e958afbd19
Unified the codebase language to English throughout. German text appeared in code comments, test file headers, CI step names, and several markdown documents. All natural-language text is now English; proper nouns (Institut für Mathematik, Technische Universität Berlin) are unchanged. Files changed: - .gitea/workflows/cpp-tests.yml — CI step names and job comments - code/include/mesh_utils.hpp — inline comment - code/tests/cgal/CMakeLists.txt — section comment block - code/tests/cgal/test_geometry_utils.cpp — full file header + all test comments - doc/math/references.md — geometry-central section - doc/math/validation.md — Section 9 (geometry-central cross-validation) - doc/roadmap/phases.md — Optional geometry-central track (GC-1/2/3) Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
511 lines
26 KiB
C++
511 lines
26 KiB
C++
// test_geometry_utils.cpp
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//
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// Port of the Java ConformalLab geometry utility tests.
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//
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// Java source Java test method Status
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// ─────────────────────────────────────────────────────────────────────────────────────
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// CuttinUtilityTest.java testIsInConvexTextureFace_False PORTED
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// CuttinUtilityTest.java testIsInConvexTextureFace_True PORTED
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// UnwrapUtilityTest.java testGetAngleReturnsPI PORTED
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// ConvergenceUtilityTests.java testGetTextureCircumRadius PORTED
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// ConvergenceUtilityTests.java testGetTextureTriangleArea PORTED
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// ConvergenceUtilityTests.java testScaleInvariantCircumCircleRadius PORTED
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// HomologyTest.java testHomology PORTED
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// EuclideanLayoutTest.java testDoLayout PORTED
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// EuclideanCyclicConvergenceTest.java testEuclideanConvergence PORTED
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// SphericalConvergenceTest.java testSphericalConvergence PORTED
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//
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// ─── Geometric background ────────────────────────────────────────────────────────────
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//
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// Tests 1–2 Point-in-convex-triangle (2D UV space, barycentric sign method)
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// Java: CuttingUtility.isInConvexTextureFace(pp, face, adapters)
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// Note: Java test 2 has a 5-element T-array with w=0 (point at
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// infinity), which is a typo in the original. Equivalent, well-formed
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// coordinates are used here instead.
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//
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// Test 3 Corner angle for collinear vertices via the law of cosines.
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// Java: UnwrapUtility.getAngle(edge, adapters) — returns the angle at
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// the target vertex. For v0=(-1,0,0), v1=(0,0,0), v2=(1,0,0) the
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// angle at v1 is exactly π (degenerate triangle inequality).
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//
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// Tests 4–5 2D circumradius and triangle area.
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// Java: ConvergenceUtility.getTextureCircumCircleRadius(face)
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// ConvergenceUtility.getTextureTriangleArea(face)
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// Formulas: Area = |det([B-A, C-A])| / 2
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// R = (a·b·c) / (4·Area)
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//
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// Test 6 Scale-invariant circumradius over a mesh.
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// Java: ConvergenceUtility.getMaxMeanSumScaleInvariantCircumRadius(hds)
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// Returns [max, mean, sum] of R_f / sqrt(total_texture_area).
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// Invariant under uniform scaling of texture coordinates (tested with
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// homogeneous weight w: position = (T[0]/w, T[1]/w)).
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//
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// Test 7 Genus-2 homology generators.
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// Java: HomologyTest.testHomology (brezel2.obj)
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// Expected: getGeneratorPaths(root).size() == 4 (2g = 4 for g = 2)
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// C++: compute_cut_graph(mesh).cut_edge_indices.size() == 4
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// Mesh: code/data/obj/brezel2.obj (V=2622, F=5248, χ=−2, g=2)
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// Path set at compile time via CONFORMALLAB_DATA_DIR (CMakeLists.txt).
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//
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// Tests 8–9 Layout edge-length preservation (tetraflat.obj).
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// Java: EuclideanLayoutTest.testDoLayout
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// After layout with u=0, UV edge lengths must equal 3D edge lengths (±1e-10).
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//
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// Test 10 Euclidean Newton on cathead.obj — convergence + angle deficit.
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// Java: EuclideanLayoutTest.testLayout02 (130-value array for cathead.heml)
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// C++: Newton from u=0, checks convergence + Σα_v ≈ 2π for all interior nodes.
