refactor(fill): use native entity geometry for linear copy distance

Replaces PartBoundary polygon edges with PartGeometry.GetOffsetPerimeterEntities
(inflated Line/Arc entities) so arcs are handled exactly without the polygon
sampling error that previously required a bboxDim + PartSpacing clamp. Adds
bbox DirectionalGap / PerpendicularOverlap early-outs to skip pair checks
that can't produce a valid slide, and removes the now-unused PartBoundary
cache, GetPatternLines/GetOffsetPatternLines helpers, and ComputeCopyDistance
clamp.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

OpenNest.Engine/Fill/FillLinear.cs

@@ -61,92 +61,91 @@ namespace OpenNest.Engine.Fill
                 : NestDirection.Horizontal;
         }
 
-        /// <summary>
-        /// Computes the slide distance for the push algorithm, returning the
-        /// geometry-aware copy distance along the given axis.
-        /// </summary>
-        private double ComputeCopyDistance(double bboxDim, double slideDistance)
-        {
-            if (slideDistance >= double.MaxValue || slideDistance < 0)
-                return bboxDim + PartSpacing;
-
-            // The geometry-aware slide can produce a copy distance smaller than
-            // the part itself when inflated corner/arc vertices interact spuriously.
-            // Clamp to bboxDim + PartSpacing to prevent bounding box overlap.
-            return System.Math.Max(bboxDim - slideDistance, bboxDim + PartSpacing);
-        }
-
         /// <summary>
         /// Finds the geometry-aware copy distance between two identical parts along an axis.
-        /// Both parts are inflated by half-spacing for symmetric spacing.
+        /// Uses native Line/Arc entities (inflated by half-spacing) so curves are handled
+        /// exactly without polygon sampling error.
         /// </summary>
-        private double FindCopyDistance(Part partA, NestDirection direction, PartBoundary boundary)
+        private double FindCopyDistance(Part partA, NestDirection direction)
         {
             var bboxDim = GetDimension(partA.BoundingBox, direction);
             var pushDir = GetPushDirection(direction);
+            var startOffset = bboxDim + PartSpacing + Tolerance.Epsilon;
+            var offset = MakeOffset(direction, startOffset);
 
-            var locationBOffset = MakeOffset(direction, bboxDim);
+            var stationaryEntities = PartGeometry.GetOffsetPerimeterEntities(partA, HalfSpacing);
+            var movingEntities = PartGeometry.GetOffsetPerimeterEntities(
+                partA.CloneAtOffset(offset), HalfSpacing);
 
-            // Use the most efficient array-based overload to avoid all allocations.
             var slideDistance = SpatialQuery.DirectionalDistance(
-                boundary.GetEdges(pushDir), partA.Location + locationBOffset,
+                movingEntities, stationaryEntities, pushDir);
-                boundary.GetEdges(SpatialQuery.OppositeDirection(pushDir)), partA.Location,
-                pushDir);
 
-            return ComputeCopyDistance(bboxDim, slideDistance);
+            if (slideDistance >= double.MaxValue || slideDistance < 0)
+                return bboxDim + PartSpacing;
+
+            return startOffset - slideDistance;
         }
 
         /// <summary>
         /// Finds the geometry-aware copy distance between two identical patterns along an axis.
-        /// Checks every pair of parts across adjacent patterns so that multi-part
+        /// Checks every pair of parts across adjacent pattern copies so multi-part patterns
-        /// patterns (e.g. interlocking pairs) maintain spacing between ALL parts.
+        /// (e.g. interlocking pairs) maintain spacing between ALL parts. Uses native entity
-        /// Both sides are inflated by half-spacing for symmetric spacing.
+        /// geometry inflated by half-spacing — same primitive the Compactor uses — so arcs
+        /// are exact and no bbox clamp is needed.
         /// </summary>
-        private double FindPatternCopyDistance(Pattern patternA, NestDirection direction, PartBoundary[] boundaries)
+        private double FindPatternCopyDistance(Pattern patternA, NestDirection direction)
         {
-            if (patternA.Parts.Count <= 1)
+            if (patternA.Parts.Count == 1)
-                return FindSinglePartPatternCopyDistance(patternA, direction, boundaries[0]);
+                return FindCopyDistance(patternA.Parts[0], direction);
 
             var bboxDim = GetDimension(patternA.BoundingBox, direction);
             var pushDir = GetPushDirection(direction);
             var opposite = SpatialQuery.OppositeDirection(pushDir);
+            var dirVec = SpatialQuery.DirectionToOffset(pushDir, 1.0);
 
