Merge pull request #16547 from Ultimaker/optimal_offset

Find optimal offset for grid arrange

cura/Arranging/GridArrange.py

@@ -1,11 +1,11 @@
 import math
-from typing import List, TYPE_CHECKING, Optional, Tuple, Set
+from typing import List, TYPE_CHECKING, Tuple, Set
 
 if TYPE_CHECKING:
     from UM.Scene.SceneNode import SceneNode
+    from cura.BuildVolume import BuildVolume
 
 from UM.Application import Application
-from UM.Math import AxisAlignedBox
 from UM.Math.Vector import Vector
 from UM.Operations.AddSceneNodeOperation import AddSceneNodeOperation
 from UM.Operations.GroupedOperation import GroupedOperation
@@ -22,14 +22,25 @@ class GridArrange(Arranger):
         self._build_volume_bounding_box = build_volume.getBoundingBox()
         self._fixed_nodes = fixed_nodes
 
-        self._offset_x: float = 10
+        self._margin_x: float = 1
-        self._offset_y: float = 10
+        self._margin_y: float = 1
+
         self._grid_width = 0
         self._grid_height = 0
         for node in self._nodes_to_arrange:
             bounding_box = node.getBoundingBox()
             self._grid_width = max(self._grid_width, bounding_box.width)
             self._grid_height = max(self._grid_height, bounding_box.depth)
+        self._grid_width += self._margin_x
+        self._grid_height += self._margin_y
+
+        # Round up the grid size to the nearest cm
+        self._grid_width = math.ceil(self._grid_width / 10) * 10
+        self._grid_height = math.ceil(self._grid_height / 10) * 10
+
+        self._offset_x = 0
+        self._offset_y = 0
+        self._findOptimalGridOffset()
 
         coord_initial_leftover_x = self._build_volume_bounding_box.right + 2 * self._grid_width
         coord_initial_leftover_y = (self._build_volume_bounding_box.back + self._build_volume_bounding_box.front) * 0.5
@@ -37,32 +48,31 @@ class GridArrange(Arranger):
         self._initial_leftover_grid_x = math.floor(self._initial_leftover_grid_x)
         self._initial_leftover_grid_y = math.floor(self._initial_leftover_grid_y)
 
-    def createGroupOperationForArrange(self, add_new_nodes_in_scene: bool = False) -> Tuple[GroupedOperation, int]:
         # Find grid indexes that intersect with fixed objects
-        fixed_nodes_grid_ids = set()
+        self._fixed_nodes_grid_ids = set()
         for node in self._fixed_nodes:
-            fixed_nodes_grid_ids = fixed_nodes_grid_ids.union(self.intersectingGridIdxInclusive(node.getBoundingBox()))
+            self._fixed_nodes_grid_ids = self._fixed_nodes_grid_ids.union(
+                self.intersectingGridIdxInclusive(node.getBoundingBox()))
 
-        build_plate_grid_ids = self.intersectingGridIdxExclusive(self._build_volume_bounding_box)
+        self._build_plate_grid_ids = self.intersectingGridIdxExclusive(self._build_volume_bounding_box)
 
         # Filter out the corner grid squares if the build plate shape is elliptic
         if self._build_volume.getShape() == "elliptic":
-            build_plate_grid_ids = set(filter(lambda grid_id: self.checkGridUnderDiscSpace(grid_id[0], grid_id[1]), build_plate_grid_ids))
+            self._build_plate_grid_ids = set(
+                filter(lambda grid_id: self.checkGridUnderDiscSpace(grid_id[0], grid_id[1]),
+                       self._build_plate_grid_ids))
 
-        allowed_grid_idx = build_plate_grid_ids.difference(fixed_nodes_grid_ids)
+        self._allowed_grid_idx = self._build_plate_grid_ids.difference(self._fixed_nodes_grid_ids)
 
+    def createGroupOperationForArrange(self, add_new_nodes_in_scene: bool = False) -> Tuple[GroupedOperation, int]:
         # Find the sequence in which items are placed
         coord_build_plate_center_x = self._build_volume_bounding_box.width * 0.5 + self._build_volume_bounding_box.left
         coord_build_plate_center_y = self._build_volume_bounding_box.depth * 0.5 + self._build_volume_bounding_box.back
         grid_build_plate_center_x, grid_build_plate_center_y = self.coordSpaceToGridSpace(coord_build_plate_center_x, coord_build_plate_center_y)
 