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//
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// Test 11 Spherical Newton on octahedron — convergence + angle deficit.
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// Java: SphericalConvergenceTest.testSphericalConvergence (octahedron, randomly
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// perturbed radii, seed=1). C++: constructed regular octahedron, checks
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// convergence and that Σα_v ≈ 2π (target for sphere after prepareInvariantData).
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//
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// ─────────────────────────────────────────────────────────────────────────────────────
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#include "cut_graph.hpp"
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#include "gauss_bonnet.hpp"
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#include "conformal_mesh.hpp"
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#include "mesh_builder.hpp"
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#include "mesh_io.hpp"
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#include "euclidean_functional.hpp"
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#include "spherical_functional.hpp"
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#include "newton_solver.hpp"
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#include "layout.hpp"
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#include <gtest/gtest.h>
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#include <Eigen/Dense>
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#include <array>
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#include <cmath>
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#include <string>
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#include <vector>
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using namespace conformallab;
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// ─────────────────────────────────────────────────────────────────────────────
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// Local geometry helper functions
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// (ported from Java CuttingUtility / ConvergenceUtility)
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// ─────────────────────────────────────────────────────────────────────────────
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/// Point-in-triangle test (2D, barycentric sign method).
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/// Returns true if p lies strictly inside or on the boundary of v0-v1-v2.
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/// Java: CuttingUtility.isInConvexTextureFace
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static bool point_in_triangle_2d(
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Eigen::Vector2d p,
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Eigen::Vector2d v0, Eigen::Vector2d v1, Eigen::Vector2d v2)
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{
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auto cross2d = [](Eigen::Vector2d a, Eigen::Vector2d b) -> double {
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return a.x() * b.y() - a.y() * b.x();
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};
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double d0 = cross2d(v1 - v0, p - v0);
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double d1 = cross2d(v2 - v1, p - v1);
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double d2 = cross2d(v0 - v2, p - v2);
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bool has_neg = (d0 < 0.0) || (d1 < 0.0) || (d2 < 0.0);
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bool has_pos = (d0 > 0.0) || (d1 > 0.0) || (d2 > 0.0);
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return !(has_neg && has_pos);
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}
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/// 2D triangle area (half cross product).
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/// Java: ConvergenceUtility.getTextureTriangleArea
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static double triangle_area_2d(
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Eigen::Vector2d A, Eigen::Vector2d B, Eigen::Vector2d C)
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{
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return std::abs((B - A).x() * (C - A).y()
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- (B - A).y() * (C - A).x()) * 0.5;
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}
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/// 2D circumradius: R = (a·b·c) / (4·Area).
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/// Java: ConvergenceUtility.getTextureCircumCircleRadius
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static double circumradius_2d(
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Eigen::Vector2d A, Eigen::Vector2d B, Eigen::Vector2d C)
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{
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double a = (B - C).norm();
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double b = (A - C).norm();
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double c = (A - B).norm();
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double area = triangle_area_2d(A, B, C);
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if (area < 1e-14) return 0.0;
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return (a * b * c) / (4.0 * area);
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}
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/// Scale-invariant circumradius for a mesh:
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/// scale_R_f = R_f / sqrt(total_area)
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/// Returns {max, mean, sum} over all faces.
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/// Java: ConvergenceUtility.getMaxMeanSumScaleInvariantCircumRadius
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///
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/// Homogeneous coordinates: position = (x/w, y/w).
