Jorijn van der Graaf
087c8b32c3
- A 4-vector doubles as a unit quaternion in (x, y, z, w) order: QuanternionMultiply, QuanternionConjugate, QuanternionFromAxisAngle, QuanternionFromUnitVectors (shortest arc), QuanternionNlerp and QuanternionSlerp, next to the existing QuanternionFromBasis. - MatrixRowMajor gains Rotation (from a quaternion), TRS, InverseAffine, Transpose and Decompose. The 4x4 transforms row vectors and the 4x3 column vectors (the VkTransformMatrixKHR layout); each of these means the same transform in both. The 4x3 Rotation copied the 4x4's rows, which rotated by the inverse. - The static Normalize no longer assumes three components. - Tests: Quaternion, and Matrix extended. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
456 lines
16 KiB
C++
456 lines
16 KiB
C++
//SPDX-License-Identifier: LGPL-3.0-only
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//SPDX-FileCopyrightText: Copyright (C) 2026 Catcrafts®
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#include <cmath>
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import Crafter.Math;
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import std;
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using namespace Crafter;
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namespace {
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constexpr float kEps = 1e-4f;
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constexpr bool FloatEquals(float a, float b, float epsilon = kEps) {
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return std::abs(a - b) < epsilon;
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}
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VectorF32<3, 1> Vec3(float x, float y, float z) {
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alignas(16) float buf[4] = { x, y, z, 0.0f };
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return VectorF32<3, 1>(buf);
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}
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std::string* CheckVec3(VectorF32<3, 1> got, float x, float y, float z, std::string_view label) {
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std::array<float, 4> v = got.template Store<float>();
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if (!FloatEquals(v[0], x) || !FloatEquals(v[1], y) || !FloatEquals(v[2], z))
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return new std::string(std::format(
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"{}: expected ({},{},{}), got ({},{},{})",
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label, x, y, z, v[0], v[1], v[2]));
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return nullptr;
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}
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std::string* CheckMat43(MatrixRowMajor<float, 4, 3, 1> const& m, std::array<float, 12> expected, std::string_view label) {
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std::array<float, 12> got = m.Store();
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for (std::uint8_t i = 0; i < 12; ++i) {
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if (!FloatEquals(got[i], expected[i]))
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return new std::string(std::format(
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"{} element {}: expected {}, got {}", label, i, expected[i], got[i]));
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}
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return nullptr;
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}
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std::string* CheckMat44(MatrixRowMajor<float, 4, 4, 1> const& m, std::array<float, 16> expected, std::string_view label) {
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std::array<float, 16> got = m.Store();
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for (std::uint8_t i = 0; i < 16; ++i) {
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if (!FloatEquals(got[i], expected[i]))
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return new std::string(std::format(
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"{} element {}: expected {}, got {}", label, i, expected[i], got[i]));
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}
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return nullptr;
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}
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// ---------- Identity / Store roundtrip ----------
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std::string* TestIdentity43() {
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auto m = MatrixRowMajor<float, 4, 3, 1>::Identity();
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return CheckMat43(m, {
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1, 0, 0, 0,
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0, 1, 0, 0,
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0, 0, 1, 0,
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}, "Identity 4x3");
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}
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std::string* TestIdentity44() {
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auto m = MatrixRowMajor<float, 4, 4, 1>::Identity();
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return CheckMat44(m, {
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1, 0, 0, 0,
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0, 1, 0, 0,
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0, 0, 1, 0,
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0, 0, 0, 1,
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}, "Identity 4x4");
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}
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std::string* TestStoreRoundtrip() {
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MatrixRowMajor<float, 4, 4, 1> m(
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1, 2, 3, 4,
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5, 6, 7, 8,
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9, 10, 11, 12,
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13, 14, 15, 16
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);
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return CheckMat44(m, {
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1, 2, 3, 4,
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5, 6, 7, 8,
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9, 10, 11, 12,
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13, 14, 15, 16,
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}, "Store roundtrip 4x4");
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}
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// ---------- Factory matrices ----------
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std::string* TestTranslation() {
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auto m = MatrixRowMajor<float, 4, 3, 1>::Translation(10, 20, 30);
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if (auto e = CheckMat43(m, {
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1, 0, 0, 10,
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0, 1, 0, 20,
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0, 0, 1, 30,
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}, "Translation 4x3")) return e;
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auto m4 = MatrixRowMajor<float, 4, 4, 1>::Translation(10, 20, 30);
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if (auto e = CheckMat44(m4, {
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1, 0, 0, 0,
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0, 1, 0, 0,
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0, 0, 1, 0,
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10, 20, 30, 1,
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}, "Translation 4x4")) return e;
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return nullptr;
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}
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std::string* TestScaling() {
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auto m = MatrixRowMajor<float, 4, 3, 1>::Scaling(2, 3, 4);
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if (auto e = CheckMat43(m, {
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2, 0, 0, 0,
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0, 3, 0, 0,
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0, 0, 4, 0,
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}, "Scaling 4x3")) return e;
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auto m4 = MatrixRowMajor<float, 4, 4, 1>::Scaling(2, 3, 4);
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return CheckMat44(m4, {
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2, 0, 0, 0,
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0, 3, 0, 0,
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0, 0, 4, 0,
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0, 0, 0, 1,
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}, "Scaling 4x4");
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}
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// ---------- Matrix * Vector ----------
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std::string* TestMatVecIdentity() {
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auto m = MatrixRowMajor<float, 4, 3, 1>::Identity();
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VectorF32<3, 1> v = Vec3(7, -2, 3);
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return CheckVec3(m * v, 7, -2, 3, "I * v");
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}
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std::string* TestMatVecTranslation() {
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auto m = MatrixRowMajor<float, 4, 3, 1>::Translation(1, 2, 3);
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// Affine multiply with implicit w=1 -> result = v + (1,2,3).
