diff --git a/core/math/basis.cpp b/core/math/basis.cpp index 9796ac59c22..cd8c87b1588 100644 --- a/core/math/basis.cpp +++ b/core/math/basis.cpp @@ -89,13 +89,26 @@ Basis Basis::orthogonalized() const { return c; } +// Returns true if the basis vectors are orthogonal (perpendicular), so it has no skew or shear, and can be decomposed into rotation and scale. +// See https://en.wikipedia.org/wiki/Orthogonal_basis bool Basis::is_orthogonal() const { - Basis identity; - Basis m = (*this) * transposed(); - - return m.is_equal_approx(identity); + const Vector3 x = get_column(0); + const Vector3 y = get_column(1); + const Vector3 z = get_column(2); + return Math::is_zero_approx(x.dot(y)) && Math::is_zero_approx(x.dot(z)) && Math::is_zero_approx(y.dot(z)); } +// Returns true if the basis vectors are orthonormal (orthogonal and normalized), so it has no scale, skew, or shear. +// See https://en.wikipedia.org/wiki/Orthonormal_basis +bool Basis::is_orthonormal() const { + const Vector3 x = get_column(0); + const Vector3 y = get_column(1); + const Vector3 z = get_column(2); + return Math::is_equal_approx(x.length_squared(), 1) && Math::is_equal_approx(y.length_squared(), 1) && Math::is_equal_approx(z.length_squared(), 1) && Math::is_zero_approx(x.dot(y)) && Math::is_zero_approx(x.dot(z)) && Math::is_zero_approx(y.dot(z)); +} + +// Returns true if the basis is conformal (orthogonal, uniform scale, preserves angles and distance ratios). +// See https://en.wikipedia.org/wiki/Conformal_linear_transformation bool Basis::is_conformal() const { const Vector3 x = get_column(0); const Vector3 y = get_column(1); @@ -104,6 +117,7 @@ bool Basis::is_conformal() const { return Math::is_equal_approx(x_len_sq, y.length_squared()) && Math::is_equal_approx(x_len_sq, z.length_squared()) && Math::is_zero_approx(x.dot(y)) && Math::is_zero_approx(x.dot(z)) && Math::is_zero_approx(y.dot(z)); } +// Returns true if the basis only has diagonal elements, so it may only have scale or flip, but no rotation, skew, or shear. bool Basis::is_diagonal() const { return ( Math::is_zero_approx(rows[0][1]) && Math::is_zero_approx(rows[0][2]) && @@ -111,8 +125,9 @@ bool Basis::is_diagonal() const { Math::is_zero_approx(rows[2][0]) && Math::is_zero_approx(rows[2][1])); } +// Returns true if the basis is a pure rotation matrix, so it has no scale, skew, shear, or flip. bool Basis::is_rotation() const { - return Math::is_equal_approx(determinant(), 1, (real_t)UNIT_EPSILON) && is_orthogonal(); + return is_conformal() && Math::is_equal_approx(determinant(), 1, (real_t)UNIT_EPSILON); } #ifdef MATH_CHECKS diff --git a/core/math/basis.h b/core/math/basis.h index adacd1c2169..b4d971464e4 100644 --- a/core/math/basis.h +++ b/core/math/basis.h @@ -138,6 +138,7 @@ struct _NO_DISCARD_ Basis { _FORCE_INLINE_ Basis operator*(const real_t p_val) const; bool is_orthogonal() const; + bool is_orthonormal() const; bool is_conformal() const; bool is_diagonal() const; bool is_rotation() const; diff --git a/tests/core/math/test_basis.h b/tests/core/math/test_basis.h index fcac9a62318..a9bc2e9b991 100644 --- a/tests/core/math/test_basis.h +++ b/tests/core/math/test_basis.h @@ -324,6 +324,100 @@ TEST_CASE("[Basis] Is conformal checks") { CHECK_FALSE_MESSAGE( Basis(Vector3(Math_SQRT12, Math_SQRT12, 0), Vector3(0, 1, 0), Vector3(0, 0, 1)).is_conformal(), "Basis with the X axis skewed 45 degrees should not be conformal."); + + CHECK_MESSAGE( + Basis(0, 0, 0, 0, 0, 0, 0, 0, 0).is_conformal(), + "Edge