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static std::array<double, 3> scale_invariant_circumradius_stats(
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const std::vector<Eigen::Vector2d>& verts,
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const std::vector<std::array<int, 3>>& faces)
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{
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// Total area
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double total_area = 0.0;
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for (auto& f : faces)
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total_area += triangle_area_2d(verts[f[0]], verts[f[1]], verts[f[2]]);
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if (total_area < 1e-14) return {0, 0, 0};
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double sqrt_total = std::sqrt(total_area);
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double max_r = 0.0, sum_r = 0.0;
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for (auto& f : faces) {
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double R = circumradius_2d(verts[f[0]], verts[f[1]], verts[f[2]]);
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double sr = R / sqrt_total;
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max_r = std::max(max_r, sr);
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sum_r += sr;
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}
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double mean_r = sum_r / static_cast<double>(faces.size());
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return {max_r, mean_r, sum_r};
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}
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// ════════════════════════════════════════════════════════════════════════════
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// Tests 1–2 — CuttingUtility: point-in-convex-triangle (2D UV space)
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// Java: CuttinUtilityTest.testIsInConvexTextureFace_False / _True
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// ════════════════════════════════════════════════════════════════════════════
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// Test 1: point lies far outside — exact Java coordinates
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TEST(CuttingUtility, IsInConvexTextureFace_False)
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{
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// Tiny triangle around (0.7488, 0.0629) — Java test coordinates (T[3]=1, w=1)
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Eigen::Vector2d v0(0.7488102998904661, 0.06293998610761144);
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Eigen::Vector2d v1(0.7487811940754379, 0.06289451051246124);
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Eigen::Vector2d v2(0.7487254625255592, 0.06291429499873116);
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// Test point far away at (0.447, 0.000228)
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Eigen::Vector2d pp(0.44661534423161037, 2.2808373704822393e-4);
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EXPECT_FALSE(point_in_triangle_2d(pp, v0, v1, v2));
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}
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// Test 2: point lies inside
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// Note: the original Java array p2 has 5 elements with w=0 (typo in the
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// Java original). Equivalent, well-formed coordinates are used here
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// that represent the same geometric scenario.
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TEST(CuttingUtility, IsInConvexTextureFace_True)
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{
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// Triangle: (0,0) — (1e-8, 0) — (0, 1e-8)
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Eigen::Vector2d v0(0.0, 0.0);
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Eigen::Vector2d v1(1e-8, 0.0);
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Eigen::Vector2d v2(0.0, 1e-8);
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// Centroid of the triangle — always lies inside
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Eigen::Vector2d pp(1e-8 / 3.0, 1e-8 / 3.0);
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EXPECT_TRUE(point_in_triangle_2d(pp, v0, v1, v2));
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}
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// Additional: simple unit triangle for clarity
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TEST(CuttingUtility, IsInConvexTextureFace_UnitTriangle_InAndOut)
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{
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Eigen::Vector2d v0(0.0, 0.0), v1(1.0, 0.0), v2(0.0, 1.0);
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EXPECT_TRUE( point_in_triangle_2d(Eigen::Vector2d(0.25, 0.25), v0, v1, v2));
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EXPECT_FALSE(point_in_triangle_2d(Eigen::Vector2d(2.0, 2.0), v0, v1, v2));
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EXPECT_FALSE(point_in_triangle_2d(Eigen::Vector2d(0.6, 0.6), v0, v1, v2)); // beyond hypotenuse
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}
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// ════════════════════════════════════════════════════════════════════════════
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// Test 3 — UnwrapUtility: corner angle = π for collinear vertices
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// Java: UnwrapUtilityTest.testGetAngleReturnsPI
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// ════════════════════════════════════════════════════════════════════════════
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// Java: v0=(-1,0,0), v1=(0,0,0), v2=(1,0,0) collinear.
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// Edge e from v2 to v1. getAngle(e) = angle at v1 = π.
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//
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// C++: law of cosines with edge lengths a=|v0-v1|=1, b=|v1-v2|=1, c=|v0-v2|=2.
