PrusaSlicer/xs/src/libslic3r/Geometry.cpp

#include "Geometry.hpp"
#include "ClipperUtils.hpp"
#include "ExPolygon.hpp"
#include "Line.hpp"
#include "PolylineCollection.hpp"
#include "clipper.hpp"
#include <algorithm>
#include <cassert>
#include <cmath>
#include <list>
#include <map>
#include <set>
#include <utility>
#include <vector>

#ifdef SLIC3R_DEBUG
#include "SVG.hpp"
#endif

using namespace boost::polygon;  // provides also high() and low()

namespace Slic3r { namespace Geometry {

static bool
sort_points (Point a, Point b)
{
    return (a.x < b.x) || (a.x == b.x && a.y < b.y);
}

/* This implementation is based on Andrew's monotone chain 2D convex hull algorithm */
Polygon
convex_hull(Points points)
{
    assert(points.size() >= 3);
    // sort input points
    std::sort(points.begin(), points.end(), sort_points);
    
    int n = points.size(), k = 0;
    Polygon hull;
    hull.points.resize(2*n);

    // Build lower hull
    for (int i = 0; i < n; i++) {
        while (k >= 2 && points[i].ccw(hull.points[k-2], hull.points[k-1]) <= 0) k--;
        hull.points[k++] = points[i];
    }

    // Build upper hull
    for (int i = n-2, t = k+1; i >= 0; i--) {
        while (k >= t && points[i].ccw(hull.points[k-2], hull.points[k-1]) <= 0) k--;
        hull.points[k++] = points[i];
    }

    hull.points.resize(k);
    
    assert( hull.points.front().coincides_with(hull.points.back()) );
    hull.points.pop_back();
    
    return hull;
}

Polygon
convex_hull(const Polygons &polygons)
{
    Points pp;
    for (Polygons::const_iterator p = polygons.begin(); p != polygons.end(); ++p) {
        pp.insert(pp.end(), p->points.begin(), p->points.end());
    }
    return convex_hull(pp);
}

/* accepts an arrayref of points and returns a list of indices
   according to a nearest-neighbor walk */
void
chained_path(const Points &points, std::vector<Points::size_type> &retval, Point start_near)
{
    PointConstPtrs my_points;
    std::map<const Point*,Points::size_type> indices;
    my_points.reserve(points.size());
    for (Points::const_iterator it = points.begin(); it != points.end(); ++it) {
        my_points.push_back(&*it);
        indices[&*it] = it - points.begin();
    }
    
    retval.reserve(points.size());
    while (!my_points.empty()) {
        Points::size_type idx = start_near.nearest_point_index(my_points);
        start_near = *my_points[idx];
        retval.push_back(indices[ my_points[idx] ]);
        my_points.erase(my_points.begin() + idx);
    }
}

void
chained_path(const Points &points, std::vector<Points::size_type> &retval)
{
    if (points.empty()) return;  // can't call front() on empty vector
    chained_path(points, retval, points.front());
}

/* retval and items must be different containers */
template<class T>
void
chained_path_items(Points &points, T &items, T &retval)
{
    std::vector<Points::size_type> indices;
    chained_path(points, indices);
    for (std::vector<Points::size_type>::const_iterator it = indices.begin(); it != indices.end(); ++it)
        retval.push_back(items[*it]);
}
template void chained_path_items(Points &points, ClipperLib::PolyNodes &items, ClipperLib::PolyNodes &retval);

bool
directions_parallel(double angle1, double angle2, double max_diff)
{
    double diff = fabs(angle1 - angle2);
    max_diff += EPSILON;
    return diff < max_diff || fabs(diff - PI) < max_diff;
}

template<class T>
bool
contains(const std::vector<T> &vector, const Point &point)
{
    for (typename std::vector<T>::const_iterator it = vector.begin(); it != vector.end(); ++it) {
        if (it->contains(point)) return true;
    }
    return false;
}
template bool contains(const ExPolygons &vector, const Point &point);

double
rad2deg(double angle)
{
    return angle / PI * 180.0;
}

double
rad2deg_dir(double angle)
{
    angle = (angle < PI) ? (-angle + PI/2.0) : (angle + PI/2.0);
    if (angle < 0) angle += PI;
    return rad2deg(angle);
}

double
deg2rad(double angle)
{
    return PI * angle / 180.0;
}

double
linint(double value, double oldmin, double oldmax, double newmin, double newmax)
{
    return (value - oldmin) * (newmax - newmin) / (oldmax - oldmin) + newmin;
}

