// Port of de.varylab.discreteconformal.functional.HyperIdealUtilityTest (Java/JUnit).

#include "hyper_ideal_utility.hpp"
#include "clausen.hpp"

#include <gtest/gtest.h>
#include <cmath>

using conformallab::calculateTetrahedronVolume;
using conformallab::calculateTetrahedronVolumeWithIdealVertexAtGamma;
using conformallab::Lobachevsky;

constexpr double PI = 3.14159265358979323846264338328;

// Regular tetrahedron at the Euclidean boundary (beta = arccos(1/3) for each
// vertex angle) has volume 0 — it degenerates to a flat configuration.
TEST(HyperIdealUtilityTest, VolumeEuclidean) {
    double b = std::acos(1.0 / 3.0);
    double V = calculateTetrahedronVolume(b, b, b, b, b, b);
    EXPECT_NEAR(0.0, V, 1e-7);
}

// Regular ideal tetrahedron with all angles pi/3.
// Formula: sum of Lobachevsky values at each angle.
TEST(HyperIdealUtilityTest, VolumeRegularIdeal1) {
    double b = PI / 3.0;
    double Ve = Lobachevsky(b) + Lobachevsky(b) + Lobachevsky(b);
    double V  = calculateTetrahedronVolume(b, b, b, b, b, b);
    EXPECT_NEAR(Ve, V, 1e-12);
}

// Right-angled ideal tetrahedron (pi/2, pi/4, pi/4).
TEST(HyperIdealUtilityTest, VolumeRegularIdeal2) {
    double bi = PI / 2.0, bj = PI / 4.0, bk = PI / 4.0;
    double Ve = Lobachevsky(bi) + Lobachevsky(bj) + Lobachevsky(bk);
    double V  = calculateTetrahedronVolume(bi, bj, bk, bi, bj, bk);
    EXPECT_NEAR(Ve, V, 1e-12);
}

// Hyperideal octahedron: all angles 0, volume = 8*Л(pi/4).
TEST(HyperIdealUtilityTest, VolumeOctahedron) {
    double Ve = 8.0 * Lobachevsky(PI / 4.0);
    double V  = calculateTetrahedronVolume(0, 0, 0, 0, 0, 0);
    EXPECT_NEAR(Ve, V, 1e-12);
}

// Hyperideal tetrahedron with one hyperideal vertex.
// Manual formula from the paper vs. general formula.
TEST(HyperIdealUtilityTest, VolumeSingleHyperidealVertex) {
    double bi = PI / 5.0, bj = PI / 4.0, bk = PI / 4.0;
    double ai  = (PI + bi - bj - bk) / 2.0;
    double aj  = (PI + bj - bi - bk) / 2.0;
    double ak  = (PI + bk - bi - bj) / 2.0;
    double aijk= (PI - bk - bi - bj) / 2.0;
    double Ve = 0.5 * (Lobachevsky(bi) + Lobachevsky(bj) + Lobachevsky(bk)
                     + Lobachevsky(ai)  + Lobachevsky(aj)  + Lobachevsky(ak)
                     + Lobachevsky(aijk));
    double V  = calculateTetrahedronVolume(bi, bj, bk, ai, aj, ak);
    EXPECT_NEAR(Ve, V, 1e-12);
}

// A degenerate triangle (angle = pi) must give volume 0 without NaN.
TEST(HyperIdealUtilityTest, VolumeWithDegenerateTriangle) {
    double V = calculateTetrahedronVolume(0.0, PI, 0.0, 0.0, 0.0, PI);
    EXPECT_NEAR(0.0, V, 1e-12);
    EXPECT_FALSE(std::isnan(V));
}

// The two volume formulas (general and ideal-vertex specialization) must agree
// on the same input — numerical consistency check.
TEST(HyperIdealUtilityTest, CompareGeneralAndIdealFormulaCase1) {
    constexpr double EPS = 0.1;
    double bi = PI / 3.0, bj = PI / 3.0, bk = PI / 3.0;
    double ai = PI / 3.0 - EPS, aj = PI / 3.0 - EPS, ak = PI / 3.0 - EPS;
    double Ve = calculateTetrahedronVolumeWithIdealVertexAtGamma(bi, bj, bk, ai, aj, ak);
    double V  = calculateTetrahedronVolume(bi, bj, bk, ai, aj, ak);
    EXPECT_NEAR(Ve, V, 1e-12);
}

// Second consistency check with non-symmetric angles that sum to pi.
TEST(HyperIdealUtilityTest, CompareGeneralAndIdealFormulaCase2) {
    double bi = 0.6623267054958116;
    double bj = 1.437248992086214;
    double bk = 1.0420169560077686;
    double ai = 0.6896178197389236;
    double aj = 0.5195634857410114;
    double ak = 0.6304500578493993;
    EXPECT_NEAR(PI, bi + bj + bk, 1e-12);
    double Ve = calculateTetrahedronVolumeWithIdealVertexAtGamma(bi, bj, bk, ai, aj, ak);
    double V  = calculateTetrahedronVolume(bi, bj, bk, ai, aj, ak);
    EXPECT_NEAR(Ve, V, 1e-12);
}