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// cos(γ_v1) = (a² + b² − c²) / (2ab) = (1 + 1 − 4) / 2 = −1 → γ = π
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TEST(UnwrapUtility, GetAngle_CollinearVertices_ReturnsPI)
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{
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const double a = 1.0; // |v0 − v1|
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const double b = 1.0; // |v1 − v2|
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const double c = 2.0; // |v0 − v2| (= a + b, degenerate)
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double cos_angle = (a*a + b*b - c*c) / (2.0 * a * b);
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cos_angle = std::max(-1.0, std::min(1.0, cos_angle)); // numeric clamp
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double angle = std::acos(cos_angle);
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EXPECT_NEAR(M_PI, angle, 1e-15);
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}
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// Counter-check: equilateral triangle → angle = π/3
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TEST(UnwrapUtility, GetAngle_EquilateralTriangle_ReturnsPiOver3)
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{
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const double s = 1.0;
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double cos_angle = (s*s + s*s - s*s) / (2.0 * s * s); // = 0.5
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double angle = std::acos(cos_angle);
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EXPECT_NEAR(M_PI / 3.0, angle, 1e-15);
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}
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// ════════════════════════════════════════════════════════════════════════════
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// Test 4 — ConvergenceUtility: 2D circumradius
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// Java: ConvergenceUtilityTests.testGetTextureCircumRadius
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// ════════════════════════════════════════════════════════════════════════════
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TEST(ConvergenceUtility, TextureCircumRadius_RightTriangle)
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{
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// A=(0,0), B=(1,0), C=(0,1): right isosceles triangle
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// Sides: 1, 1, √2. R = √2 / (4 · 0.5) = √2/2
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Eigen::Vector2d A(0.0, 0.0), B(1.0, 0.0), C(0.0, 1.0);
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EXPECT_NEAR(std::sqrt(2.0) / 2.0, circumradius_2d(A, B, C), 1e-10);
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}
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TEST(ConvergenceUtility, TextureCircumRadius_SmallerTriangle)
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{
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// A=(0,0), B=(0.5,0.5), C=(0,1): Java variant with B.T={0.5,0.5,0,1}
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// Sides: √0.5, √0.5, 1. Area = 0.25. R = (√0.5·√0.5·1)/(4·0.25) = 0.5
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Eigen::Vector2d A(0.0, 0.0), B(0.5, 0.5), C(0.0, 1.0);
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EXPECT_NEAR(0.5, circumradius_2d(A, B, C), 1e-10);
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}
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// ════════════════════════════════════════════════════════════════════════════
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// Test 5 — ConvergenceUtility: 2D triangle area
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// Java: ConvergenceUtilityTests.testGetTextureTriangleArea
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// ════════════════════════════════════════════════════════════════════════════
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TEST(ConvergenceUtility, TextureTriangleArea_RightTriangle)
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{
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// A=(0,0), B=(1,0), C=(0,1) → area = 0.5
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Eigen::Vector2d A(0.0, 0.0), B(1.0, 0.0), C(0.0, 1.0);
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EXPECT_NEAR(0.5, triangle_area_2d(A, B, C), 1e-10);
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}
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TEST(ConvergenceUtility, TextureTriangleArea_SmallerTriangle)
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{
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// A=(0,0), B=(0.5,0.5), C=(0,1) → area = 0.25
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Eigen::Vector2d A(0.0, 0.0), B(0.5, 0.5), C(0.0, 1.0);
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EXPECT_NEAR(0.25, triangle_area_2d(A, B, C), 1e-10);
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}
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// ════════════════════════════════════════════════════════════════════════════
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// Test 6 — ConvergenceUtility: scale-invariant circumradius
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// Java: ConvergenceUtilityTests.testScaleInvariantCircumCircleRadius
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//
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// Mesh: 4 vertices (v1..v4), 2 faces (f1: v1-v2-v3, f2: v1-v3-v4).
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// Scale-invariant quantity: R_f / sqrt(total_area) — invariant under
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// uniform scaling (homogeneous weight w: pos = (x/w, y/w)).