case: Basis with all zeroes should return true for is_conformal (because a 0 scale is uniform)."); +} + +TEST_CASE("[Basis] Is orthogonal checks") { + CHECK_MESSAGE( + Basis().is_orthogonal(), + "Identity Basis should be orthogonal."); + + CHECK_MESSAGE( + Basis::from_euler(Vector3(1.2, 3.4, 5.6)).is_orthogonal(), + "Basis with only rotation should be orthogonal."); + + CHECK_MESSAGE( + Basis::from_scale(Vector3(-1, -1, -1)).is_orthogonal(), + "Basis with only a flip should be orthogonal."); + + CHECK_MESSAGE( + Basis::from_scale(Vector3(1.2, 3.4, 5.6)).is_orthogonal(), + "Basis with only scale should be orthogonal."); + + CHECK_MESSAGE( + Basis(Vector3(3, 4, 0), Vector3(4, -3, 0), Vector3(0, 0, 5)).is_orthogonal(), + "Basis with a flip, rotation, and uniform scale should be orthogonal."); + + CHECK_FALSE_MESSAGE( + Basis(Vector3(Math_SQRT12, Math_SQRT12, 0), Vector3(0, 1, 0), Vector3(0, 0, 1)).is_orthogonal(), + "Basis with the X axis skewed 45 degrees should not be orthogonal."); + + CHECK_MESSAGE( + Basis(0, 0, 0, 0, 0, 0, 0, 0, 0).is_orthogonal(), + "Edge case: Basis with all zeroes should return true for is_orthogonal, since zero vectors are orthogonal to all vectors."); +} + +TEST_CASE("[Basis] Is orthonormal checks") { + CHECK_MESSAGE( + Basis().is_orthonormal(), + "Identity Basis should be orthonormal."); + + CHECK_MESSAGE( + Basis::from_euler(Vector3(1.2, 3.4, 5.6)).is_orthonormal(), + "Basis with only rotation should be orthonormal."); + + CHECK_MESSAGE( + Basis::from_scale(Vector3(-1, -1, -1)).is_orthonormal(), + "Basis with only a flip should be orthonormal."); + + CHECK_FALSE_MESSAGE( + Basis::from_scale(Vector3(1.2, 3.4, 5.6)).is_orthonormal(), + "Basis with only scale should not be orthonormal."); + + CHECK_FALSE_MESSAGE( + Basis(Vector3(3, 4, 0), Vector3(4, -3, 0), Vector3(0, 0, 5)).is_orthonormal(), + "Basis with a flip, rotation, and uniform scale should not be orthonormal."); + + CHECK_FALSE_MESSAGE( + Basis(Vector3(Math_SQRT12, Math_SQRT12, 0), Vector3(0, 1, 0), Vector3(0, 0, 1)).is_orthonormal(), + "Basis with the X axis skewed 45 degrees should not be orthonormal."); + + CHECK_FALSE_MESSAGE( + Basis(0, 0, 0, 0, 0, 0, 0, 0, 0).is_orthonormal(), + "Edge case: Basis with all zeroes should return false for is_orthonormal, since the vectors do not have a length of 1."); +} + +TEST_CASE("[Basis] Is rotation checks") { + CHECK_MESSAGE( + Basis().is_rotation(), + "Identity Basis should be a rotation (a rotation of zero)."); + + CHECK_MESSAGE( + Basis::from_euler(Vector3(1.2, 3.4, 5.6)).is_rotation(), + "Basis with only rotation should be a rotation."); + + CHECK_FALSE_MESSAGE( + Basis::from_scale(Vector3(-1, -1, -1)).is_rotation(), + "Basis with only a flip should not be a rotation."); + + CHECK_FALSE_MESSAGE( + Basis::from_scale(Vector3(1.2, 3.4, 5.6)).is_rotation(), + "Basis with only scale should not be a rotation."); + + CHECK_FALSE_MESSAGE( + Basis(Vector3(2, 0, 0), Vector3(0, 0.5, 0), Vector3(0, 0, 1)).is_rotation(), + "Basis with a squeeze should not be a rotation."); + + CHECK_FALSE_MESSAGE( + Basis(Vector3(Math_SQRT12, Math_SQRT12, 0), Vector3(0, 1, 0), Vector3(0, 0, 1)).is_rotation(), + "Basis with the X axis skewed 45 degrees should not be a rotation."); + + CHECK_FALSE_MESSAGE( + Basis(0, 0, 0, 0, 0, 0, 0, 0, 0).is_rotation(), + "Edge case: Basis with all zeroes should return false for is_rotation, because it is not just a rotation (has a scale of 0)."); } } // namespace TestBasis