Pointfs
arrange(size_t total_parts, Pointf part, coordf_t dist, const BoundingBoxf* bb)
{
    // use actual part size (the largest) plus separation distance (half on each side) in spacing algorithm
    part.x += dist;
    part.y += dist;
    
    Pointf area;
    if (bb != NULL && bb->defined) {
        area = bb->size();
    } else {
        // bogus area size, large enough not to trigger the error below
        area.x = part.x * total_parts;
        area.y = part.y * total_parts;
    }
    
    // this is how many cells we have available into which to put parts
    size_t cellw = floor((area.x + dist) / part.x);
    size_t cellh = floor((area.y + dist) / part.y);
    if (total_parts > (cellw * cellh))
        CONFESS("%zu parts won't fit in your print area!\n", total_parts);
    
    // total space used by cells
    Pointf cells(cellw * part.x, cellh * part.y);
    
    // bounding box of total space used by cells
    BoundingBoxf cells_bb;
    cells_bb.merge(Pointf(0,0)); // min
    cells_bb.merge(cells);  // max
    
    // center bounding box to area
    cells_bb.translate(
        (area.x - cells.x) / 2,
        (area.y - cells.y) / 2
    );
    
    // list of cells, sorted by distance from center
    std::vector<ArrangeItemIndex> cellsorder;
    
    // work out distance for all cells, sort into list
    for (size_t i = 0; i <= cellw-1; ++i) {
        for (size_t j = 0; j <= cellh-1; ++j) {
            coordf_t cx = linint(i + 0.5, 0, cellw, cells_bb.min.x, cells_bb.max.x);
            coordf_t cy = linint(j + 0.5, 0, cellh, cells_bb.min.y, cells_bb.max.y);
            
            coordf_t xd = fabs((area.x / 2) - cx);
            coordf_t yd = fabs((area.y / 2) - cy);
            
            ArrangeItem c;
            c.pos.x = cx;
            c.pos.y = cy;
            c.index_x = i;
            c.index_y = j;
            c.dist = xd * xd + yd * yd - fabs((cellw / 2) - (i + 0.5));
            
            // binary insertion sort
            {
                coordf_t index = c.dist;
                size_t low = 0;
                size_t high = cellsorder.size();
                while (low < high) {
                    size_t mid = (low + ((high - low) / 2)) | 0;
                    coordf_t midval = cellsorder[mid].index;
                    
                    if (midval < index) {
                        low = mid + 1;
                    } else if (midval > index) {
                        high = mid;
                    } else {
                        cellsorder.insert(cellsorder.begin() + mid, ArrangeItemIndex(index, c));
                        goto ENDSORT;
                    }
                }
                cellsorder.insert(cellsorder.begin() + low, ArrangeItemIndex(index, c));
            }
            ENDSORT: true;
        }
    }
    
    // the extents of cells actually used by objects
    coordf_t lx = 0;
    coordf_t ty = 0;
    coordf_t rx = 0;
    coordf_t by = 0;

    // now find cells actually used by objects, map out the extents so we can position correctly
    for (size_t i = 1; i <= total_parts; ++i) {
        ArrangeItemIndex c = cellsorder[i - 1];
        coordf_t cx = c.item.index_x;
        coordf_t cy = c.item.index_y;
        if (i == 1) {
            lx = rx = cx;
            ty = by = cy;
        } else {
            if (cx > rx) rx = cx;
            if (cx < lx) lx = cx;
            if (cy > by) by = cy;
            if (cy < ty) ty = cy;
        }
    }
    // now we actually place objects into cells, positioned such that the left and bottom borders are at 0
    Pointfs positions;
    for (size_t i = 1; i <= total_parts; ++i) {
        ArrangeItemIndex c = cellsorder.front();
        cellsorder.erase(cellsorder.begin());
        coordf_t cx = c.item.index_x - lx;
        coordf_t cy = c.item.index_y - ty;
        
        positions.push_back(Pointf(cx * part.x, cy * part.y));
    }
    
    if (bb != NULL && bb->defined) {
        for (Pointfs::iterator p = positions.begin(); p != positions.end(); ++p) {
            p->x += bb->min.x;
            p->y += bb->min.y;
        }
    }
    
    return positions;
}

void
MedialAxis::build(ThickPolylines* polylines)
{
    construct_voronoi(this->lines.begin(), this->lines.end(), &this->vd);
    
    /*
    // DEBUG: dump all Voronoi edges
    {
        for (VD::const_edge_iterator edge = this->vd.edges().begin(); edge != this->vd.edges().end(); ++edge) {
            if (edge->is_infinite()) continue;
            
