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| using UnityEngine; | |
| //https://www.cs.jhu.edu/~misha/MyPapers/EUROG20.pdf Appendix A | |
| namespace PolygonCenterFinder | |
| { | |
| public static class PolygonCenter | |
| { | |
| public static Vector2 GetPolygonCenter(Vector2[] verts) | |
| { | |
| var matA = CreateAMatrix(verts); | |
| var vecB = CreateBVector(verts); | |
| alglib.rmatrixsolve(matA, vecB.Length - 1, vecB, out _, out _, out var x); | |
| return FindCenter(verts, x); | |
| } | |
| /// <summary> | |
| /// Creates an (N+1)xN matrix with 1s in the final column | |
| /// </summary> | |
| /// <param name="verts"></param> | |
| /// <returns></returns> | |
| public static double[,] CreateAMatrix(Vector2[] verts) | |
| { | |
| var outMatrix = new double[verts.Length + 1, verts.Length]; | |
| for (var i = 0; i < verts.Length; i++) | |
| { | |
| for (var j = 0; j < verts.Length; j++) | |
| { | |
| for (var k = 0; k < verts.Length; k++) | |
| { | |
| var leftSide = Vector3.Cross(verts[j], verts[(k + 1) % verts.Length] - verts[k]); | |
| var rightSide = Vector3.Cross(verts[i], verts[(k + 1) % verts.Length] - verts[k]); | |
| outMatrix[i, j] += 2 * Vector3.Dot(leftSide, rightSide); | |
| } | |
| } | |
| } | |
| for (var i = 0; i < verts.Length; i++) | |
| { | |
| outMatrix[verts.Length, i] = 1f; | |
| } | |
| return outMatrix; | |
| } | |
| /// <summary> | |
| /// Creates an (N+1)x1 Vector | |
| /// </summary> | |
| /// <param name="vertices"></param> | |
| /// <returns></returns> | |
| public static double[] CreateBVector(Vector2[] vertices) | |
| { | |
| var outVector = new double[vertices.Length + 1]; | |
| for (var i = 0; i < vertices.Length; i++) | |
| { | |
| for (var k = 0; k < vertices.Length; k++) | |
| { | |
| var leftSide = Vector3.Cross(vertices[i], vertices[(k + 1) % vertices.Length] - vertices[k]); | |
| var rightSide = Vector3.Cross(vertices[(k + 1) % vertices.Length] - vertices[k], vertices[k]); | |
| outVector[i] += 2 * Vector3.Dot(leftSide, rightSide); | |
| } | |
| } | |
| outVector[vertices.Length] = 1d; | |
| return outVector; | |
| } | |
| public static Vector2 FindCenter(Vector2[] positions, double[] weights) | |
| { | |
| var weightedAverage = Vector2.zero; | |
| for (var i = 0; i < positions.Length; i++) | |
| { | |
| weightedAverage += positions[i] * (float)-weights[i]; | |
| } | |
| return weightedAverage; | |
| } | |
| } | |
| } |
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