feat(plateview): annotate overlap centroids

OpenNest.Core/Geometry/PolygonAreaMoments.cs

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+using System.Collections.Generic;
+
+namespace OpenNest.Geometry;
+
+/// <summary>
+/// Positive area and area centroid of a simple polygon, independent of winding.
+/// Moments are evaluated about a nearby origin rather than the world origin.
+/// </summary>
+public readonly struct PolygonAreaMoments
+{
+    private PolygonAreaMoments(double area, Vector centroid)
+    {
+        Area = area;
+        Centroid = centroid;
+    }
+
+    public double Area { get; }
+    public Vector Centroid { get; }
+
+    /// <summary>
+    /// Accepts an open vertex list or an exactly repeated closing vertex. Returns false
+    /// for degenerate or nonfinite moments; does not validate polygon topology.
+    /// </summary>
+    public static bool TryCompute(IReadOnlyList<Vector> vertices, out PolygonAreaMoments moments)
+    {
+        moments = default;
+        if (vertices == null || vertices.Count < 3)
+            return false;
+        foreach (var point in vertices)
+            if (!IsFinite(point))
+                return false;
+
+        var origin = vertices[0];
+        var count = vertices.Count;
+        if (vertices[count - 1].X == origin.X && vertices[count - 1].Y == origin.Y)
+            count--;
+        if (count < 3)
+            return false;
+
+        var twiceArea = 0.0;
+        var momentX = 0.0;
+        var momentY = 0.0;
+        // The closing edges meet the local origin and contribute zero. The signed
+        // triangle fan also handles concavity without averaging polygon vertices.
+        for (var i = 1; i + 1 < count; i++)
+        {
+            var a = vertices[i] - origin;
+            var b = vertices[i + 1] - origin;
+            var cross = a.X * b.Y - a.Y * b.X;
+            twiceArea += cross;
+            momentX += (a.X + b.X) * cross;
+            momentY += (a.Y + b.Y) * cross;
+        }
+
+        var area = System.Math.Abs(twiceArea) * 0.5;
+        if (!double.IsFinite(area) || area <= 0
+            || !double.IsFinite(momentX) || !double.IsFinite(momentY))
+            return false;
+        // Dividing signed moments by signed area cancels the winding, while Area
+        // stays positive so independently wound fragments always add material.
+        var centroid = origin + new Vector(momentX / twiceArea / 3, momentY / twiceArea / 3);
+        if (!IsFinite(centroid))
+            return false;
+        moments = new PolygonAreaMoments(area, centroid);
+        return true;
+    }
+
+    /// <summary>
+    /// Combines nonoverlapping, already hole-subtracted fragments using positive area
+    /// weights and another local origin. The centroid may lie outside the material.
+    /// Empty input or any invalid fragment fails the entire result.
+    /// </summary>
+    public static bool TryCombine(IEnumerable<PolygonAreaMoments> fragments, out PolygonAreaMoments moments)
+    {
+        moments = default;
+        if (fragments == null)
+            return false;
+        var area = 0.0;
+        var origin = Vector.Zero;
+        var firstMoment = Vector.Zero;
+        foreach (var fragment in fragments)
+        {
+            if (!double.IsFinite(fragment.Area) || fragment.Area <= 0 || !IsFinite(fragment.Centroid))
+                return false;
+            if (area == 0)
+                origin = fragment.Centroid;
+            firstMoment += (fragment.Centroid - origin) * fragment.Area;
+            area += fragment.Area;
+        }
+
+        if (!double.IsFinite(area) || area <= 0 || !IsFinite(firstMoment))
+            return false;
+        var centroid = origin + firstMoment / area;
+        if (!IsFinite(centroid))
+            return false;
+        moments = new PolygonAreaMoments(area, centroid);
+        return true;
+    }
+
+    private static bool IsFinite(Vector point) => double.IsFinite(point.X) && double.IsFinite(point.Y);
+}