Jschakib

tests/geometry/functions/determinant.cc

+#include "test.hh"
+
+static tg::mat3 rndMat3(tg::rng& rng)
+{
+    auto b = 5.0f;
+    auto dBox = tg::box3(-tg::pos3(b), tg::pos3(b));
+
+    auto mat = tg::mat3();
+    for (auto c = 0; c < 3; c++)
+        mat.col(c) = tg::vec3(uniform(rng, dBox));
+
+    return mat;
+}
+
+static tg::mat2 rndMat2(tg::rng& rng)
+{
+    auto b = 5.0f;
+    auto dBox = tg::box2(-tg::pos2(b), tg::pos2(b));
+
+    auto mat = tg::mat2();
+    for (auto c = 0; c < 2; c++)
+        mat.col(c) = tg::vec2(uniform(rng, dBox));
+
+    return mat;
+}
+
+static tg::mat3 rndInvertibleMat3(tg::rng& rng)
+{
+    // build matrix from random transformations (invertible)
+    auto rd1 = tg::box1(-1.0f, 1.0f);
+    auto a = uniform(rng, rd1).x;
+    auto b = uniform(rng, rd1).x;
+    auto c = uniform(rng, rd1).x;
+
+    auto mat = tg::scaling(tg::size2(b, c));
+    mat = tg::rotation_around(tg::pos2(a, c), tg::degree(b * 360.0f)) * mat;
+    mat = tg::translation(tg::vec2(a, b) * 10.0f) * mat;
+
+    return mat;
+}
+
+static tg::mat2 rndInvertibleMat2(tg::rng& rng)
+{
+    auto rd1 = tg::box1(-1.0f, 1.0f);
+    auto a = uniform(rng, rd1).x;
+    auto b = uniform(rng, rd1).x;
+
+    auto mat = tg::scaling(tg::size1(b));
+    mat = tg::translation(tg::vec1(a) * 10.0f) * mat;
+
+    return mat;
+}
+
+TG_FUZZ_TEST(TypedGeometry, Determinant)
+{
+    auto rd1 = tg::box1(0.0f, 1.0f);
+
+    // matrices with obvious determinants
+    {
+        // 1D
+        const auto D = 1;
+        auto mat = tg::mat<D, D, tg::f32>::zero;
+        CHECK(determinant(mat) == 0.0f);
+
+        mat = tg::mat<D, D, tg::f32>::identity;
+        CHECK(determinant(mat) == doctest::Approx(1.0f).epsilon(1e-5));
+
+        auto rf = uniform(rng, rd1).x;
+        mat = tg::mat<D, D, tg::f32>::diag(rf);
+        auto res = tg::pow(rf, D);
+        CHECK(determinant(mat) == doctest::Approx(res).epsilon(1e-5));
+    }
+
+    {
+        // 2D
+        const auto D = 2;
+        auto mat = tg::mat<D, D, tg::f32>::zero;
+        CHECK(determinant(mat) == 0.0f);
+
+        mat = tg::mat<D, D, tg::f32>::identity;
+        CHECK(determinant(mat) == doctest::Approx(1.0f).epsilon(1e-5));
+
+        auto rf = uniform(rng, rd1).x;
+        mat = tg::mat<D, D, tg::f32>::diag(rf);
+        auto res = tg::pow(rf, D);
+        CHECK(determinant(mat) == doctest::Approx(res).epsilon(1e-5));
+    }
+
+    {
+        // 3D
+        const auto D = 3;
+        auto mat = tg::mat<D, D, tg::f32>::zero;
+        CHECK(determinant(mat) == 0.0f);
+
+        mat = tg::mat<D, D, tg::f32>::identity;
+        CHECK(determinant(mat) == doctest::Approx(1.0f).epsilon(1e-5));
+
+        auto rf = uniform(rng, rd1).x;
+        mat = tg::mat<D, D, tg::f32>::diag(rf);
+        auto res = tg::pow(rf, D);
+        CHECK(determinant(mat) == doctest::Approx(res).epsilon(1e-5));
+    }
+
+    // random DxD matrices for 3D
+    {
+        auto matA = rndMat3(rng);
+        auto matB = rndMat3(rng);
+        // confirm multiplicativity
+        CHECK(determinant(matA * matB) == doctest::Approx(determinant(matA) * determinant(matB)).epsilon(1e-5));
+
+        matA = rndInvertibleMat3(rng);
+        matB = rndInvertibleMat3(rng);
+
+        // if invertible det != 0
+        CHECK(determinant(matA) != doctest::Approx(0.0f).epsilon(1e-5));
+        // CHECK(determinant(matB) != doctest::Approx(0.0f).epsilon(1e-5));
+
+        // confirm multiplicativity
+        auto detA = determinant(matA);
+        auto detB = determinant(matB);
+        CHECK(determinant(matA * matB) == doctest::Approx(detA * detB).epsilon(1e-5));
+
+        auto invA = inverse(matA);
+        auto invB = inverse(matB);
+
+        CHECK(determinant(invA) == doctest::Approx(1.0f / detA).epsilon(1e-5));
+        CHECK(determinant(invB) == doctest::Approx(1.0f / detB).epsilon(1e-5));
+    }
+
+    // random DxD matrices for 2D
+    {
+        auto matA = rndMat2(rng);
+        auto matB = rndMat2(rng);
+        // confirm multiplicativity
+        CHECK(determinant(matA * matB) == doctest::Approx(determinant(matA) * determinant(matB)).epsilon(1e-5));
+
+        matA = rndInvertibleMat2(rng);
+        matB = rndInvertibleMat2(rng);
+
+        // if invertible det != 0
+        CHECK(determinant(matA) != doctest::Approx(0.0f).epsilon(1e-5));
+        CHECK(determinant(matB) != doctest::Approx(0.0f).epsilon(1e-5));
+
+        // confirm multiplicativity
+        auto detA = determinant(matA);
+        auto detB = determinant(matB);
+        CHECK(determinant(matA * matB) == doctest::Approx(detA * detB).epsilon(1e-5));
+
+        auto invA = inverse(matA);
+        auto invB = inverse(matB);
+
+        CHECK(determinant(invA) == doctest::Approx(1.0f / detA).epsilon(1e-5));
+        CHECK(determinant(invB) == doctest::Approx(1.0f / detB).epsilon(1e-5));
+    }
+}