             // bboxDim already spans max(upper) - min(lower) across all parts,
             // so the start offset just needs to push beyond that plus spacing.
             var startOffset = bboxDim + PartSpacing + Tolerance.Epsilon;
             var offset = MakeOffset(direction, startOffset);
 
-            var maxCopyDistance = FindMaxPairDistance(
+            var parts = patternA.Parts;
-                patternA.Parts, boundaries, offset, pushDir, opposite, startOffset);
+            var stationaryBoxes = new Box[parts.Count];
+            var movingBoxes = new Box[parts.Count];
+            var stationaryEntities = new List<Entity>[parts.Count];
+            var movingEntities = new List<Entity>[parts.Count];
 
-            // The copy distance must be at least bboxDim + PartSpacing to prevent
+            for (var i = 0; i < parts.Count; i++)
-            // bounding box overlap. Cross-pair slides can underestimate when the
+            {
-            // circumscribed polygon boundary overshoots the true arc, creating
+                stationaryBoxes[i] = parts[i].BoundingBox;
-            // spurious contacts between diagonal parts in adjacent copies.
+                movingBoxes[i] = stationaryBoxes[i].Translate(offset);
-            return System.Math.Max(maxCopyDistance, bboxDim + PartSpacing);
+            }
-        }
 
-        /// <summary>
-        /// Tests every pair of parts across adjacent pattern copies and returns the
-        /// maximum copy distance found. Returns 0 if no valid slide was found.
-        /// </summary>
-        private static double FindMaxPairDistance(
-            List<Part> parts, PartBoundary[] boundaries, Vector offset,
-            PushDirection pushDir, PushDirection opposite, double startOffset)
-        {
             var maxCopyDistance = 0.0;
 
             for (var j = 0; j < parts.Count; j++)
             {
-                var movingEdges = boundaries[j].GetEdges(pushDir);
+                var movingBox = movingBoxes[j];
-                var locationB = parts[j].Location + offset;
 
                 for (var i = 0; i < parts.Count; i++)
                 {
+                    var stationaryBox = stationaryBoxes[i];
+
+                    // Skip if stationary is already ahead of moving in the push direction
+                    // (sliding forward would take them further apart).
+                    if (SpatialQuery.DirectionalGap(movingBox, stationaryBox, opposite) > 0)
+                        continue;
+
+                    // Skip if bboxes can't overlap along the axis perpendicular to the push.
+                    if (!SpatialQuery.PerpendicularOverlap(movingBox, stationaryBox, dirVec))
+                        continue;
+
+                    stationaryEntities[i] ??= PartGeometry.GetOffsetPerimeterEntities(
+                        parts[i], HalfSpacing);
+                    movingEntities[j] ??= PartGeometry.GetOffsetPerimeterEntities(
+                        parts[j].CloneAtOffset(offset), HalfSpacing);
+
                     var slideDistance = SpatialQuery.DirectionalDistance(
-                        movingEdges, locationB,
+                        movingEntities[j], stationaryEntities[i], pushDir);
-                        boundaries[i].GetEdges(opposite), parts[i].Location,
-                        pushDir);
 
                     if (slideDistance >= double.MaxValue || slideDistance < 0)
                         continue;
@@ -161,86 +160,15 @@ namespace OpenNest.Engine.Fill
             return maxCopyDistance;
         }
 
