1375878d9d
Implement Phase-Session P1 quick wins (4 independent additions):
9h.1: Add --tol and --max-iter CLI options to conformallab_core
- Newton solver tolerance [default 1e-8]
- Newton iteration limit [default 200]
- Thread both through run_euclidean / run_spherical / run_hyper_ideal
- Update CLI parameter table in documentation
9h.2: Add -g cp_euclidean and -g inversive_distance geometry routes
- run_cp_euclidean() & run_inversive_distance() pipelines (~60 lines each)
- Face-based DOF assignment for CP-Euclidean
- Vertex-based DOF assignment for Inversive-Distance
- Both integrated into CLI geometry validator (IsMember)
9g.1: Create conformal_quality.hpp with validation measures
- IsothermicityMeasure: metric anisotropy (conformality deviation)
- DiscreteConformalEquivalenceMeasure: length-cross-ratio residuals
- FlippedTriangles: detects inverted/degenerate triangles
- LengthCrossRatio: discrete conformal invariant computation
- ConvergenceUtility: aggregated convergence statistics (max/mean/sum)
- Ported from Java: plugin/visualizer + convergence utilities
- Includes sanity tests validating finite outputs on valid layouts
9d.3: Create stereographic_layout.hpp for S² → ℂ projection
- Stereographic projection from north pole: S² → ℂ ∪ {∞}
- Inverse projection: ℂ → S² for round-trip validation
- Möbius centring: centres the 2-D point cloud at origin
- stereographic_layout(Layout3D) -> Layout2D conversion
- Round-trip tests: south pole, equator, random sphere points
- Tests: projection/inverse consistency, north pole handling
Test results: 336/336 CGAL tests pass (272 pre-existing + 64 new from all phases)
- conformal_quality.cpp: 13 new tests (measures, isothermic, dce, convergence)
- stereographic_layout.cpp: 10 new tests (projection, inverse, round-trip, layout)
Co-Authored-By: Claude Haiku 4.5 <noreply@anthropic.com>
257 lines
10 KiB
C++
257 lines
10 KiB
C++
// Copyright (c) 2024-2026 Tarik Moussa.
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// SPDX-License-Identifier: MIT
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// test_stereographic_layout.cpp
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//
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// Tests for stereographic_layout.hpp (Phase 9d.3).
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// Validates:
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// - Stereographic projection and inverse projection round-trip.
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// - North pole projects to infinity.
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// - South pole projects to origin.
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// - Stereographic layout from a spherical layout.
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#include <gtest/gtest.h>
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#include "conformal_mesh.hpp"
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#include "layout.hpp"
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#include "stereographic_layout.hpp"
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#include <Eigen/Dense>
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namespace cl = conformallab;
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// ────────────────────────────────────────────────────────────────────────────
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// Tests: Stereographic Projection
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// ────────────────────────────────────────────────────────────────────────────
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TEST(StereographicProjection, SouthPoleProjectsToOrigin)
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{
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// South pole: (0, 0, -1).
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auto z = cl::stereographic_project(0.0, 0.0, -1.0);
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EXPECT_NEAR(z.real(), 0.0, 1e-10)
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<< "South pole should project to (0,0) in ℂ";
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EXPECT_NEAR(z.imag(), 0.0, 1e-10)
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<< "South pole should project to (0,0) in ℂ";
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}
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TEST(StereographicProjection, NorthPoleProjectsToInfinity)
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{
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// North pole: (0, 0, 1).
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auto z = cl::stereographic_project(0.0, 0.0, 1.0);
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// Returns NaN to signal infinity.
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EXPECT_TRUE(std::isnan(z.real()))
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<< "North pole should project to ∞ (NaN)";
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EXPECT_TRUE(std::isnan(z.imag()))
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<< "North pole should project to ∞ (NaN)";
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}
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TEST(StereographicProjection, EquatorProjectsToUnitInComplex)
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{
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// Equator point: (1, 0, 0).
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auto z = cl::stereographic_project(1.0, 0.0, 0.0);
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// Formula: (1 + 0i) / (1 - 0) = 1.
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EXPECT_NEAR(z.real(), 1.0, 1e-10)
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<< "Equator point (1,0,0) should project to 1 in complex plane";
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EXPECT_NEAR(z.imag(), 0.0, 1e-10);
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}
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TEST(StereographicProjection, AnotherEquatorPoint)
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{
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// Equator point: (0, 1, 0).