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// ════════════════════════════════════════════════════════════════════════════
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TEST(ConvergenceUtility, ScaleInvariantCircumRadius_BaseScale)
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{
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// Positions at w=1 (T[3]=1): v1=(0,0), v2=(1,0), v3=(0,1), v4=(-1,0)
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std::vector<Eigen::Vector2d> verts = {
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{0.0, 0.0}, // v1
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{1.0, 0.0}, // v2
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{0.0, 1.0}, // v3
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{-1.0, 0.0}, // v4
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};
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// f1: v1-v2-v3, f2: v1-v3-v4
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std::vector<std::array<int, 3>> faces = { {0, 1, 2}, {0, 2, 3} };
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// Per-face check (Java testGetTextureTriangleArea requirement)
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EXPECT_NEAR(0.5, triangle_area_2d(verts[0], verts[1], verts[2]), 1e-10);
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EXPECT_NEAR(0.5, triangle_area_2d(verts[0], verts[2], verts[3]), 1e-10);
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auto [max_r, mean_r, sum_r] = scale_invariant_circumradius_stats(verts, faces);
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// Expected: sin(π/4) = √2/2 for max and mean (both triangles identical)
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EXPECT_NEAR(std::sin(M_PI / 4.0), max_r, 1e-10);
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EXPECT_NEAR(std::sin(M_PI / 4.0), mean_r, 1e-10);
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EXPECT_NEAR(2.0 * std::sin(M_PI / 4.0), sum_r, 1e-10);
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}
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TEST(ConvergenceUtility, ScaleInvariantCircumRadius_HalvedByW2_SameResult)
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{
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// Scaling by w=2: all positions halved (homogeneous coordinates)
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// pos_scaled = (T[0]/2, T[1]/2)
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std::vector<Eigen::Vector2d> verts = {
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{0.0, 0.0}, // v1/2
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{0.5, 0.0}, // v2/2
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{0.0, 0.5}, // v3/2
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{-0.5, 0.0}, // v4/2
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};
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std::vector<std::array<int, 3>> faces = { {0, 1, 2}, {0, 2, 3} };
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// Areas are one quarter of the original (lengths halved → Area / 4)
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EXPECT_NEAR(0.125, triangle_area_2d(verts[0], verts[1], verts[2]), 1e-10);
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EXPECT_NEAR(0.125, triangle_area_2d(verts[0], verts[2], verts[3]), 1e-10);
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auto [max_r, mean_r, sum_r] = scale_invariant_circumradius_stats(verts, faces);
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// Scale-invariant quantity must be identical to the w=1 case
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EXPECT_NEAR(std::sin(M_PI / 4.0), max_r, 1e-10);
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EXPECT_NEAR(std::sin(M_PI / 4.0), mean_r, 1e-10);
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EXPECT_NEAR(2.0 * std::sin(M_PI / 4.0), sum_r, 1e-10);
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}
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// ════════════════════════════════════════════════════════════════════════════
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// Test 7 — HomologyTest: genus-2 homology generators
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// Java: HomologyTest.testHomology
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//
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// Java test:
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// CoHDS hds = TestUtility.readOBJ("brezel2.obj"); // genus-2 pretzel surface
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// List<Set<CoEdge>> paths = getGeneratorPaths(hds.getVertex(0), weightAdapter);
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// Assert.assertEquals(4, paths.size()); // 2g = 4 for g = 2
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//
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// C++ equivalent:
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// ConformalMesh mesh = load_mesh("code/data/obj/brezel2.obj");
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// CutGraph cg = compute_cut_graph(mesh);
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// EXPECT_EQ(4u, cg.cut_edge_indices.size()); // 2g = 4
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// EXPECT_EQ(2, cg.genus);
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//
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// Mesh: V=2622, F=5248, E=7872, χ=−2, genus=2.
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// Path via CONFORMALLAB_DATA_DIR (CMakeLists.txt: ${CMAKE_SOURCE_DIR}/data).
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// ════════════════════════════════════════════════════════════════════════════
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TEST(HomologyGenerators, Genus2_FourCutEdges)
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{
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const std::string path = std::string(CONFORMALLAB_DATA_DIR) + "/obj/brezel2.obj";
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ConformalMesh mesh;
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ASSERT_NO_THROW(mesh = load_mesh(path)) << "brezel2.obj not found at: " << path;
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// Topology check: genus-2 surface has χ = -2.
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EXPECT_EQ(-2, euler_characteristic(mesh));
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// Tree-cotree algorithm must produce exactly 2g = 4 cut edges.
|
||
CutGraph cg = compute_cut_graph(mesh);
|
||
EXPECT_EQ(4u, cg.cut_edge_indices.size())
|
||
<< "Genus-2 surface must have 2g = 4 cut edges (homology generators).";
|
||
EXPECT_EQ(2, cg.genus);
|
||
}
|
||
|
||
// ════════════════════════════════════════════════════════════════════════════
|
||
// Tests 8–9 — EuclideanLayoutTest: edge-length preservation on tetraflat.obj
|
||
// Java: EuclideanLayoutTest.testDoLayout
|
||
//
|
||
// Java test:
|
||
// Vector u = new SparseVector(n); // u = 0 (no conformal factor)
|
||
// EuclideanLayout.doLayout(hds, fun, u);
|
||
// for (CoEdge e : hds.getEdges())
|
||
// assertEquals(Pn.distanceBetween(s.P, t.P), Pn.distanceBetween(s.T, t.T), 1E-11);
|
||
//
|
||
// Meaning: with u=0 the conformal factor is 0, so ℓ̃ = ℓ (no deformation).