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VectorF32<3, 1> v = Vec3(10, 20, 30);
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return CheckVec3(m * v, 11, 22, 33, "Translation * v");
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}
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std::string* TestMatVecScaling() {
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auto m = MatrixRowMajor<float, 4, 3, 1>::Scaling(2, 3, 4);
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VectorF32<3, 1> v = Vec3(1, 1, 1);
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return CheckVec3(m * v, 2, 3, 4, "Scaling * v");
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}
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std::string* TestMatVecCombined() {
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// Scale then translate: full matrix is [diag(s) | t].
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MatrixRowMajor<float, 4, 3, 1> m(
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2, 0, 0, 10,
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0, 3, 0, 20,
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0, 0, 4, 30
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);
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VectorF32<3, 1> v = Vec3(1, 1, 1);
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return CheckVec3(m * v, 12, 23, 34, "Scale+Translate * v");
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}
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std::string* TestTransformNormal() {
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// TransformNormal ignores the translation column.
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MatrixRowMajor<float, 4, 3, 1> m(
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2, 0, 0, 100,
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0, 3, 0, 200,
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0, 0, 4, 300
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);
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VectorF32<3, 1> v = Vec3(1, 1, 1);
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return CheckVec3(m.TransformNormal(v), 2, 3, 4, "TransformNormal");
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}
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// ---------- Matrix * Matrix ----------
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std::string* TestMatMulIdentityLeft44() {
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MatrixRowMajor<float, 4, 4, 1> a = MatrixRowMajor<float, 4, 4, 1>::Identity();
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MatrixRowMajor<float, 4, 4, 1> b(
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1, 2, 3, 4,
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5, 6, 7, 8,
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9, 10, 11, 12,
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13, 14, 15, 16
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);
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auto r = a * b;
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return CheckMat44(r, {
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1, 2, 3, 4,
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5, 6, 7, 8,
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9, 10, 11, 12,
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13, 14, 15, 16,
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}, "I * M");
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}
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std::string* TestMatMulIdentityRight44() {
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MatrixRowMajor<float, 4, 4, 1> a(
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1, 2, 3, 4,
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5, 6, 7, 8,
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9, 10, 11, 12,
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13, 14, 15, 16
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);
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MatrixRowMajor<float, 4, 4, 1> b = MatrixRowMajor<float, 4, 4, 1>::Identity();
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auto r = a * b;
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return CheckMat44(r, {
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1, 2, 3, 4,
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5, 6, 7, 8,
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9, 10, 11, 12,
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13, 14, 15, 16,
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}, "M * I");
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}
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std::string* TestMatMul44() {
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// Hand-computed: standard row-major (B*A)[i][j] = sum_k B[i][k]*A[k][j].