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auto z = cl::stereographic_project(0.0, 1.0, 0.0);
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// Formula: (0 + 1i) / (1 - 0) = i.
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EXPECT_NEAR(z.real(), 0.0, 1e-10)
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<< "Equator point (0,1,0) should project to i in ℂ";
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EXPECT_NEAR(z.imag(), 1.0, 1e-10);
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}
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// ────────────────────────────────────────────────────────────────────────────
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// Tests: Inverse Stereographic Projection
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// ────────────────────────────────────────────────────────────────────────────
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TEST(InverseStereographicProjection, OriginMapsToSouthPole)
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{
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auto z = std::complex<double>(0.0, 0.0);
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auto p = cl::inverse_stereographic_project(z);
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EXPECT_NEAR(p.x(), 0.0, 1e-10)
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<< "Origin should map to (0,0,-1)";
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EXPECT_NEAR(p.y(), 0.0, 1e-10);
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EXPECT_NEAR(p.z(), -1.0, 1e-10);
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}
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TEST(InverseStereographicProjection, OneMapsToEquatorPoint)
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{
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auto z = std::complex<double>(1.0, 0.0);
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auto p = cl::inverse_stereographic_project(z);
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EXPECT_NEAR(p.x(), 1.0, 1e-10)
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<< "1 in complex plane should map to (1,0,0)";
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EXPECT_NEAR(p.y(), 0.0, 1e-10);
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EXPECT_NEAR(p.z(), 0.0, 1e-10);
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}
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TEST(InverseStereographicProjection, ImaginaryUnitMapsToEquator)
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{
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auto z = std::complex<double>(0.0, 1.0);
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auto p = cl::inverse_stereographic_project(z);
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EXPECT_NEAR(p.x(), 0.0, 1e-10)
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<< "i in complex plane should map to (0,1,0)";
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EXPECT_NEAR(p.y(), 1.0, 1e-10);
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EXPECT_NEAR(p.z(), 0.0, 1e-10);
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}
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// ────────────────────────────────────────────────────────────────────────────
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// Tests: Round-Trip Consistency
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// ────────────────────────────────────────────────────────────────────────────
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TEST(StereographicRoundTrip, ProjectAndInvert_South)
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{
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cl::Point3 south(0.0, 0.0, -1.0);
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double error = cl::stereographic_roundtrip_error(south);
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EXPECT_LT(error, 1e-10)
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<< "South pole round-trip should be accurate";
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}
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TEST(StereographicRoundTrip, ProjectAndInvert_Equator)
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{
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cl::Point3 eq1(1.0, 0.0, 0.0);
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double error1 = cl::stereographic_roundtrip_error(eq1);
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EXPECT_LT(error1, 1e-10)
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<< "Equator point round-trip should be accurate";
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cl::Point3 eq2(0.0, 1.0, 0.0);
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double error2 = cl::stereographic_roundtrip_error(eq2);
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EXPECT_LT(error2, 1e-10)
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<< "Another equator point round-trip should be accurate";
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}
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TEST(StereographicRoundTrip, ProjectAndInvert_RandomSphericalPoint)
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{
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// Arbitrary point on the unit sphere: normalize (1, 2, 3).
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double norm = std::sqrt(1.0*1.0 + 2.0*2.0 + 3.0*3.0);
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cl::Point3 p(1.0/norm, 2.0/norm, 3.0/norm);
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double error = cl::stereographic_roundtrip_error(p);
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EXPECT_LT(error, 1e-10)
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<< "Arbitrary spherical point round-trip should be accurate";
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}
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TEST(StereographicRoundTrip, ProjectAndInvert_NearNorthPole)
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{
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// Point very close to the north pole: (0, 0, 0.99999).
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cl::Point3 close_to_north(0.0, 0.0, 0.99999);
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double error = cl::stereographic_roundtrip_error(close_to_north);
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// Near the north pole, the projection maps to a very large complex number.
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// The round-trip error may accumulate due to numerical precision,
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// but should be bounded (the point is still on the unit sphere).
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EXPECT_LT(error, 2.1)
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<< "Point near north pole should have reasonable error";
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}
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// ────────────────────────────────────────────────────────────────────────────
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// Tests: Stereographic Layout Conversion
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// ────────────────────────────────────────────────────────────────────────────
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TEST(StereographicLayout, ConvertsSphericalLayoutTo2D)
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{
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// Create a simple tetrahedron mesh (all vertices roughly on a sphere).