|
||
// The layout must reproduce the original 3D edge lengths exactly.
|
||
// ════════════════════════════════════════════════════════════════════════════
|
||
|
||
TEST(EuclideanLayout, DoLayout_TetraFlat_EdgeLengthsPreserved)
|
||
{
|
||
const std::string path = std::string(CONFORMALLAB_DATA_DIR) + "/obj/tetraflat.obj";
|
||
ConformalMesh mesh;
|
||
ASSERT_NO_THROW(mesh = load_mesh(path)) << "tetraflat.obj not found at: " << path;
|
||
|
||
auto maps = setup_euclidean_maps(mesh);
|
||
compute_euclidean_lambda0_from_mesh(mesh, maps);
|
||
|
||
// u = 0: no conformal deformation — layout must preserve 3D edge lengths exactly.
|
||
// tetraflat.obj is an open mesh; pin boundary vertices, sequential DOFs interior.
|
||
int idx = 0;
|
||
for (auto v : mesh.vertices())
|
||
maps.v_idx[v] = mesh.is_border(v) ? -1 : idx++;
|
||
const int n = idx;
|
||
std::vector<double> x(static_cast<std::size_t>(n), 0.0);
|
||
|
||
Layout2D layout = euclidean_layout(mesh, x, maps);
|
||
|
||
// For every edge: UV length must equal 3D length within 1e-10.
|
||
for (auto e : mesh.edges()) {
|
||
auto h = mesh.halfedge(e);
|
||
auto vs = mesh.source(h);
|
||
auto vt = mesh.target(h);
|
||
|
||
auto ps = mesh.point(vs);
|
||
auto pt = mesh.point(vt);
|
||
double l3d = std::sqrt(
|
||
(pt.x()-ps.x())*(pt.x()-ps.x()) +
|
||
(pt.y()-ps.y())*(pt.y()-ps.y()) +
|
||
(pt.z()-ps.z())*(pt.z()-ps.z()));
|
||
|
||
auto us = layout.uv[vs.idx()];
|
||
auto ut = layout.uv[vt.idx()];
|
||
double luv = (ut - us).norm();
|
||
|
||
EXPECT_NEAR(l3d, luv, 1e-10)
|
||
<< "Edge " << e.idx() << ": 3D=" << l3d << " UV=" << luv;
|
||
}
|
||
}
|
||
|
||
// ════════════════════════════════════════════════════════════════════════════
|
||
// Test 10 — EuclideanCyclicConvergenceTest: Newton on cathead.obj
|
||
// Java: EuclideanLayoutTest.testLayout02 (130-value regression on cathead.heml)
|
||
// EuclideanCyclicConvergenceTest.testEuclideanConvergence
|
||
//
|
||
// Java test:
|
||
// EuclideanLayout.doLayout(hdsCat, fun, uCat);
|
||
// for (CoVertex v : interior vertices)
|
||
// assertEquals(2*PI, calculateAngleSum(v), 1E-6);
|
||
// for (CoEdge e : positiveEdges)
|
||
// assertEquals(fun.getNewLength(e, u), tLength, 1E-6);
|
||
//
|
||
// C++ equivalent: Newton converges on cathead.obj; interior angle sums ≈ 2π.
|
||
// The 130-value u-vector from the Java test is cathead-topology-specific and
|
||
// depends on vertex ordering in the Java CoHDS — not portable directly.
|
||
// Instead we verify the same mathematical invariant: convergence + angle sums.
|
||
// ════════════════════════════════════════════════════════════════════════════
|
||
|
||
TEST(EuclideanLayout, CatHead_NewtonConverges_AngleSumsTwoPi)
|
||
{
|
||
const std::string path = std::string(CONFORMALLAB_DATA_DIR) + "/obj/cathead.obj";
|
||
ConformalMesh mesh;
|
||
ASSERT_NO_THROW(mesh = load_mesh(path)) << "cathead.obj not found at: " << path;
|
||
|
||
auto maps = setup_euclidean_maps(mesh);
|
||
compute_euclidean_lambda0_from_mesh(mesh, maps);
|
||
|
||
// cathead.obj is an open mesh (boundary present).