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MatrixRowMajor<float, 4, 4, 1> a(
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1, 2, 0, 0,
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0, 1, 3, 0,
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4, 0, 1, 0,
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0, 0, 0, 1
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);
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MatrixRowMajor<float, 4, 4, 1> b(
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1, 0, 2, 0,
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0, 1, 0, 3,
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0, 0, 1, 0,
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0, 0, 0, 1
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);
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auto r = a * b;
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// result.m[i][j] = sum_k b.m[i][k] * a.m[k][j]
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// row 0: [1*1+0*0+2*4+0*0, 1*2+0*1+2*0+0*0, 1*0+0*3+2*1+0*0, 1*0+0*0+2*0+0*1]
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// = [9, 2, 2, 0]
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// row 1: [0*1+1*0+0*4+3*0, 0*2+1*1+0*0+3*0, 0*0+1*3+0*1+3*0, 0*0+1*0+0*0+3*1]
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// = [0, 1, 3, 3]
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// row 2: [0*1+0*0+1*4+0*0, 0*2+0*1+1*0+0*0, 0*0+0*3+1*1+0*0, 0*0+0*0+1*0+0*1]
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// = [4, 0, 1, 0]
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// row 3: [0*1+0*0+0*4+1*0, 0*2+0*1+0*0+1*0, 0*0+0*3+0*1+1*0, 0*0+0*0+0*0+1*1]
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// = [0, 0, 0, 1]
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return CheckMat44(r, {
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9, 2, 2, 0,
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0, 1, 3, 3,
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4, 0, 1, 0,
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0, 0, 0, 1,
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}, "Mat * Mat 4x4");
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}
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std::string* TestMatMulTranslationCompose() {
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// Translation composition: T(a) * T(b) acting on a vector translates by a+b
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// (and the resulting matrix has the summed translation in its last column).
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auto t1 = MatrixRowMajor<float, 4, 3, 1>::Translation(1, 2, 3);
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auto t2 = MatrixRowMajor<float, 4, 3, 1>::Translation(10, 20, 30);
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auto r = t1 * t2;
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if (auto e = CheckMat43(r, {
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1, 0, 0, 11,
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0, 1, 0, 22,
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0, 0, 1, 33,
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}, "T(1,2,3) * T(10,20,30)")) return e;
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// Sanity check: applying the composed matrix to origin yields (11,22,33).
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return CheckVec3(r * Vec3(0, 0, 0), 11, 22, 33, "Composed translation * origin");
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}
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std::string* TestMatMulScaleThenTranslate() {
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// The matrix product follows the engine's row-vector / post-multiply
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// convention: a.operator*(b) yields the matrix b composed with a so that
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// applying the result is equivalent to "first apply this, then apply b"
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// when read left-to-right with a row vector (v * (a*b) = (v*a) * b).
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//
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// For column-vector intuition that means s.operator*(t) builds T·S, i.e.
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// "scale, then translate"; applying it to (1,1,1) yields s*v + t.
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auto s = MatrixRowMajor<float, 4, 3, 1>::Scaling(2, 3, 4);
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auto t = MatrixRowMajor<float, 4, 3, 1>::Translation(10, 20, 30);
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auto r = s * t;
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return CheckVec3(r * Vec3(1, 1, 1), 12, 23, 34, "scale-then-translate * (1,1,1)");
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}
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// ---------- LookTo / LookAt ----------
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std::string* TestLookToBasis() {
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// Camera at +Z looking back toward origin. eyeDirection should point from
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// focus to eye, i.e. +Z, so the resulting basis has R2 = +Z.
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VectorF32<3, 1> eye = Vec3(0, 0, 5);
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VectorF32<3, 1> dir = Vec3(0, 0, 1); // already from origin toward eye
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VectorF32<3, 1> up = Vec3(0, 1, 0);
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auto m = MatrixRowMajor<float, 4, 4, 1>::LookTo(eye, dir, up);
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// R2 normalized = (0,0,1). R0 = up x R2 = (0,1,0) x (0,0,1) = (1,0,0).
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// R1 = R2 x R0 = (0,0,1) x (1,0,0) = (0,1,0).
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// The view matrix stores basis columns in the rotation block, with the
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// translation column = -basis dot eye. So m.row[3] = (D0, D1, D2, 1).
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// D0 = R0 . -eye = -(0*0+0*0+5*0) = 0
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// D1 = R1 . -eye = -(0*0+1*0+0*5) = 0
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// D2 = R2 . -eye = -(0*0+0*0+1*5) = -5
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return CheckMat44(m, {
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1, 0, 0, 0,
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0, 1, 0, 0,
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0, 0, 1, 0,
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0, 0, -5, 1,
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}, "LookTo basis");
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}
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// ---------- Rotation conventions, quaternions, TRS, inverse ----------
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//
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// The 4x4 is row-vector (v * M, translation in row 3) and the 4x3 is
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// column-vector (M * v, translation in column 3, the VkTransformMatrixKHR
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// layout). The same call has to mean the same rotation in both.