-        def distToCenter(grid_id: Tuple[int, int]) -> float:
+        sequence: List[Tuple[int, int]] = list(self._allowed_grid_idx)
-            grid_x, grid_y = grid_id
+        sequence.sort(key=lambda grid_id: (grid_build_plate_center_x - grid_id[0]) ** 2 + (
-            distance_squared = (grid_build_plate_center_x - grid_x) ** 2 + (grid_build_plate_center_y - grid_y) ** 2
+                    grid_build_plate_center_y - grid_id[1]) ** 2)
-            return distance_squared
-
-        sequence: List[Tuple[int, int]] = list(allowed_grid_idx)
-        sequence.sort(key=distToCenter)
         scene_root = Application.getInstance().getController().getScene().getRoot()
         grouped_operation = GroupedOperation()
 
@@ -70,7 +80,7 @@ class GridArrange(Arranger):
             if add_new_nodes_in_scene:
                 grouped_operation.addOperation(AddSceneNodeOperation(node, scene_root))
             grid_x, grid_y = grid_id
-            operation = self.moveNodeOnGrid(node, grid_x, grid_y)
+            operation = self._moveNodeOnGrid(node, grid_x, grid_y)
             grouped_operation.addOperation(operation)
 
         leftover_nodes = self._nodes_to_arrange[len(sequence):]
@@ -80,18 +90,138 @@ class GridArrange(Arranger):
             if add_new_nodes_in_scene:
                 grouped_operation.addOperation(AddSceneNodeOperation(node, scene_root))
             # find the first next grid position that isn't occupied by a fixed node
-            while (self._initial_leftover_grid_x, left_over_grid_y) in fixed_nodes_grid_ids:
+            while (self._initial_leftover_grid_x, left_over_grid_y) in self._fixed_nodes_grid_ids:
                 left_over_grid_y = left_over_grid_y - 1
 
-            operation = self.moveNodeOnGrid(node, self._initial_leftover_grid_x, left_over_grid_y)
+            operation = self._moveNodeOnGrid(node, self._initial_leftover_grid_x, left_over_grid_y)
             grouped_operation.addOperation(operation)
             left_over_grid_y = left_over_grid_y - 1
+
         return grouped_operation, len(leftover_nodes)
 
