Merge pull request 'feat(geometry): pn_geometry.hpp — Pn projective-metric substrate (jReality port)' (#31) from feat/pn-geometry-substrate into main

code/tests/cgal/CMakeLists.txt

@@ -90,6 +90,11 @@ add_executable(conformallab_cgal_tests
     #    Low-level half-edge genus-2 generator + golden-vector convergence.
     test_lawson_hyperideal.cpp
 
+    # ── Pn projective-metric substrate (de.jreality.math.Pn port) ───────────
+    #    Inner product / norm / distance / geodesic interpolation in
+    #    Euclidean, Elliptic, Hyperbolic signatures.
+    test_pn_geometry.cpp
+
     # ── Phase 8b-Lite: CGAL entry wrappers for the 4 non-Euclidean modes ─────
     #    Spherical, HyperIdeal, CircleP-Euclidean, Inversive-Distance via
     #    <CGAL/Discrete_*.h> public API + Conformal_layout.h wrapper.

code/tests/cgal/test_pn_geometry.cpp

@@ -0,0 +1,135 @@
+// Copyright (c) 2024-2026 Tarik Moussa.
+// SPDX-License-Identifier: MIT
+
+// test_pn_geometry.cpp
+//
+// Verifies pn_geometry.hpp against:
+//   (a) closed-form analytic golden values, and
+//   (b) the already-verified projective_math.hpp::hyperbolicDistance
+//       (regression anchor for the HYPERBOLIC sign convention).
+//
+// Mirrored Java source: de.jreality.math.Pn
+
+#include "pn_geometry.hpp"
+#include "projective_math.hpp"
+#include <gtest/gtest.h>
+#include <Eigen/Core>
+#include <cmath>
+
+using namespace conformallab;
+
+namespace {
+Eigen::VectorXd V(std::initializer_list<double> xs) {
+    Eigen::VectorXd v(static_cast<int>(xs.size()));
+    int i = 0;
+    for (double x : xs) v(i++) = x;
+    return v;
+}
+constexpr double PN_PI = 3.14159265358979323846;
+} // namespace
+
+// ── Inner product per signature ──────────────────────────────────────────────
+TEST(PnGeometry, InnerProductSignatures)
+{
+    auto u = V({1.0, 2.0, 3.0});   // spatial=(1,2), last=3
+    auto v = V({4.0, 5.0, 6.0});   // spatial=(4,5), last=6
+    // spat = 1·4 + 2·5 = 14,  last = 3·6 = 18
+    EXPECT_NEAR(pn_inner_product(u, v, PN_EUCLIDEAN),   14.0,      1e-12);
+    EXPECT_NEAR(pn_inner_product(u, v, PN_ELLIPTIC),    14.0+18.0, 1e-12);
+    EXPECT_NEAR(pn_inner_product(u, v, PN_HYPERBOLIC),  18.0-14.0, 1e-12);
+}
+
+// ── Euclidean distance ────────────────────────────────────────────────────────
+TEST(PnGeometry, EuclideanDistance)
+{
+    // 3-4-5 right triangle in the plane (homogeneous w=1).
+    auto p  = V({0.0, 0.0, 1.0});
+    auto q  = V({3.0, 4.0, 1.0});
+    EXPECT_NEAR(pn_distance_between(p, q, PN_EUCLIDEAN), 5.0, 1e-12);
+
+    // Homogeneous scaling must not change the distance.
+    auto q2 = V({6.0, 8.0, 2.0});  // same point as q after dehomogenize
+    EXPECT_NEAR(pn_distance_between(p, q2, PN_EUCLIDEAN), 5.0, 1e-12);
+}
+
+// ── Elliptic distance = spherical angle ───────────────────────────────────────
+TEST(PnGeometry, EllipticDistanceIsAngle)
+{
+    auto e1 = V({1.0, 0.0, 0.0});
+    auto e2 = V({0.0, 1.0, 0.0});
+    auto d  = V({1.0, 1.0, 0.0});   // 45° between e1 and e2
+
