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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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49
OpenNest.Core/Geometry/SpatialQuery.cs
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@@ -631,19 +631,46 @@ namespace OpenNest.Geometry
{
for (var i = 0; i < arcEntities.Count; i++)
{
if (arcEntities[i] is Arc arc)
if (arcEntities[i] is not Arc arc)
continue;
var cx = arc.Center.X;
var cy = arc.Center.Y;
var r = arc.Radius;
for (var j = 0; j < lineEntities.Count; j++)
{
for (var j = 0; j < lineEntities.Count; j++)
if (lineEntities[j] is not Line line)
continue;
var p1x = line.pt1.X;
var p1y = line.pt1.Y;
var ex = line.pt2.X - p1x;
var ey = line.pt2.Y - p1y;
var det = ex * dirY - ey * dirX;
if (System.Math.Abs(det) < Tolerance.Epsilon)
continue;
// The directional distance from an arc point at angle θ to the
// line is t(θ) = [A + r·(ey·cosθ − ex·sinθ)] / det.
// dt/dθ = 0 at θ = atan2(−ex, ey) and θ + π.
var theta1 = Angle.NormalizeRad(System.Math.Atan2(-ex, ey));
var theta2 = Angle.NormalizeRad(theta1 + System.Math.PI);
for (var k = 0; k < 2; k++)
{
if (lineEntities[j] is Line line)
{
var linePt = line.ClosestPointTo(arc.Center);
var arcPt = arc.ClosestPointTo(linePt);
var d = RayEdgeDistance(arcPt.X, arcPt.Y,
line.pt1.X, line.pt1.Y, line.pt2.X, line.pt2.Y,
dirX, dirY);
if (d < minDist) { minDist = d; if (d <= 0) return 0; }
}
var theta = k == 0 ? theta1 : theta2;
if (!Angle.IsBetweenRad(theta, arc.StartAngle, arc.EndAngle, arc.IsReversed))
continue;
var qx = cx + r * System.Math.Cos(theta);
var qy = cy + r * System.Math.Sin(theta);
var d = RayEdgeDistance(qx, qy, p1x, p1y, line.pt2.X, line.pt2.Y,
dirX, dirY);
if (d < minDist) { minDist = d; if (d <= 0) return 0; }
}
}
}