-    def moveNodeOnGrid(self, node: "SceneNode", grid_x: int, grid_y: int) -> "Operation.Operation":
+    def _findOptimalGridOffset(self):
-        coord_grid_x, coord_grid_y = self.gridSpaceToCoordSpace(grid_x, grid_y)
+        if len(self._fixed_nodes) == 0:
-        center_grid_x = coord_grid_x + (0.5 * (self._grid_width + self._offset_x))
+            self._offset_x = 0
-        center_grid_y = coord_grid_y + (0.5 * (self._grid_height + self._offset_y))
+            self._offset_y = 0
+            return
+
+        if len(self._fixed_nodes) == 1:
+            center_grid_x = 0.5 * self._grid_width + self._build_volume_bounding_box.left
+            center_grid_y = 0.5 * self._grid_height + self._build_volume_bounding_box.back
+
+            bounding_box = self._fixed_nodes[0].getBoundingBox()
+            center_node_x = (bounding_box.left + bounding_box.right) * 0.5
+            center_node_y = (bounding_box.back + bounding_box.front) * 0.5
+
+            self._offset_x = center_node_x - center_grid_x
+            self._offset_y = center_node_y - center_grid_y
+
+            return
+
+        # If there are multiple fixed nodes, an optimal solution is not always possible
+        # We will try to find an offset that minimizes the number of grid intersections
+        # with fixed nodes. The algorithm below achieves this by utilizing a scanline
+        # algorithm. In this algorithm each axis is solved separately as offsetting
+        # is completely independent in each axis. The comments explaining the algorithm
+        # below are for the x-axis, but the same applies for the y-axis.
+        #
+        # Each node either occupies ceil((node.right - node.right) / grid_width) or
+        # ceil((node.right - node.right) / grid_width) + 1 grid squares. We will call
+        # these the node's "footprint".
+        #
+        #                      ┌────────────────┐
+        #   minimum food print │      NODE      │
+        #                      └────────────────┘
+        # │    grid 1   │    grid 2    │    grid 3    │    grid 4    |    grid 5    |
+        #                             ┌────────────────┐
+        #          maximum food print │      NODE      │
+        #                             └────────────────┘
+        #
+        # The algorithm will find the grid offset such that the number of nodes with
+        # a _minimal_ footprint is _maximized_.
+
+        # The scanline algorithm works as follows, we create events for both end points
+        # of each node's footprint. The event have two properties,
+        # - the coordinate: the amount the endpoint can move to the
+        #      left before it crosses a grid line
+        # - the change: either +1 or -1, indicating whether crossing the grid line
+        #      would result in a minimal footprint node becoming a maximal footprint
+        class Event:
+            def __init__(self, coord: float, change: float):
+                self.coord = coord
+                self.change = change
+
+        # create events for both the horizontal and vertical axis
+        events_horizontal: List[Event] = []
+        events_vertical: List[Event] = []
+
+        for node in self._fixed_nodes:
+            bounding_box = node.getBoundingBox()
+
+            left = bounding_box.left - self._build_volume_bounding_box.left
+            right = bounding_box.right - self._build_volume_bounding_box.left
+            back = bounding_box.back - self._build_volume_bounding_box.back
+            front = bounding_box.front - self._build_volume_bounding_box.back
+
+            value_left = math.ceil(left / self._grid_width) * self._grid_width - left
+            value_right = math.ceil(right / self._grid_width) * self._grid_width - right
+            value_back = math.ceil(back / self._grid_height) * self._grid_height - back
+            value_front = math.ceil(front / self._grid_height) * self._grid_height - front
+
+            # give nodes a weight according to their size. This
+            # weight is heuristically chosen to be proportional to
+            # the number of grid squares the node-boundary occupies
+            weight = bounding_box.width + bounding_box.depth
+
+            events_horizontal.append(Event(value_left, weight))
+            events_horizontal.append(Event(value_right, -weight))
+            events_vertical.append(Event(value_back, weight))
+            events_vertical.append(Event(value_front, -weight))
+
+        events_horizontal.sort(key=lambda event: event.coord)
+        events_vertical.sort(key=lambda event: event.coord)
+
+        def findOptimalShiftAxis(events: List[Event], interval: float) -> float:
+            # executing the actual scanline algorithm
+            # iteratively go through events (left to right) and keep track of the
+            # current footprint. The optimal location is the one with the minimal
+            # footprint. If there are multiple locations with the same minimal
+            # footprint, the optimal location is the one with the largest range
+            # between the left and right endpoint of the footprint.
+            prev_offset = events[-1].coord - interval
+            current_minimal_footprint_count = 0
+
+            best_minimal_footprint_count = float('inf')
+            best_offset_span = float('-inf')
+            best_offset = 0.0
+
+            for event in events:
+                offset_span = event.coord - prev_offset
+
+                if current_minimal_footprint_count < best_minimal_footprint_count or (
+                        current_minimal_footprint_count == best_minimal_footprint_count and offset_span > best_offset_span):
+                    best_minimal_footprint_count = current_minimal_footprint_count
+                    best_offset_span = offset_span
+                    best_offset = event.coord
+
+                current_minimal_footprint_count += event.change
+                prev_offset = event.coord
+
+            return best_offset - best_offset_span * 0.5
+
+        center_grid_x = 0.5 * self._grid_width
+        center_grid_y = 0.5 * self._grid_height
+
+        optimal_center_x = self._grid_width - findOptimalShiftAxis(events_horizontal, self._grid_width)
+        optimal_center_y = self._grid_height - findOptimalShiftAxis(events_vertical, self._grid_height)
+
+        self._offset_x = optimal_center_x - center_grid_x
+        self._offset_y = optimal_center_y - center_grid_y
+
+    def _moveNodeOnGrid(self, node: "SceneNode", grid_x: int, grid_y: int) -> "Operation.Operation":
+        coord_grid_x, coord_grid_y = self._gridSpaceToCoordSpace(grid_x, grid_y)
+        center_grid_x = coord_grid_x + (0.5 * self._grid_width)
+        center_grid_y = coord_grid_y + (0.5 * self._grid_height)
 
         bounding_box = node.getBoundingBox()
         center_node_x = (bounding_box.left + bounding_box.right) * 0.5
@@ -102,7 +232,7 @@ class GridArrange(Arranger):
 
         return TranslateOperation(node, Vector(delta_x, 0, delta_y))
 
