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Impl marching cubes - #70
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Pull request overview
This PR implements/updates marching-cubes tessellation for implicit solids and adds supporting numeric utilities intended to enable additional geometry operations (e.g., solving small linear systems for optimization steps).
Changes:
- Add
Matrix4x4 * Vector4andMatrix4x4.Solve(Vector4)extension helpers in Numerics. - Update marching-cubes implicit generation to precompute axis intersections and tessellate only candidate cubes; expose cube processing as
virtualand add identifier→indices decoding. - Refactor/replace the SQP-based quadric distance computation to use
Matrix4x4/Vector4solves.
Reviewed changes
Copilot reviewed 4 out of 4 changed files in this pull request and generated 4 comments.
| File | Description |
|---|---|
| TessellationAndVoxelizationGeometryLibrary/Numerics/Extensions.cs | Adds matrix→vector multiplication and Ax=b solve helpers for 4x4 systems. |
| TessellationAndVoxelizationGeometryLibrary/MarchingCubes/MarchingCubes.Implicit.cs | Changes implicit marching-cubes generation to focus cube processing around precomputed intersections and overrides cube face generation. |
| TessellationAndVoxelizationGeometryLibrary/MarchingCubes/MarchingCubes.Base.cs | Adds identifier decoding helper, makes cube processing virtual, and alters value caching behavior. |
| TessellationAndVoxelizationGeometryLibrary/Implicits and Primitives/Primitive Surfaces/GeneralQuadric.cs | Updates SQP distance approach to a Matrix4x4/Vector4-based solve loop. |
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| public override double DistanceToPoint(Vector3 point) | ||
| { | ||
| Vector3 startPoint = GetPointNearQuadric(point); | ||
| double[] u = { startPoint.X, startPoint.Y, startPoint.Z, 0 }; | ||
| double[] du = { double.PositiveInfinity, double.PositiveInfinity, double.PositiveInfinity, double.PositiveInfinity }; | ||
| int iters = 0; | ||
| while (iters < 1000 && (du[0] * du[0] + du[1] * du[1] + du[2] * du[2] + du[3] * du[3]) < 1E-6) { | ||
| double[,] H = { { 2 + 2 * XSqdCoeff * u[3], XYCoeff * u[3], XZCoeff * u[3], 2 * XSqdCoeff * u[0] + XYCoeff * u[1] + XZCoeff * u[2] + XCoeff }, | ||
| { XYCoeff * u[3], 2 + 2 * YSqdCoeff * u[3], YZCoeff * u[3], 2 * YSqdCoeff * u[1] + XYCoeff * u[0] + YZCoeff * u[2] + YCoeff }, | ||
| { XZCoeff * u[3], YZCoeff * u[3], 2 + 2 * ZSqdCoeff * u[3], 2 * YSqdCoeff * u[2] + XZCoeff * u[0] + YZCoeff * u[1] + ZCoeff }, | ||
| { 2 * XSqdCoeff * u[0] + XYCoeff * u[1] + XZCoeff * u[2] + XCoeff, 2 * YSqdCoeff * u[1] + XYCoeff * u[0] + YZCoeff * u[2] + YCoeff, 2 * YSqdCoeff * u[2] + XZCoeff * u[0] + YZCoeff * u[1] + ZCoeff, 0} }; | ||
| double[] RHS = { 2 * (u[0] - point.X) + u[3] * (2 * XSqdCoeff * u[0] + XYCoeff * u[1] + XZCoeff * u[2] + XCoeff), | ||
| 2 * (u[1] - point.Y) + 2 * YSqdCoeff * u[1] + XYCoeff * u[0] + YZCoeff * u[2] + YCoeff, | ||
| 2 * (u[2] - point.Z) + 2 * YSqdCoeff * u[2] + XZCoeff * u[0] + YZCoeff * u[1] + ZCoeff, | ||
| QuadricValue(new Vector3(u[..3]))}; | ||
| StarMath.solve(H, RHS, out du, true); | ||
| u[0] += du[0]; | ||
| u[1] += du[1]; | ||
| u[2] += du[2]; | ||
| u[3] += du[3]; | ||
| var closestPt = GetPointOnQuadric(point); | ||
| var closestPt4 = new Vector4(closestPt, 0); // the fourth number "w" here represents the Lagrange multiplier | ||
| var delta = Vector4.Zero; |
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| XZCoeff * closestPt4.W, YZCoeff * closestPt4.W, 2 + 2 * ZSqdCoeff * closestPt4.W, 2 * YSqdCoeff * closestPt4.Z + XZCoeff * closestPt4.X + YZCoeff * closestPt4.Y + ZCoeff, | ||
| 2 * XSqdCoeff * closestPt4.X + XYCoeff * closestPt4.Y + XZCoeff * closestPt4.Z + XCoeff, 2 * YSqdCoeff * closestPt4.Y + XYCoeff * closestPt4.X + YZCoeff * closestPt4.Z + YCoeff, 2 * YSqdCoeff * closestPt4.Z + XZCoeff * closestPt4.X + YZCoeff * closestPt4.Y + ZCoeff, 0); |
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| var rhs = new Vector4( | ||
| 2 * (closestPt4.X - point.X) + closestPt4.W * (2 * XSqdCoeff * closestPt4.X + XYCoeff * closestPt4.Y + XZCoeff * closestPt4.Z + XCoeff), | ||
| 2 * (closestPt4.Y - point.Y) + 2 * YSqdCoeff * closestPt4.Y + XYCoeff * closestPt4.X + YZCoeff * closestPt4.Z + YCoeff, | ||
| 2 * (closestPt4.Z - point.Z) + 2 * YSqdCoeff * closestPt4.Z + XZCoeff * closestPt4.X + YZCoeff * closestPt4.Y + ZCoeff, | ||
| QuadricValue(closestPt)); |
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| if (valueDictionary.TryGetValue(identifier, out var prevValue)) | ||
| { | ||
| if (prevValue.NumTimesCalled < 7) | ||
| prevValue.NumTimesCalled++; | ||
| else valueDictionary.Remove(identifier); | ||
| //if (prevValue.NumTimesCalled < 7) | ||
| // prevValue.NumTimesCalled++; | ||
| //else valueDictionary.Remove(identifier); | ||
| return prevValue; |
micampbell
commented
Aug 2, 2026
MemberAuthor
code has already been merged |
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