ViewDesignEngine/tests/mesh/test_delaunay_3d.cpp

#include <gtest/gtest.h>
#include "vde/mesh/delaunay_3d.h"
#include <cmath>

using namespace vde::mesh;
using namespace vde::core;

// ── Helper: compute circumsphere center and radius of 4 points ──
// Returns (center, radius_squared). If points are coplanar, radius_sq < 0.
static std::pair<Point3D, double> circumsphere(
    const Point3D& a, const Point3D& b, const Point3D& c, const Point3D& d)
{
    // Build the linear system using the property that ||p - center||² = r²
    // for all four points. Subtract first equation from others to get 3x3 system.
    Eigen::Matrix3d M;
    Eigen::Vector3d rhs;

    auto row = [&](const Point3D& pi, const Point3D& p0) {
        Eigen::Vector3d diff = (pi - p0);
        return std::make_pair(diff, (pi.squaredNorm() - p0.squaredNorm()) * 0.5);
    };

    auto [da, ra] = row(b, a);
    auto [db, rb] = row(c, a);
    auto [dc, rc] = row(d, a);

    M.row(0) = da; M.row(1) = db; M.row(2) = dc;
    rhs << ra, rb, rc;

    // Check if singular (coplanar)
    if (std::abs(M.determinant()) < 1e-12) {
        return {Point3D::Zero(), -1.0};
    }

    Point3D center = M.colPivHouseholderQr().solve(rhs);
    double r2 = (a - center).squaredNorm();
    return {center, r2};
}

// ── Helper: check Delaunay empty-sphere property ──
// For every tetrahedron, no other input point should be inside its circumsphere.
static bool verify_empty_circumsphere(
    const TetrahedronMesh& mesh,
    const std::vector<Point3D>& input_points)
{
    for (const auto& tet : mesh.tetrahedra) {
        const auto& p0 = mesh.vertices[tet[0]];
        const auto& p1 = mesh.vertices[tet[1]];
        const auto& p2 = mesh.vertices[tet[2]];
        const auto& p3 = mesh.vertices[tet[3]];

        auto [center, r2] = circumsphere(p0, p1, p2, p3);
        if (r2 < 0.0) continue; // degenerate

        double r = std::sqrt(r2);
        (void)r;  // explicitly unused, computed for potential debugging
        for (const auto& pt : input_points) {
            // Skip vertices of this tetrahedron
            double d2 = (pt - center).squaredNorm();
            // Allow small epsilon for floating point
            if (d2 < r2 - 1e-9) {
                return false; // point inside circumsphere → not Delaunay
            }
        }
    }
    return true;
}

// ═══════════════════════════════════════════════════════════
//  Test cases
// ═══════════════════════════════════════════════════════════

TEST(Delaunay3DTest, EmptyInput_ReturnsEmpty) {
    std::vector<Point3D> points;
    auto result = delaunay_3d(points);
    EXPECT_EQ(result.vertices.size(), 0u);
    EXPECT_EQ(result.tetrahedra.size(), 0u);
}

TEST(Delaunay3DTest, FourPointsTetrahedron_OneTetrahedron) {
    std::vector<Point3D> pts = {
        {1, 1, 1},
        {1, -1, -1},
        {-1, 1, -1},
        {-1, -1, 1}
    };
    auto result = delaunay_3d(pts);
    EXPECT_EQ(result.vertices.size(), 4u);
    EXPECT_GE(result.tetrahedra.size(), 1u);
}

TEST(Delaunay3DTest, FivePointsCube_VerifyDelaunayProperty) {
    std::vector<Point3D> pts = {
        {0, 0, 0},
        {1, 0, 0},
        {0, 1, 0},
        {0, 0, 1},
        {0.25, 0.25, 0.25}  // inside the tetrahedron
    };
    auto result = delaunay_3d(pts);
    EXPECT_EQ(result.vertices.size(), 5u);
    EXPECT_GE(result.tetrahedra.size(), 2u);
}

TEST(Delaunay3DTest, FivePointsDelaunayProperty_EmptyCircumsphere) {
    std::vector<Point3D> pts = {
        {1, 1, 1},
        {1, -1, -1},
        {-1, 1, -1},
        {-1, -1, 1},
        {0, 0, 0}
    };
    auto result = delaunay_3d(pts);
    EXPECT_EQ(result.vertices.size(), 5u);
    EXPECT_GE(result.tetrahedra.size(), 4u);
    EXPECT_TRUE(verify_empty_circumsphere(result, pts));
}

TEST(Delaunay3DTest, CollinearPoints_HandlesGracefully) {
    // 4 points on a line
    std::vector<Point3D> pts = {
        {0, 0, 0},
        {1, 0, 0},
        {2, 0, 0},
        {3, 0, 0}
    };
    auto result = delaunay_3d(pts);
    // Collinear points may produce 0 tetrahedra (degenerate)
    // The function should not crash
    EXPECT_GE(result.tetrahedra.size(), 0u);
}

TEST(Delaunay3DTest, CoplanarPoints_HandlesGracefully) {
    // 4 points on a plane
    std::vector<Point3D> pts = {
        {0, 0, 0},
        {1, 0, 0},
        {1, 1, 0},
        {0, 1, 0}
    };
    auto result = delaunay_3d(pts);
    // Coplanar points should not crash; may return degenerate result
    EXPECT_GE(result.tetrahedra.size(), 0u);
}