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/tests/CMakeLists.txt

@@ -1,6 +1,8 @@
 add_executable(conformallab_tests
     test_clausen.cpp
     test_hyper_ideal_utility.cpp
+    test_matrix_utility.cpp
+    test_surface_curve_utility.cpp
 )
 
 target_include_directories(conformallab_tests SYSTEM PRIVATE

code/tests/test_matrix_utility.cpp

@@ -0,0 +1,40 @@
+// Port of de.varylab.discreteconformal.math.MatrixUtilityTest (Java/JUnit).
+
+#include "matrix_utility.hpp"
+
+#include <gtest/gtest.h>
+#include <Eigen/Dense>
+
+using Eigen::Matrix4d;
+using Eigen::Vector4d;
+using conformallab::makeMappingMatrix;
+
+TEST(MatrixUtilityTest, MakeMappingMatrix) {
+    // Source points (rows = homogeneous 4-vectors).
+    Matrix4d from;
+    from.row(0) = Vector4d(2, 0, 2, 1);
+    from.row(1) = Vector4d(1, 1, 0, 0);
+    from.row(2) = Vector4d(1, 0, 8, 0);
+    from.row(3) = Vector4d(3, 4, 0, 1);
+
+    // Target points.
+    Matrix4d to;
+    to.row(0) = Vector4d(2, 0, 1, 0);
+    to.row(1) = Vector4d(0, 3, 0, 2);
+    to.row(2) = Vector4d(1, 0, 4, 0);
+    to.row(3) = Vector4d(0, 3, 0, 5);
+
+    Matrix4d R = makeMappingMatrix(from, to);
+
+    // R must map each source column to the corresponding target column.
+    for (int i = 0; i < 4; i++) {
+        Vector4d result = R * from.row(i).transpose();
+        Vector4d expected = to.row(i).transpose();
+        for (int k = 0; k < 4; k++) {
+            // Java original uses 1e-15; double-precision matrix inversion gives ~2e-15
+        // rounding, so we use 1e-12 (still far below any meaningful error).
+        EXPECT_NEAR(expected(k), result(k), 1e-12)
+                << "Row " << i << ", component " << k;
+        }
+    }
+}

code/tests/test_surface_curve_utility.cpp

@@ -0,0 +1,55 @@
+// Port of de.varylab.discreteconformal.uniformization.SurfaceCurveUtilityTest
+// (Java/JUnit) — the two pure-math tests that don't need the HDS.
+
+#include "projective_math.hpp"
+
+#include <gtest/gtest.h>
+#include <Eigen/Dense>
+
+using Eigen::VectorXd;
+using conformallab::isOnSegment;
+using conformallab::getPointOnCorrespondingSegment;
+using conformallab::dehomogenize;
+
+// Helper: make VectorXd from initializer list.
+static VectorXd V(std::initializer_list<double> vals) {
+    VectorXd v(vals.size());
+    int i = 0;
+    for (double x : vals) v(i++) = x;
+    return v;
+}
+
+// A point exactly at the midpoint of segment lies on it; a slightly perturbed
+// point perpendicular to the segment does not.
+TEST(SurfaceCurveUtilityTest, IsOnSegment) {
+    VectorXd x1 = V({1, 1, 1, 1});
+    VectorXd x2 = V({1 + 1e-5, 1, 1, 1});
+    VectorXd s0 = V({0, 0, 0, 1});
+    VectorXd s1 = V({2, 2, 2, 1});
+
+    EXPECT_TRUE(isOnSegment(x1, s0, s1));
+    EXPECT_FALSE(isOnSegment(x2, s0, s1));
+}
+
+// The edge point coincides (within floating-point) with the END of the edge
+// segment, so the corresponding point on the target segment must be its end.
+TEST(SurfaceCurveUtilityTest, GetPointOnCorrespondingSegment_SegmentEdge) {
+    VectorXd edgePoint    = V({0.352392439203295, 0.9123804930829212, 1.0});
+    VectorXd edgeSrc0     = V({0.34745306897719913, 0.912568467121888, 1.0});
+    VectorXd edgeSrc1     = V({0.35239243920431296, 0.912380493082885, 1.0});
+    VectorXd tgt0         = V({-0.2896352574166635,  0.03146361746587523,
+                                0.10643898885661185,  0.44373020886051084});
+    VectorXd tgt1         = V({-0.2666822290964323,  0.019034256494171405,
+                                0.10525293907970201,  0.44373020886051084});
+
+    VectorXd result = getPointOnCorrespondingSegment(
+        edgePoint, edgeSrc0, edgeSrc1, tgt0, tgt1);
+
+    // Expected: dehomogenized tgt1 (edgePoint is at the end of the source segment).
+    VectorXd expected = dehomogenize(tgt1);
+
+    ASSERT_EQ(expected.size(), result.size());
+    for (int i = 0; i < result.size(); i++) {
+        EXPECT_NEAR(expected(i), result(i), 1e-9) << "component " << i;
+    }
+}