quo = ans_.state / rans_precision; + rem = ans_.state % rans_precision; + sym = fetch_sym() + ans_.state = quo * sym.prob + rem - sym.cum_prob; + return sym.val; +} +~~~~~ + + +### fetch_sym() + +~~~~~ +fetch_sym() { + symbol = lut_table[rem] + out->val = symbol + out->prob = probability_table_[symbol].prob; + out->cum_prob = probability_table_[symbol].cum_prob; +} +~~~~~ + + + +## Rans Bit Decoder + +### RansBitDecoder_StartDecoding() + +~~~~~ +RansBitDecoder_StartDecoding(DecoderBuffer *source_buffer) { + prob_zero_ UI8 + size UI32 + buffer_ size * UI8 + ans_read_init(&ans_decoder_, buffer_, size) +} +~~~~~ + + +### DecodeNextBit() + +~~~~~ +DecodeNextBit() { + uint8_t bit = rabs_desc_read(&ans_decoder_, prob_zero_); + return bit > 0; +} +~~~~~ + + +## Core Functions + +### DecodeVarint + +~~~~~ +DecodeVarint() { + If (std::is_unsigned::value) { + in UI8 + If (in & (1 << 7)) { + out = DecodeVarint() + out = (out << 7) | (in & ((1 << 7) - 1)) + } else { + typename std::make_unsigned::type UIT; + out = DecodeVarint() + out = ConvertSymbolToSignedInt(out) + } + return out; +} +~~~~~ + + + +### ConvertSymbolToSignedInt() + +~~~~~ +ConvertSymbolToSignedInt() { + abs_val = val >> 1 + If (val & 1 == 0) { + return abs_val + } else { + signed_val = -abs_val - 1 + } + return signed_val +} +~~~~~ + + + +Sequential Decoder + +### decode_connectivity() + +~~~~~ +decode_connectivity() { + num_faces I32 + num_points I32 + connectivity _method UI8 + If (connectivity _method == 0) { + // TODO + } else { + loop num_faces { + If (num_points < 256) { + face[] UI8 + } else if (num_points < (1 << 16)) { + face[] UI16 + } else { + face[] UI32 + } + } + } +} +~~~~~ diff --git a/docs/spec/index.md b/docs/spec/index.md new file mode 100644 index 0000000..b94da7f --- /dev/null +++ b/docs/spec/index.md @@ -0,0 +1,32 @@ +--- +layout: spec +title: Draco Bitstream Specification (Draft) +version: Version 1,2 +version_date: Released 2017-xx-xx +--- + +{% include_relative 00.00.00.title.md %} +{% include_relative 00.00.01.version.md %} +{% include_relative 00.00.02.authors.md %} +{% include_relative 00.00.03.last.modified.md %} +{% include_relative 00.00.04.abstract.md %} +{% include_relative 00.00.05.toc.md %} + +{% include_relative 01.00.00.scope.md %} + +{% include_relative 02.00.00.terms.md %} + +{% include_relative 03.00.00.symbols.md %} + +{% include_relative 04.00.00.conventions.md %} + +{% include_relative draco.decoder.md %} + +{% include_relative mesh.decoder.md %} + +{% include_relative edgebreaker.decoder.md %} + + +{% comment %} +{% include_relative 99.00.01.testing.md %} +{% endcomment %} diff --git a/docs/spec/mesh.decoder.md b/docs/spec/mesh.decoder.md new file mode 100644 index 0000000..c283bea --- /dev/null +++ b/docs/spec/mesh.decoder.md @@ -0,0 +1,11 @@ +## Mesh Decoder + +### DecodeConnectivityData() + +
      +DecodeConnectivityData() Type + InitializeDecoder() + DecodeConnectivity() +} + +