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Fix Basis is_orthogonal and is_rotation methods, add is_orthonormal

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This commit is contained in:
Aaron Franke 2023-10-12 19:38:43 -05:00
parent 2f73a059ce
commit 7ee273723d
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GPG Key ID: 40A1750B977E56BF
3 changed files with 115 additions and 5 deletions
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25
core/math/basis.cpp
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@ -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

1
core/math/basis.h
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@ -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;

94
tests/core/math/test_basis.h
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@ -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