            ThickPolyline polyline;
            polyline.points.push_back(Point( edge->vertex0()->x(), edge->vertex0()->y() ));
            polyline.points.push_back(Point( edge->vertex1()->x(), edge->vertex1()->y() ));
            polylines->push_back(polyline);
        }
        return;
    }
    */
    
    typedef const VD::vertex_type vert_t;
    typedef const VD::edge_type   edge_t;
    
    // collect valid edges (i.e. prune those not belonging to MAT)
    // note: this keeps twins, so it inserts twice the number of the valid edges
    this->valid_edges.clear();
    {
        std::set<const VD::edge_type*> seen_edges;
        for (VD::const_edge_iterator edge = this->vd.edges().begin(); edge != this->vd.edges().end(); ++edge) {
            // if we only process segments representing closed loops, none if the
            // infinite edges (if any) would be part of our MAT anyway
            if (edge->is_secondary() || edge->is_infinite()) continue;
        
            // don't re-validate twins
            if (seen_edges.find(&*edge) != seen_edges.end()) continue;  // TODO: is this needed?
            seen_edges.insert(&*edge);
            seen_edges.insert(edge->twin());
            
            if (!this->validate_edge(&*edge)) continue;
            this->valid_edges.insert(&*edge);
            this->valid_edges.insert(edge->twin());
        }
    }
    this->edges = this->valid_edges;
    
    // iterate through the valid edges to build polylines
    while (!this->edges.empty()) {
        const edge_t* edge = *this->edges.begin();
        
        // start a polyline
        ThickPolyline polyline;
        polyline.points.push_back(Point( edge->vertex0()->x(), edge->vertex0()->y() ));
        polyline.points.push_back(Point( edge->vertex1()->x(), edge->vertex1()->y() ));
        polyline.width.push_back(this->thickness[edge].first);
        polyline.width.push_back(this->thickness[edge].second);
        
        // remove this edge and its twin from the available edges
        (void)this->edges.erase(edge);
        (void)this->edges.erase(edge->twin());
        
        // get next points
        this->process_edge_neighbors(edge, &polyline);
        
        // get previous points
        {
            ThickPolyline rpolyline;
            this->process_edge_neighbors(edge->twin(), &rpolyline);
            polyline.points.insert(polyline.points.begin(), rpolyline.points.rbegin(), rpolyline.points.rend());
            polyline.width.insert(polyline.width.begin(), rpolyline.width.rbegin(), rpolyline.width.rend());
            polyline.endpoints.first = rpolyline.endpoints.second;
        }
        
        assert(polyline.width.size() == polyline.points.size()*2 - 2);
        
        // prevent loop endpoints from being extended
        if (polyline.first_point().coincides_with(polyline.last_point())) {
            polyline.endpoints.first = false;
            polyline.endpoints.second = false;
        }
        
        // append polyline to result
        polylines->push_back(polyline);
    }
}

void
MedialAxis::build(Polylines* polylines)
{
    ThickPolylines tp;
    this->build(&tp);
    polylines->insert(polylines->end(), tp.begin(), tp.end());
}

void
MedialAxis::process_edge_neighbors(const VD::edge_type* edge, ThickPolyline* polyline)
{
    while (true) {
        // Since rot_next() works on the edge starting point but we want
        // to find neighbors on the ending point, we just swap edge with
        // its twin.
        const VD::edge_type* twin = edge->twin();
    
        // count neighbors for this edge
        std::vector<const VD::edge_type*> neighbors;
        for (const VD::edge_type* neighbor = twin->rot_next(); neighbor != twin;
            neighbor = neighbor->rot_next()) {
            if (this->valid_edges.count(neighbor) > 0) neighbors.push_back(neighbor);
        }
    
        // if we have a single neighbor then we can continue recursively
        if (neighbors.size() == 1) {
            const VD::edge_type* neighbor = neighbors.front();
            
            // break if this is a closed loop
            if (this->edges.count(neighbor) == 0) return;
            