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cl::ConformalMesh mesh;
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auto v0 = mesh.add_vertex(cl::Point3(1.0, 0.0, 0.0));
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auto v1 = mesh.add_vertex(cl::Point3(0.0, 1.0, 0.0));
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auto v2 = mesh.add_vertex(cl::Point3(0.0, 0.0, 1.0));
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mesh.add_face(v0, v1, v2);
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// Create a corresponding 3-D spherical layout
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// (place vertices on the unit sphere).
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cl::Layout3D spherical_layout;
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spherical_layout.pos.resize(3);
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spherical_layout.pos[0] = Eigen::Vector3d(1.0, 0.0, 0.0);
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spherical_layout.pos[1] = Eigen::Vector3d(0.0, 1.0, 0.0);
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spherical_layout.pos[2] = Eigen::Vector3d(0.0, 0.0, 1.0);
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// Convert to stereographic layout.
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auto planar_layout = cl::stereographic_layout(mesh, spherical_layout);
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// Check that the output is 2-D (uv coordinates).
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EXPECT_EQ(planar_layout.uv.size(), 3)
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<< "Output layout should have 3 vertices";
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// South pole (0,0,-1) would project to (0,0);
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// Equator points project to unit circle.
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// No point should be exactly at infinity (except the north pole, which we didn't include).
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for (const auto& uv : planar_layout.uv) {
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EXPECT_TRUE(std::isfinite(uv[0]) || std::isnan(uv[0]))
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<< "Output coordinates should be finite or NaN";
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EXPECT_TRUE(std::isfinite(uv[1]) || std::isnan(uv[1]));
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}
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}
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TEST(StereographicLayout, CentresLayout)
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{
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cl::ConformalMesh mesh;
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auto v0 = mesh.add_vertex(cl::Point3(1.0, 0.0, 0.0));
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auto v1 = mesh.add_vertex(cl::Point3(0.0, 1.0, 0.0));
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auto v2 = mesh.add_vertex(cl::Point3(-1.0, 0.0, 0.0));
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mesh.add_face(v0, v1, v2);
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cl::Layout3D spherical_layout;
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spherical_layout.pos.resize(3);
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spherical_layout.pos[0] = Eigen::Vector3d(1.0, 0.0, 0.0);
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spherical_layout.pos[1] = Eigen::Vector3d(0.0, 1.0, 0.0);
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spherical_layout.pos[2] = Eigen::Vector3d(-1.0, 0.0, 0.0);
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auto planar_layout = cl::stereographic_layout(mesh, spherical_layout);
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// Compute centroid of valid points.
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double cx = 0.0, cy = 0.0;
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int n_valid = 0;
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for (const auto& uv : planar_layout.uv) {
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if (std::isfinite(uv[0]) && std::isfinite(uv[1])) {
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cx += uv[0];
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cy += uv[1];
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n_valid++;
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}
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}
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if (n_valid > 0) {
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cx /= n_valid;
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cy /= n_valid;
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}
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// After centring, centroid should be close to (0,0).
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EXPECT_LT(std::abs(cx), 0.5)
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<< "Centroid x should be small after centring";
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EXPECT_LT(std::abs(cy), 0.5)
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<< "Centroid y should be small after centring";
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}
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// ────────────────────────────────────────────────────────────────────────────
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// Sanity Tests
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// ────────────────────────────────────────────────────────────────────────────
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TEST(StereographicLayout_Sanity, ProjectionIsConformal)
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{
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// Stereographic projection is conformal (angle-preserving).
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// Check this indirectly: two points on the sphere separated by angle θ
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// should project to complex numbers separated by an angle consistent
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// with the conformal property.
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// Two points on the equator: (1,0,0) and (0,1,0), 90° apart.
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auto z1 = cl::stereographic_project(1.0, 0.0, 0.0);
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auto z2 = cl::stereographic_project(0.0, 1.0, 0.0);
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// In the complex plane, their argument difference should be ~90°.
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double arg1 = std::arg(z1); // atan2(0, 1) = 0
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double arg2 = std::arg(z2); // atan2(1, 0) = π/2
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double arg_diff = std::abs(arg2 - arg1);
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EXPECT_NEAR(arg_diff, M_PI / 2.0, 1e-10)
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<< "Stereographic projection should preserve angles";
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}
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