-        /// <summary>
-        /// Fast path for single-part patterns — no cross-part conflicts possible.
-        /// </summary>
-        private double FindSinglePartPatternCopyDistance(Pattern patternA, NestDirection direction, PartBoundary boundary)
-        {
-            var template = patternA.Parts[0];
-            return FindCopyDistance(template, direction, boundary);
-        }
-
-        /// <summary>
-        /// Gets offset boundary lines for all parts in a pattern using a shared boundary.
-        /// </summary>
-        private static List<Line> GetPatternLines(Pattern pattern, PartBoundary boundary, PushDirection direction)
-        {
-            var lines = new List<Line>();
-
-            foreach (var part in pattern.Parts)
-                lines.AddRange(boundary.GetLines(part.Location, direction));
-
-            return lines;
-        }
-
-        /// <summary>
-        /// Gets boundary lines for all parts in a pattern, with an additional
-        /// location offset applied. Avoids cloning the pattern.
-        /// </summary>
-        private static List<Line> GetOffsetPatternLines(Pattern pattern, Vector offset, PartBoundary boundary, PushDirection direction)
-        {
-            var lines = new List<Line>();
-
-            foreach (var part in pattern.Parts)
-                lines.AddRange(boundary.GetLines(part.Location + offset, direction));
-
-            return lines;
-        }
-
-        /// <summary>
-        /// Creates boundaries for all parts in a pattern. Parts that share the same
-        /// program geometry (same drawing and rotation) reuse the same boundary instance.
-        /// </summary>
-        private PartBoundary[] CreateBoundaries(Pattern pattern)
-        {
-            var boundaries = new PartBoundary[pattern.Parts.Count];
-            var cache = new List<(Drawing drawing, double rotation, PartBoundary boundary)>();
-
-            for (var i = 0; i < pattern.Parts.Count; i++)
-            {
-                var part = pattern.Parts[i];
-                PartBoundary found = null;
-
-                foreach (var entry in cache)
-                {
-                    if (entry.drawing == part.BaseDrawing && entry.rotation.IsEqualTo(part.Rotation))
-                    {
-                        found = entry.boundary;
-                        break;
-                    }
-                }
-
-                if (found == null)
-                {
-                    found = new PartBoundary(part, HalfSpacing);
-                    cache.Add((part.BaseDrawing, part.Rotation, found));
-                }
-
-                boundaries[i] = found;
-            }
-
-            return boundaries;
-        }
-
         /// <summary>
         /// Tiles a pattern along the given axis, returning the cloned parts
         /// (does not include the original pattern's parts). For multi-part
         /// patterns, also adds individual parts from the next incomplete copy
         /// that still fit within the work area.
         /// </summary>
-        private List<Part> TilePattern(Pattern basePattern, NestDirection direction, PartBoundary[] boundaries)
+        private List<Part> TilePattern(Pattern basePattern, NestDirection direction)
         {
-            var copyDistance = FindPatternCopyDistance(basePattern, direction, boundaries);
+            var copyDistance = FindPatternCopyDistance(basePattern, direction);
 
             if (copyDistance <= 0)
                 return new List<Part>();
@@ -394,11 +322,10 @@ namespace OpenNest.Engine.Fill
         private List<Part> FillGrid(Pattern pattern, NestDirection direction)
         {
             var perpAxis = PerpendicularAxis(direction);
-            var boundaries = CreateBoundaries(pattern);
 
             // Step 1: Tile along primary axis
             var row = new List<Part>(pattern.Parts);
-            row.AddRange(TilePattern(pattern, direction, boundaries));
+            row.AddRange(TilePattern(pattern, direction));
 
             if (pattern.Parts.Count > 1 && HasOverlappingParts(row, out var a1, out var b1))
             {
@@ -410,7 +337,7 @@ namespace OpenNest.Engine.Fill
             // If primary tiling didn't produce copies, just tile along perpendicular
             if (row.Count <= pattern.Parts.Count)
             {
-                row.AddRange(TilePattern(pattern, perpAxis, boundaries));
+                row.AddRange(TilePattern(pattern, perpAxis));
 
                 if (pattern.Parts.Count > 1 && HasOverlappingParts(row, out var a2, out var b2))
                 {
@@ -427,9 +354,8 @@ namespace OpenNest.Engine.Fill
             rowPattern.Parts.AddRange(row);
             rowPattern.UpdateBounds();
 
-            var rowBoundaries = CreateBoundaries(rowPattern);
             var gridResult = new List<Part>(rowPattern.Parts);
-            gridResult.AddRange(TilePattern(rowPattern, perpAxis, rowBoundaries));
+            gridResult.AddRange(TilePattern(rowPattern, perpAxis));
 
             if (HasOverlappingParts(gridResult, out var a3, out var b3))
             {
@@ -481,9 +407,8 @@ namespace OpenNest.Engine.Fill
                 return seed;
 
             var template = seed.Parts[0];
-            var boundary = new PartBoundary(template, HalfSpacing);
 
-            var copyDistance = FindCopyDistance(template, direction, boundary);
+            var copyDistance = FindCopyDistance(template, direction);
 
             if (copyDistance <= 0)
                 return seed;