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using Mat43 = MatrixRowMajor<float, 4, 3, 1>;
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using Mat44 = MatrixRowMajor<float, 4, 4, 1>;
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using Q = Vector<float, 4, 0>;
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using V3 = Vector<float, 3, 0>;
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// v as a row vector times a 4x4, translation included.
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V3 RowTimes44(Mat44 const& m, V3 v) {
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const std::array<float, 16> a = m.Store();
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return V3(v.x * a[0] + v.y * a[4] + v.z * a[8] + a[12],
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v.x * a[1] + v.y * a[5] + v.z * a[9] + a[13],
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v.x * a[2] + v.y * a[6] + v.z * a[10] + a[14]);
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}
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// A 4x3 times v as a column vector, translation included.
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V3 Times43(Mat43 const& m, V3 v) {
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const std::array<float, 12> a = m.Store();
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return V3(a[0] * v.x + a[1] * v.y + a[2] * v.z + a[3],
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a[4] * v.x + a[5] * v.y + a[6] * v.z + a[7],
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a[8] * v.x + a[9] * v.y + a[10] * v.z + a[11]);
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}
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std::string* CheckV3(V3 got, V3 expected, std::string_view label) {
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if (!FloatEquals(got.x, expected.x) || !FloatEquals(got.y, expected.y) || !FloatEquals(got.z, expected.z))
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return new std::string(std::format("{}: expected ({},{},{}), got ({},{},{})",
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label, expected.x, expected.y, expected.z, got.x, got.y, got.z));
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return nullptr;
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}
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Q SampleRotation() {
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return Q::QuanternionFromAxisAngle(V3::Normalize(V3(1, 2, 3)), 0.9f);
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}
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std::string* TestRotation43MatchesRotation44() {
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// The 4x3 Euler Rotation used to copy the 4x4's row-vector rows, so as a
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// column-vector transform it rotated the other way.
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const V3 v(1, 2, 3);
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const V3 expected = RowTimes44(Mat44::Rotation(0.3f, 0.7f, -0.4f), v);
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return CheckV3(Times43(Mat43::Rotation(0.3f, 0.7f, -0.4f), v), expected, "4x3 Rotation vs 4x4 Rotation");
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}
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std::string* TestRotationFromQuaternion() {
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const Q q = SampleRotation();
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const V3 v(1, -2, 0.5f);
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const V3 expected = V3::Rotate(v, q);
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if (auto err = CheckV3(Times43(Mat43::Rotation(q), v), expected, "4x3 Rotation(q)")) return err;
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return CheckV3(RowTimes44(Mat44::Rotation(q), v), expected, "4x4 Rotation(q)");
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}
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std::string* TestTRS() {
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// Scale, then rotate, then translate.
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const V3 t(1, -2, 3), s(2, 0.5f, 1.5f), v(0.3f, 1, -2);
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const Q q = SampleRotation();
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const V3 rotated = V3::Rotate(V3(v.x * s.x, v.y * s.y, v.z * s.z), q);
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const V3 expected(rotated.x + t.x, rotated.y + t.y, rotated.z + t.z);
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if (auto err = CheckV3(Times43(Mat43::TRS(t, q, s), v), expected, "4x3 TRS")) return err;
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return CheckV3(RowTimes44(Mat44::TRS(t, q, s), v), expected, "4x4 TRS");
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}
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std::string* TestInverseAffine() {
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const V3 t(1, -2, 3), s(2, 0.5f, 1.5f), v(0.3f, 1, -2);
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const Q q = SampleRotation();
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const Mat43 m43 = Mat43::TRS(t, q, s);
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const Mat44 m44 = Mat44::TRS(t, q, s);
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if (auto err = CheckV3(Times43(m43.InverseAffine(), Times43(m43, v)), v, "4x3 inverse undoes the transform")) return err;