-    def getGridCornerPoints(self, bounding_box: "BoundingVolume") -> Tuple[float, float, float, float]:
+    def _getGridCornerPoints(self, bounding_box: "BoundingVolume") -> Tuple[float, float, float, float]:
         coord_x1 = bounding_box.left
         coord_x2 = bounding_box.right
         coord_y1 = bounding_box.back
@@ -112,7 +242,7 @@ class GridArrange(Arranger):
         return grid_x1, grid_y1, grid_x2, grid_y2
 
     def intersectingGridIdxInclusive(self, bounding_box: "BoundingVolume") -> Set[Tuple[int, int]]:
-        grid_x1, grid_y1, grid_x2, grid_y2 = self.getGridCornerPoints(bounding_box)
+        grid_x1, grid_y1, grid_x2, grid_y2 = self._getGridCornerPoints(bounding_box)
         grid_idx = set()
         for grid_x in range(math.floor(grid_x1), math.ceil(grid_x2)):
             for grid_y in range(math.floor(grid_y1), math.ceil(grid_y2)):
@@ -120,26 +250,26 @@ class GridArrange(Arranger):
         return grid_idx
 
     def intersectingGridIdxExclusive(self, bounding_box: "BoundingVolume") -> Set[Tuple[int, int]]:
-        grid_x1, grid_y1, grid_x2, grid_y2 = self.getGridCornerPoints(bounding_box)
+        grid_x1, grid_y1, grid_x2, grid_y2 = self._getGridCornerPoints(bounding_box)
         grid_idx = set()
         for grid_x in range(math.ceil(grid_x1), math.floor(grid_x2)):
             for grid_y in range(math.ceil(grid_y1), math.floor(grid_y2)):
                 grid_idx.add((grid_x, grid_y))
         return grid_idx
 
-    def gridSpaceToCoordSpace(self, x: float, y: float) -> Tuple[float, float]:
+    def _gridSpaceToCoordSpace(self, x: float, y: float) -> Tuple[float, float]:
-        grid_x = x * (self._grid_width + self._offset_x) + self._build_volume_bounding_box.left
+        grid_x = x * self._grid_width + self._build_volume_bounding_box.left + self._offset_x
-        grid_y = y * (self._grid_height + self._offset_y) + self._build_volume_bounding_box.back
+        grid_y = y * self._grid_height + self._build_volume_bounding_box.back + self._offset_y
         return grid_x, grid_y
 
     def coordSpaceToGridSpace(self, grid_x: float, grid_y: float) -> Tuple[float, float]:
-        coord_x = (grid_x - self._build_volume_bounding_box.left) / (self._grid_width + self._offset_x)
+        coord_x = (grid_x - self._build_volume_bounding_box.left - self._offset_x) / self._grid_width
-        coord_y = (grid_y - self._build_volume_bounding_box.back) / (self._grid_height + self._offset_y)
+        coord_y = (grid_y - self._build_volume_bounding_box.back - self._offset_y) / self._grid_height
         return coord_x, coord_y
 
     def checkGridUnderDiscSpace(self, grid_x: int, grid_y: int) -> bool:
-        left, back = self.gridSpaceToCoordSpace(grid_x, grid_y)
+        left, back = self._gridSpaceToCoordSpace(grid_x, grid_y)
-        right, front = self.gridSpaceToCoordSpace(grid_x + 1, grid_y + 1)
+        right, front = self._gridSpaceToCoordSpace(grid_x + 1, grid_y + 1)
         corners = [(left, back), (right, back), (right, front), (left, front)]
         return all([self.checkPointUnderDiscSpace(x, y) for x, y in corners])
 
@@ -166,15 +296,14 @@ class GridArrange(Arranger):
         disc_y = ((y - self._build_volume_bounding_box.back) / self._build_volume_bounding_box.depth) * 2.0 - 1.0
         return disc_x, disc_y
 
-    def drawDebugSvg(self):
+    def _drawDebugSvg(self):
         with open("Builvolume_test.svg", "w") as f:
             build_volume_bounding_box = self._build_volume_bounding_box
 
             f.write(
                 f"<svg xmlns='http://www.w3.org/2000/svg' viewBox='{build_volume_bounding_box.left - 100} {build_volume_bounding_box.back - 100} {build_volume_bounding_box.width + 200} {build_volume_bounding_box.depth + 200}'>\n")
 
