feat: quaternion operations, and transforms that mean the same in 4x4 and 4x3
- 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>
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6 changed files with 533 additions and 8 deletions
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@ -286,13 +286,135 @@ std::string* TestLookToBasis() {
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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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{
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const auto [dt, dq, ds] = Mat44::TRS(t, q, s).Decompose();
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if (auto err = CheckV3(dt, t, "4x4 Decompose translation")) return err;
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if (auto err = CheckV3(ds, s, "4x4 Decompose scale")) return err;
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if (auto err = CheckSameRotation(dq, q, "4x4 Decompose rotation")) return err;
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}
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{
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const auto [dt, dq, ds] = Mat43::TRS(t, q, s).Decompose();
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if (auto err = CheckV3(dt, t, "4x3 Decompose translation")) return err;
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if (auto err = CheckV3(ds, s, "4x3 Decompose scale")) return err;
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if (auto err = CheckSameRotation(dq, q, "4x3 Decompose rotation")) return err;
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}
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// A mirrored matrix has no unique split; recomposing has to give the same
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// transform back.
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const Mat44 mirrored = Mat44::TRS(t, q, V3(-2, 0.5f, 1.5f));
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const auto [mt, mq, ms] = mirrored.Decompose();
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const V3 v(0.3f, 1, -2);
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return CheckV3(RowTimes44(Mat44::TRS(mt, mq, ms), v), RowTimes44(mirrored, v), "mirrored Decompose recomposes");
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}
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// ---------- Test harness ----------
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} // namespace
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int main() {
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using Fn = std::string* (*)();
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constexpr std::array<std::pair<const char*, Fn>, 15> tests = {{
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constexpr std::array<std::pair<const char*, Fn>, 21> tests = {{
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{ "Identity43", TestIdentity43 },
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{ "Identity44", TestIdentity44 },
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{ "StoreRoundtrip", TestStoreRoundtrip },
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@ -308,6 +430,12 @@ int main() {
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{ "MatMul44", TestMatMul44 },
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{ "MatMulTranslation", TestMatMulTranslationCompose },
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{ "MatMulScaleTranslate",TestMatMulScaleThenTranslate },
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{ "Rotation43Matches44", TestRotation43MatchesRotation44 },
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{ "RotationQuaternion", TestRotationFromQuaternion },
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{ "TRS", TestTRS },
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{ "InverseAffine", TestInverseAffine },
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{ "Transpose44", TestTranspose44 },
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{ "Decompose", TestDecompose },
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}};
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for (auto const& [name, fn] : tests) {
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