+    EXPECT_NEAR(pn_distance_between(e1, e2, PN_ELLIPTIC), PN_PI / 2.0, 1e-12);
+    EXPECT_NEAR(pn_distance_between(e1, d,  PN_ELLIPTIC), PN_PI / 4.0, 1e-12);
+    EXPECT_NEAR(pn_distance_between(e1, e1, PN_ELLIPTIC), 0.0,      1e-12);
+}
+
+// ── Hyperbolic distance: closed form + projective_math.hpp anchor ─────────────
+TEST(PnGeometry, HyperbolicDistanceClosedFormAndAnchor)
+{
+    // Upper hyperboloid: p = apex (0,0,1); q = (sinh r, 0, cosh r) at distance r.
+    const double r = 0.873;
+    auto p  = V({0.0, 0.0, 1.0});
+    auto q  = V({std::sinh(r), 0.0, std::cosh(r)});
+
+    EXPECT_NEAR(pn_distance_between(p, q, PN_HYPERBOLIC), r, 1e-10);
+
+    // Regression anchor: identical to projective_math.hpp::hyperbolicDistance.
+    EXPECT_NEAR(pn_distance_between(p, q, PN_HYPERBOLIC),
+                hyperbolicDistance(p, q), 1e-12);
+
+    // Scale-invariance: homogeneous rescaling must not change distance.
+    auto q2 = (2.5 * q).eval();
+    EXPECT_NEAR(pn_distance_between(p, q2, PN_HYPERBOLIC), r, 1e-10);
+}
+
+// ── Norm / setToLength / normalize ───────────────────────────────────────────
+TEST(PnGeometry, NormAndScaling)
+{
+    auto p = V({3.0, 4.0, 0.0});
+    EXPECT_NEAR(pn_norm(p, PN_ELLIPTIC), 5.0, 1e-12);
+
+    auto s = pn_set_to_length(p, 2.0, PN_ELLIPTIC);
+    EXPECT_NEAR(pn_norm(s, PN_ELLIPTIC), 2.0, 1e-12);
+
+    auto u = pn_normalize(p, PN_ELLIPTIC);
+    EXPECT_NEAR(pn_norm(u, PN_ELLIPTIC), 1.0, 1e-12);
+
+    // A unit hyperboloid sheet point already has hyperbolic norm 1.
+    auto h = V({std::sinh(0.6), 0.0, std::cosh(0.6)});
+    EXPECT_NEAR(pn_norm(h, PN_HYPERBOLIC), 1.0, 1e-12);
+}
+
+// ── Geodesic interpolation ────────────────────────────────────────────────────
+TEST(PnGeometry, LinearInterpolationGeodesic)
+{
+    // EUCLIDEAN: affine midpoint.
+    {
+        auto p = V({0.0, 0.0, 1.0});
+        auto q = V({4.0, 0.0, 1.0});
+        auto m = pn_linear_interpolation(p, q, 0.5, PN_EUCLIDEAN);
+        EXPECT_NEAR(m(0), 2.0, 1e-12);
+    }
+
+    // ELLIPTIC: midpoint of e1,e2 is at half the π/2 arc = π/4 from each.
+    {
+        auto e1 = V({1.0, 0.0, 0.0});
+        auto e2 = V({0.0, 1.0, 0.0});
+        auto m  = pn_linear_interpolation(e1, e2, 0.5, PN_ELLIPTIC);
+        EXPECT_NEAR(pn_distance_between(e1, m, PN_ELLIPTIC), PN_PI / 4.0, 1e-10);
+        EXPECT_NEAR(pn_distance_between(e2, m, PN_ELLIPTIC), PN_PI / 4.0, 1e-10);
+        // Endpoint recovery at t=0.
+        auto m0 = pn_linear_interpolation(e1, e2, 0.0, PN_ELLIPTIC);
+        EXPECT_NEAR(pn_distance_between(e1, m0, PN_ELLIPTIC), 0.0, 1e-10);
+    }
+
+    // HYPERBOLIC: midpoint is at exactly half the geodesic distance from each end.
+    {
+        const double r = 1.2;
+        auto p = V({0.0, 0.0, 1.0});
+        auto q = V({std::sinh(r), 0.0, std::cosh(r)});
+        auto m = pn_linear_interpolation(p, q, 0.5, PN_HYPERBOLIC);
+        EXPECT_NEAR(pn_distance_between(p, m, PN_HYPERBOLIC), r / 2.0, 1e-9);
+        EXPECT_NEAR(pn_distance_between(q, m, PN_HYPERBOLIC), r / 2.0, 1e-9);
+    }
+}