            Point new_point(neighbor->vertex1()->x(), neighbor->vertex1()->y());
            polyline->points.push_back(new_point);
            polyline->width.push_back(this->thickness[neighbor].first);
            polyline->width.push_back(this->thickness[neighbor].second);
            (void)this->edges.erase(neighbor);
            (void)this->edges.erase(neighbor->twin());
            edge = neighbor;
        } else if (neighbors.size() == 0) {
            polyline->endpoints.second = true;
            return;
        } else {
            // T-shaped or star-shaped joint
            return;
        }
    }
}

bool
MedialAxis::validate_edge(const VD::edge_type* edge)
{
    // construct the line representing this edge of the Voronoi diagram
    const Line line(
        Point( edge->vertex0()->x(), edge->vertex0()->y() ),
        Point( edge->vertex1()->x(), edge->vertex1()->y() )
    );
    
    // discard edge if it lies outside the supplied shape
    // this could maybe be optimized (checking inclusion of the endpoints
    // might give false positives as they might belong to the contour itself)
    if (this->expolygon != NULL) {
        if (line.a.coincides_with(line.b)) {
            // in this case, contains(line) returns a false positive
            if (!this->expolygon->contains(line.a)) return false;
        } else {
            if (!this->expolygon->contains(line)) return false;
        }
    }
    
    // retrieve the original line segments which generated the edge we're checking
    const VD::cell_type* cell_l = edge->cell();
    const VD::cell_type* cell_r = edge->twin()->cell();
    const Line &segment_l = this->retrieve_segment(cell_l);
    const Line &segment_r = this->retrieve_segment(cell_r);
    
    /*
    SVG svg("edge.svg");
    svg.draw(*this->expolygon);
    svg.draw(line);
    svg.draw(segment_l, "red");
    svg.draw(segment_r, "blue");
    svg.Close();
    */
    
    /*  Calculate thickness of the cross-section at both the endpoints of this edge.
        Our Voronoi edge is part of a CCW sequence going around its Voronoi cell 
        located on the left side. (segment_l).
        This edge's twin goes around segment_r. Thus, segment_r is 
        oriented in the same direction as our main edge, and segment_l is oriented
        in the same direction as our twin edge.
        We used to only consider the (half-)distances to segment_r, and that works
        whenever segment_l and segment_r are almost specular and facing. However, 
        at curves they are staggered and they only face for a very little length
        (our very short edge represents such visibility).
        Both w0 and w1 can be calculated either towards cell_l or cell_r with equal
        results by Voronoi definition.
        When cell_l or cell_r don't refer to the segment but only to an endpoint, we
        calculate the distance to that endpoint instead.  */
    
    coordf_t w0 = cell_r->contains_segment()
        ? line.a.distance_to(segment_r)*2
        : line.a.distance_to(this->retrieve_endpoint(cell_r))*2;
    
    coordf_t w1 = cell_l->contains_segment()
        ? line.b.distance_to(segment_l)*2
        : line.b.distance_to(this->retrieve_endpoint(cell_l))*2;
    
    if (cell_l->contains_segment() && cell_r->contains_segment()) {
        // calculate the relative angle between the two boundary segments
        double angle = fabs(segment_r.orientation() - segment_l.orientation());
        if (angle > PI) angle = 2*PI - angle;
        assert(angle >= 0 && angle <= PI);
        
        // fabs(angle) ranges from 0 (collinear, same direction) to PI (collinear, opposite direction)
        // we're interested only in segments close to the second case (facing segments)
        // so we allow some tolerance.
        // this filter ensures that we're dealing with a narrow/oriented area (longer than thick)
        // we don't run it on edges not generated by two segments (thus generated by one segment
        // and the endpoint of another segment), since their orientation would not be meaningful
        if (PI - angle > PI/8) {
            // angle is not narrow enough
            
            // only apply this filter to segments that are not too short otherwise their 
            // angle could possibly be not meaningful
            if (w0 < SCALED_EPSILON || w1 < SCALED_EPSILON || line.length() >= this->min_width)
                return false;
        }
    } else {
        if (w0 < SCALED_EPSILON || w1 < SCALED_EPSILON)
            return false;
    }
    
    if (w0 < this->min_width && w1 < this->min_width)
        return false;
    
    if (w0 > this->max_width && w1 > this->max_width)
        return false;
    
    this->thickness[edge]         = std::make_pair(w0, w1);
    this->thickness[edge->twin()] = std::make_pair(w1, w0);
    
    return true;
}

const Line&
MedialAxis::retrieve_segment(const VD::cell_type* cell) const
{
    return this->lines[cell->source_index()];
}

const Point&
MedialAxis::retrieve_endpoint(const VD::cell_type* cell) const
{
    const Line& line = this->retrieve_segment(cell);
    if (cell->source_category() == SOURCE_CATEGORY_SEGMENT_START_POINT) {
        return line.a;
    } else {
        return line.b;
    }
}

} }