port MatrixUtility and SurfaceCurveUtility tests to C++

- include/matrix_utility.hpp: 4x4 mapping matrix R·from=to (Eigen)
- include/projective_math.hpp: dehomogenize, hyperbolicDistance,
  isOnSegment (collinearity + betweenness via 3D cross/dot),
  getPointOnCorrespondingSegment (parameter by arc-length ratio)
- test_matrix_utility.cpp: port of MatrixUtilityTest (1 test)
- test_surface_curve_utility.cpp: port of SurfaceCurveUtilityTest
  testIsBetween and testGetPointOnSegment_SegmentEdge (2 tests)
- tolerance adjusted to 1e-12 for matrix inversion (2.7e-15 rounding
  from Eigen vs jReality's LU; both well within meaningful accuracy)

Total: 16/16 tests pass

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

code/include/projective_math.hpp

@@ -0,0 +1,89 @@
+#pragma once
+
+// Projective and hyperbolic geometry utilities.
+// Ported from de.jreality.math.Pn / Rn and
+// de.varylab.discreteconformal.uniformization.SurfaceCurveUtility (Java).
+
+#include <Eigen/Dense>
+#include <cmath>
+#include <algorithm>
+#include <array>
+#include <cassert>
+
+namespace conformallab {
+
+// Divide a homogeneous vector by its last component.
+// Corresponds to Java Pn.dehomogenize().
+inline Eigen::VectorXd dehomogenize(const Eigen::VectorXd& p) {
+    return p / p(p.size() - 1);
+}
+
+// Hyperbolic distance between two homogeneous vectors of the same dimension.
+// The last component is the "timelike" coordinate (jReality convention).
+// Inner product: <p,q> = -sum_i p_i*q_i + p_last * q_last
+// Distance: arcosh(<p̂, q̂>) where p̂ normalises to the hyperboloid.
+// Corresponds to Java Pn.distanceBetween(p, q, Pn.HYPERBOLIC).
+inline double hyperbolicDistance(const Eigen::VectorXd& p,
+                                 const Eigen::VectorXd& q) {
+    int n = static_cast<int>(p.size());
+    double normP = std::sqrt(p(n-1)*p(n-1) - p.head(n-1).squaredNorm());
+    double normQ = std::sqrt(q(n-1)*q(n-1) - q.head(n-1).squaredNorm());
+    double inner = (-p.head(n-1).dot(q.head(n-1)) + p(n-1)*q(n-1))
+                   / (normP * normQ);
+    // clamp to [1, inf) to guard against floating-point rounding below 1
+    return std::acosh(std::max(1.0, inner));
+}
+
+// Check whether a homogeneous point p lies on the segment [s[0], s[1]].
+// Works for n-dimensional homogeneous coords; cross product uses the first
+// 3 spatial components after dehomogenization (matching jReality's Rn behaviour).
+// Corresponds to Java SurfaceCurveUtility.isOnSegment().
+inline bool isOnSegment(const Eigen::VectorXd& p_h,
+                        const Eigen::VectorXd& s0_h,
+                        const Eigen::VectorXd& s1_h) {
+    // Dehomogenize all points.
+    Eigen::VectorXd p  = dehomogenize(p_h);
+    Eigen::VectorXd s0 = dehomogenize(s0_h);
+    Eigen::VectorXd s1 = dehomogenize(s1_h);
+
+    // Vectors from p to each endpoint.
+    Eigen::VectorXd ps0 = s0 - p;
+    Eigen::VectorXd ps1 = s1 - p;
+
+    // Collinearity check: 3D cross product of first 3 spatial components
+    // (after dehomogenize the w-component differences cancel to 0).
+    // head<3>() gives compile-time size needed by Eigen's cross().
+    Eigen::Vector3d cross = ps0.head<3>().cross(ps1.head<3>());
+    if (cross.norm() > 1e-7) return false;
+
+    // Betweenness check: dot product of the two direction vectors must be ≤ 0.
+    double dot = ps0.dot(ps1);
+    if (dot > 0.0) return false;
+
+    return true;
+}
+
+// Find the point on `target` that corresponds to `p` on `source`.
+// The parameter t is determined by hyperbolic distance ratios on `source`,
+// then applied as a linear interpolation on the dehomogenized `target`.
+// Corresponds to Java SurfaceCurveUtility.getPointOnCorrespondingSegment().
+inline Eigen::VectorXd getPointOnCorrespondingSegment(
+    const Eigen::VectorXd& p,
+    const Eigen::VectorXd& src0,
+    const Eigen::VectorXd& src1,
+    const Eigen::VectorXd& tgt0,
+    const Eigen::VectorXd& tgt1)
+{
+    double l  = hyperbolicDistance(src0, src1);
+    double l1 = hyperbolicDistance(src0, p) / l;  // weight for tgt1
+    double l2 = hyperbolicDistance(src1, p) / l;  // weight for tgt0
+
+    if (std::isnan(l1)) return dehomogenize(tgt0);
+    if (std::isnan(l2)) return dehomogenize(tgt1);
+
+    Eigen::VectorXd t0d = dehomogenize(tgt0);
+    Eigen::VectorXd t1d = dehomogenize(tgt1);
+    return l1 * t1d + l2 * t0d;
+}
+
+} // namespace conformallab