|
||
// Pin boundary vertices (v_idx = -1), assign sequential DOFs to interior.
|
||
int idx = 0;
|
||
for (auto v : mesh.vertices())
|
||
maps.v_idx[v] = mesh.is_border(v) ? -1 : idx++;
|
||
const int n = idx;
|
||
ASSERT_GT(n, 0) << "No interior vertices found in cathead.obj";
|
||
|
||
enforce_gauss_bonnet(mesh, maps);
|
||
|
||
std::vector<double> x0(static_cast<std::size_t>(n), 0.0);
|
||
|
||
auto res = newton_euclidean(mesh, x0, maps, 1e-8, 200);
|
||
EXPECT_TRUE(res.converged)
|
||
<< "Newton did not converge on cathead.obj (iterations=" << res.iterations
|
||
<< ", |G|inf=" << res.grad_inf_norm << ")";
|
||
EXPECT_LT(res.grad_inf_norm, 1e-8);
|
||
EXPECT_LT(res.iterations, 200);
|
||
|
||
// After convergence: all interior vertex angle sums must equal θ_v (2π for flat).
|
||
// Matches Java: assertEquals(2*PI, calculateAngleSum(v), 1E-6) for interior v.
|
||
auto G_final = euclidean_gradient(mesh, res.x, maps);
|
||
for (std::size_t i = 0; i < G_final.size(); ++i)
|
||
EXPECT_NEAR(0.0, G_final[i], 1e-6)
|
||
<< "Angle sum residual at DOF " << i << " = " << G_final[i];
|
||
}
|
||
|
||
// ════════════════════════════════════════════════════════════════════════════
|
||
// Test 11 — SphericalConvergenceTest: Newton on octahedron
|
||
// Java: SphericalConvergenceTest.testSphericalConvergence
|
||
//
|
||
// Java test:
|
||
// FunctionalTest.createOctahedron(hds, aSet);
|
||
// // randomly perturb vertex radii (seed=1)
|
||
// prepareInvariantDataHyperbolicAndSpherical(functional, hds, aSet, u);
|
||
// optimizer.minimize(u, opt);
|
||
// for (CoVertex v) assertEquals(2*PI, sum of angles at v, 1E-8);
|
||
//
|
||
// C++: regular octahedron (all vertices on S², no perturbation), spherical Newton,
|
||
// checks convergence + residual gradients (≡ angle deficit = 0 after convergence).
|
||
// ════════════════════════════════════════════════════════════════════════════
|
||
|
||
TEST(SphericalLayout, SphericalTetrahedron_NewtonConverges_AngleSumsTwoPi)
|
||
{
|
||
// Build a spherical tetrahedron (genus 0, 4 vertices, 4 faces).
|
||
// Java uses a randomly-perturbed octahedron; we use the canonical
|
||
// spherical tetrahedron from mesh_builder.hpp for reproducibility.
|
||
ConformalMesh mesh = make_spherical_tetrahedron();
|
||
|
||
auto maps = setup_spherical_maps(mesh);
|
||
compute_lambda0_from_mesh(mesh, maps); // SphericalMaps version
|
||
int n = assign_vertex_dof_indices(mesh, maps); // pins gauge_vertex, assigns DOFs
|
||
// Note: enforce_gauss_bonnet not needed — natural theta from mesh satisfies Σ(2π-Θ)>0.
|
||
|
||
std::vector<double> x0(static_cast<std::size_t>(n), 0.0);
|
||
|
||
auto res = newton_spherical(mesh, x0, maps, 1e-8, 200);
|
||
EXPECT_TRUE(res.converged)
|
||
<< "Spherical Newton did not converge (iterations=" << res.iterations
|
||
<< ", |G|inf=" << res.grad_inf_norm << ")";
|
||
EXPECT_LT(res.grad_inf_norm, 1e-8);
|
||
|
||
// Angle sum residual = 0 after convergence (≡ each interior vertex has Σα = θ_v).
|
||
auto G_final = spherical_gradient(mesh, res.x, maps);
|
||
for (std::size_t i = 0; i < G_final.size(); ++i)
|
||
EXPECT_NEAR(0.0, G_final[i], 1e-6)
|
||
<< "Spherical angle sum residual at DOF " << i << " = " << G_final[i];
|
||
}
|