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if (auto err = CheckV3(RowTimes44(m44.InverseAffine(), RowTimes44(m44, v)), v, "4x4 inverse undoes the transform")) return err;
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if (auto err = CheckMat43(m43 * m43.InverseAffine(), { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0 }, "4x3 M * M^-1")) return err;
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return CheckMat44(m44 * m44.InverseAffine(), { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 }, "4x4 M * M^-1");
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}
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std::string* TestTranspose44() {
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const Mat44 m(
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1, 2, 3, 4,
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5, 6, 7, 8,
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9, 10, 11, 12,
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13, 14, 15, 16);
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return CheckMat44(m.Transpose(), {
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1, 5, 9, 13,
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2, 6, 10, 14,
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3, 7, 11, 15,
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4, 8, 12, 16,
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}, "Transpose 4x4");
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}
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std::string* CheckSameRotation(Q got, Q expected, std::string_view label) {
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const float sign = (got.x * expected.x + got.y * expected.y + got.z * expected.z + got.w * expected.w) < 0 ? -1.0f : 1.0f;
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if (!FloatEquals(got.x * sign, expected.x) || !FloatEquals(got.y * sign, expected.y)
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|| !FloatEquals(got.z * sign, expected.z) || !FloatEquals(got.w * sign, expected.w))
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return new std::string(std::format("{}: expected ({},{},{},{}), got ({},{},{},{})",
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label, expected.x, expected.y, expected.z, expected.w, got.x, got.y, got.z, got.w));
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return nullptr;
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}
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std::string* TestDecompose() {
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const V3 t(1, -2, 3), s(2, 0.5f, 1.5f);
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const Q q = SampleRotation();
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|
{
|
|
const auto [dt, dq, ds] = Mat44::TRS(t, q, s).Decompose();
|
|
if (auto err = CheckV3(dt, t, "4x4 Decompose translation")) return err;
|
|
if (auto err = CheckV3(ds, s, "4x4 Decompose scale")) return err;
|
|
if (auto err = CheckSameRotation(dq, q, "4x4 Decompose rotation")) return err;
|
|
}
|
|
{
|
|
const auto [dt, dq, ds] = Mat43::TRS(t, q, s).Decompose();
|
|
if (auto err = CheckV3(dt, t, "4x3 Decompose translation")) return err;
|
|
if (auto err = CheckV3(ds, s, "4x3 Decompose scale")) return err;
|
|
if (auto err = CheckSameRotation(dq, q, "4x3 Decompose rotation")) return err;
|
|
}
|
|
// A mirrored matrix has no unique split; recomposing has to give the same
|
|
// transform back.
|
|
const Mat44 mirrored = Mat44::TRS(t, q, V3(-2, 0.5f, 1.5f));
|
|
const auto [mt, mq, ms] = mirrored.Decompose();
|
|
const V3 v(0.3f, 1, -2);
|
|
return CheckV3(RowTimes44(Mat44::TRS(mt, mq, ms), v), RowTimes44(mirrored, v), "mirrored Decompose recomposes");
|
|
}
|
|
|
|
// ---------- Test harness ----------
|
|
|
|
} // namespace
|
|
|
|
int main() {
|
|
using Fn = std::string* (*)();
|
|
constexpr std::array<std::pair<const char*, Fn>, 21> tests = {{
|
|
{ "Identity43", TestIdentity43 },
|
|
{ "Identity44", TestIdentity44 },
|
|
{ "StoreRoundtrip", TestStoreRoundtrip },
|
|
{ "Translation", TestTranslation },
|
|
{ "Scaling", TestScaling },
|
|
{ "MatVecIdentity", TestMatVecIdentity },
|
|
{ "MatVecTranslation", TestMatVecTranslation },
|
|
{ "MatVecScaling", TestMatVecScaling },
|
|
{ "MatVecCombined", TestMatVecCombined },
|
|
{ "TransformNormal", TestTransformNormal },
|
|
{ "MatMulIdentityLeft", TestMatMulIdentityLeft44 },
|
|
{ "MatMulIdentityRight", TestMatMulIdentityRight44 },
|
|
{ "MatMul44", TestMatMul44 },
|
|
{ "MatMulTranslation", TestMatMulTranslationCompose },
|
|
{ "MatMulScaleTranslate",TestMatMulScaleThenTranslate },
|
|
{ "Rotation43Matches44", TestRotation43MatchesRotation44 },
|
|
{ "RotationQuaternion", TestRotationFromQuaternion },
|
|
{ "TRS", TestTRS },
|
|
{ "InverseAffine", TestInverseAffine },
|
|
{ "Transpose44", TestTranspose44 },
|
|
{ "Decompose", TestDecompose },
|
|
}};
|
|
|
|
for (auto const& [name, fn] : tests) {
|
|
if (auto err = std::unique_ptr<std::string>(fn())) {
|
|
std::println(std::cerr, "[{}] {}", name, *err);
|
|
return 1;
|
|
}
|
|
}
|
|
|
|
// LookTo is tested separately - its expected result depends on the
|
|
// internal basis convention and a single failure here is informative
|
|
// enough to keep in the matrix suite.
|
|
if (auto err = std::unique_ptr<std::string>(TestLookToBasis())) {
|
|
std::println(std::cerr, "[LookTo] {}", *err);
|
|
return 1;
|
|
}
|
|
return 0;
|
|
}
|