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fix(geometry): replace closest-point heuristic with analytical arc-to-line directional distance

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ArcToLineClosestDistance used geometric closest-point as a proxy for
directional push distance, which are fundamentally different queries.
The heuristic could overestimate the safe push distance when an arc
faces an inclined line, causing the Compactor to over-push parts into
overlapping positions.

Replace with analytical computation: for each arc/line pair, solve
dt/dθ = 0 to find the two critical angles where the directional
distance is stationary, evaluate both (if within the arc's angular
span), and fire a ray to verify the hit is within the line segment.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
This commit is contained in:
AJ Isaacs
2026-04-12 22:33:48 -04:00
parent a5e5e78c4e
commit 838a247ef9
2 changed files with 108 additions and 11 deletions
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70
OpenNest.Tests/Fill/CompactorTests.cs
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@@ -8,6 +8,76 @@ namespace OpenNest.Tests.Fill
{
public class CompactorTests
{
[Fact]
public void DirectionalDistance_ArcVsInclinedLine_DoesNotOverPush()
{
// Arc (top semicircle) pushed upward toward a 45° inclined line.
// The critical angle on the arc gives a shorter distance than any
// sampled vertex (endpoints + cardinal extremes).
var arc = new Arc(5, 0, 2, 0, System.Math.PI);
var line = new Line(new Vector(3, 4), new Vector(7, 6));
var moving = new List<Entity> { arc };
var stationary = new List<Entity> { line };
var direction = new Vector(0, 1); // push up
var dist = SpatialQuery.DirectionalDistance(moving, stationary, direction);
// Move the arc up by the computed distance, then verify no overlap.
// The topmost reachable point on the arc at the critical angle θ ≈ 2.034
// (between π/2 and π) should just touch the line.
Assert.True(dist < double.MaxValue, "Should find a finite distance");
Assert.True(dist > 0, "Should be a positive distance");
// Verify: after moving, the closest point on the arc should be within
// tolerance of the line, not past it.
var theta = System.Math.Atan2(
line.pt2.X - line.pt1.X, -(line.pt2.Y - line.pt1.Y));
theta = OpenNest.Math.Angle.NormalizeRad(theta + System.Math.PI);
var qx = arc.Center.X + arc.Radius * System.Math.Cos(theta);
var qy = arc.Center.Y + arc.Radius * System.Math.Sin(theta) + dist;
// The moved point should be on or just touching the line, not past it.
// Line equation: (y - 4) / (x - 3) = (6 - 4) / (7 - 3) = 0.5
// y = 0.5x + 2.5
var lineYAtQx = 0.5 * qx + 2.5;
Assert.True(qy <= lineYAtQx + 0.001,
$"Arc point ({qx:F4}, {qy:F4}) should not be past line (line Y={lineYAtQx:F4} at X={qx:F4}). " +
$"dist={dist:F6}, overshot by {qy - lineYAtQx:F6}");
}
[Fact]
public void DirectionalDistance_ArcVsInclinedLine_BetterThanVertexSampling()
{
// Same geometry — verify the analytical Phase 3 finds a shorter
// distance than the Phase 1/2 vertex sampling alone would.
var arc = new Arc(5, 0, 2, 0, System.Math.PI);
var line = new Line(new Vector(3, 4), new Vector(7, 6));
// Phase 1/2 vertex-only distance: sample arc endpoints + cardinal extreme.
var vertices = new[]
{
new Vector(7, 0), // arc endpoint θ=0
new Vector(3, 0), // arc endpoint θ=π
new Vector(5, 2), // cardinal extreme θ=π/2
};
var vertexMin = double.MaxValue;
foreach (var v in vertices)
{
var d = SpatialQuery.RayEdgeDistance(v.X, v.Y,
line.pt1.X, line.pt1.Y, line.pt2.X, line.pt2.Y, 0, 1);
if (d < vertexMin) vertexMin = d;
}
// Full directional distance (includes Phase 3 arc-to-line).
var moving = new List<Entity> { arc };
var stationary = new List<Entity> { line };
var fullDist = SpatialQuery.DirectionalDistance(moving, stationary, new Vector(0, 1));
Assert.True(fullDist < vertexMin,
$"Full distance ({fullDist:F6}) should be less than vertex-only ({vertexMin:F6})");
}
private static Drawing MakeRectDrawing(double w, double h)
{
var pgm = new OpenNest.CNC.Program();