-            ellipse = True
+            if self._build_volume.getShape() == "elliptic":
-            if ellipse:
                 f.write(
                     f"""
                     <ellipse
@@ -182,7 +311,7 @@ class GridArrange(Arranger):
                         cy='{(build_volume_bounding_box.back + build_volume_bounding_box.front) * 0.5}'
                         rx='{build_volume_bounding_box.width * 0.5}' 
                         ry='{build_volume_bounding_box.depth * 0.5}' 
-                        fill=\"blue\"
+                        fill=\"lightgrey\"
                     />
                     """)
             else:
@@ -197,30 +326,32 @@ class GridArrange(Arranger):
                     />
                     """)
 
-            for grid_x in range(0, 100):
+            for grid_x in range(-10, 10):
-                for grid_y in range(0, 100):
+                for grid_y in range(-10, 10):
-                    # if (grid_x, grid_y) in intersecting_grid_idx:
+                    if (grid_x, grid_y) in self._allowed_grid_idx:
-                    #     fill_color = "red"
+                        fill_color = "rgba(0, 255, 0, 0.5)"
-                    # elif (grid_x, grid_y) in build_plate_grid_idx:
+                    elif (grid_x, grid_y) in self._build_plate_grid_ids:
-                    #     fill_color = "green"
+                        fill_color = "rgba(255, 165, 0, 0.5)"
-                    # else:
+                    else:
-                    #     fill_color = "orange"
+                        fill_color = "rgba(255, 0, 0, 0.5)"
 
-                    coord_grid_x, coord_grid_y = self.gridSpaceToCoordSpace(grid_x, grid_y)
+                    coord_grid_x, coord_grid_y = self._gridSpaceToCoordSpace(grid_x, grid_y)
                     f.write(
                         f"""
                         <rect
-                            x="{coord_grid_x}"
+                            x="{coord_grid_x + self._margin_x * 0.5}"
-                            y="{coord_grid_y}"
+                            y="{coord_grid_y + self._margin_y * 0.5}"
-                            width="{self._grid_width}" 
+                            width="{self._grid_width - self._margin_x}" 
-                            height="{self._grid_height}" 
+                            height="{self._grid_height - self._margin_y}" 
-                            fill="#ff00ff88"
+                            fill="{fill_color}"
                             stroke="black"
                         />
                         """)
                     f.write(f"""
                         <text 
-                            font-size="8"
+                            font-size="4"
+                            text-anchor="middle"
+                            alignment-baseline="middle"
                             x="{coord_grid_x + self._grid_width * 0.5}" 
                             y="{coord_grid_y + self._grid_height * 0.5}"
                         >
@@ -238,24 +369,25 @@ class GridArrange(Arranger):
                         fill="red" 
                     />
                 """)
-            for node in self._nodes_to_arrange:
-                bounding_box = node.getBoundingBox()
-                f.write(f"""
-                    <rect
-                        x="{bounding_box.left}" 
-                        y="{bounding_box.back}"
-                        width="{bounding_box.width}"
-                        height="{bounding_box.depth}" 
-                        fill="rgba(0,0,0,0.1)" 
-                        stroke="blue"
-                        stroke-width="3"
-                    />
-                """)
 
-            for x in range(math.floor(self._build_volume_bounding_box.left), math.floor(self._build_volume_bounding_box.right), 50):
-                for y in range(math.floor(self._build_volume_bounding_box.back), math.floor(self._build_volume_bounding_box.front), 50):
-                    color = "green" if self.checkPointUnderDiscSpace(x, y) else "red"
             f.write(f"""
-                      <circle cx="{x}" cy="{y}" r="10" fill="{color}" />
+                <circle 
-                    """)
+                    cx="{self._offset_x}" 
+                    cy="{self._offset_y}" 
+                    r="2" 
+                    stroke="red"
+                    fill="none" 
+                />""")
+
+            # coord_build_plate_center_x = self._build_volume_bounding_box.width * 0.5 + self._build_volume_bounding_box.left
+            # coord_build_plate_center_y = self._build_volume_bounding_box.depth * 0.5 + self._build_volume_bounding_box.back
+            # f.write(f"""
+            #     <circle
+            #         cx="{coord_build_plate_center_x}"
+            #         cy="{coord_build_plate_center_y}"
+            #         r="2"
+            #         stroke="blue"
+            #         fill="none"
+            #     />""")
+
             f.write(f"</svg>")