Mesh Optimizer: sibling StaticMesh duplicate remover (UE 5.7)

Editor plugin that detects geometrically-identical sibling StaticMeshes across a
level, rebases each placement onto one canonical mesh with a corrected transform
(W' = D * W, verified by exact vertex matching), and can collapse groups into HISM.
Native Slate tool panel + BlueprintCallable UOptimizerSubsystem.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

Source/OptimizerEditor/Private/OptimizerGeometry.h

@@ -0,0 +1,53 @@
+// Copyright IHY.
+#pragma once
+
+#include "CoreMinimal.h"
+
+class UStaticMesh;
+
+/**
+ * Rotation/translation-invariant geometry fingerprint of a single UStaticMesh, plus the
+ * (lazily loaded) welded vertex cloud used for exact pairwise verification.
+ *
+ * Source is always LOD0 FMeshDescription (the imported authoring geometry) so the fingerprint
+ * is stable across LOD reduction / Nanite / build settings. Render data is a tagged fallback.
+ */
+struct FOptMeshGeom
+{
+	static constexpr int32 NumRadialBins = 16;
+
+	bool bValid = false;
+	bool bRenderDerived = false;   // true if extracted from render data (compare only against other render-derived)
+
+	int32 RawVertexCount = 0;
+	int32 WeldedVertexCount = 0;   // unique positions after welding -> the hard fingerprint gate
+	int32 TriangleCount = 0;
+
+	double SurfaceArea = 0.0;      // local space, rigid-invariant, scales as s^2
+	double Volume = 0.0;           // |signed tetrahedron sum|, scales as s^3
+	FVector Centroid = FVector::ZeroVector;            // mean of welded positions (local origin for cov/hist)
+	double EigenValues[3] = { 0.0, 0.0, 0.0 };         // covariance eigenvalues, sorted DESC (rotation-invariant)
+	double RadialHistogram[NumRadialBins] = { 0.0 };   // normalized hist of |v - centroid|
+	FBox LocalBounds = FBox(ForceInit);
+
+	// Heavy payload, populated only when this mesh enters pairwise recovery (bWantPositions).
+	TArray<FVector> Positions;     // welded unique positions, local space
+
+	// Material / section signature (NOT part of geometry grouping; used to partition for HISM).
+	uint32 MaterialHash = 0;
+	int32 SectionCount = 0;
+};
+
+namespace OptimizerGeometry
+{
+	/**
+	 * Extract the fingerprint (and optionally the welded position cloud) for a static mesh.
+	 * @param WeldEps   position weld grid in cm.
+	 * @param bWantPositions  also fill Out.Positions (the expensive part) for verification.
+	 * @return false if no usable geometry could be read.
+	 */
+	bool ExtractGeom(const UStaticMesh* Mesh, float WeldEps, bool bWantPositions, FOptMeshGeom& Out);
+
+	/** Symmetric 3x3 Jacobi eigensolver. Eigenvalues returned sorted DESC; eigenvectors as columns of OutVecs. */
+	void SymmetricEigen3x3(const double M[3][3], double OutValues[3], double OutVecs[3][3]);
+}