diff options
Diffstat (limited to 'core/math/basis.cpp')
| -rw-r--r-- | core/math/basis.cpp | 37 |
1 files changed, 26 insertions, 11 deletions
diff --git a/core/math/basis.cpp b/core/math/basis.cpp index 9796ac59c2..34ed1c2d85 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(); + 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)); +} - return m.is_equal_approx(identity); +// 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 @@ -263,7 +278,7 @@ Basis Basis::scaled_orthogonal(const Vector3 &p_scale) const { return m; } -float Basis::get_uniform_scale() const { +real_t Basis::get_uniform_scale() const { return (rows[0].length() + rows[1].length() + rows[2].length()) / 3.0f; } @@ -278,7 +293,7 @@ Vector3 Basis::get_scale_abs() const { Vector3(rows[0][2], rows[1][2], rows[2][2]).length()); } -Vector3 Basis::get_scale_local() const { +Vector3 Basis::get_scale_global() const { real_t det_sign = SIGN(determinant()); return det_sign * Vector3(rows[0].length(), rows[1].length(), rows[2].length()); } @@ -670,7 +685,7 @@ void Basis::set_euler(const Vector3 &p_euler, EulerOrder p_order) { *this = zmat * ymat * xmat; } break; default: { - ERR_FAIL_MSG("Invalid order parameter for set_euler(vec3,order)"); + ERR_FAIL_MSG("Invalid Euler order parameter."); } } } @@ -707,7 +722,7 @@ Basis::operator String() const { Quaternion Basis::get_quaternion() const { #ifdef MATH_CHECKS - ERR_FAIL_COND_V_MSG(!is_rotation(), Quaternion(), "Basis must be normalized in order to be casted to a Quaternion. Use get_rotation_quaternion() or call orthonormalized() if the Basis contains linearly independent vectors."); + ERR_FAIL_COND_V_MSG(!is_rotation(), Quaternion(), "Basis " + operator String() + " must be normalized in order to be casted to a Quaternion. Use get_rotation_quaternion() or call orthonormalized() if the Basis contains linearly independent vectors."); #endif /* Allow getting a quaternion from an unnormalized transform */ Basis m = *this; @@ -834,7 +849,7 @@ void Basis::set_quaternion(const Quaternion &p_quaternion) { void Basis::set_axis_angle(const Vector3 &p_axis, real_t p_angle) { // Rotation matrix from axis and angle, see https://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_angle #ifdef MATH_CHECKS - ERR_FAIL_COND_MSG(!p_axis.is_normalized(), "The axis Vector3 must be normalized."); + ERR_FAIL_COND_MSG(!p_axis.is_normalized(), "The axis Vector3 " + p_axis.operator String() + " must be normalized."); #endif Vector3 axis_sq(p_axis.x * p_axis.x, p_axis.y * p_axis.y, p_axis.z * p_axis.z); real_t cosine = Math::cos(p_angle); @@ -892,7 +907,7 @@ void Basis::_set_diagonal(const Vector3 &p_diag) { rows[2][2] = p_diag.z; } -Basis Basis::lerp(const Basis &p_to, const real_t &p_weight) const { +Basis Basis::lerp(const Basis &p_to, real_t p_weight) const { Basis b; b.rows[0] = rows[0].lerp(p_to.rows[0], p_weight); b.rows[1] = rows[1].lerp(p_to.rows[1], p_weight); @@ -901,7 +916,7 @@ Basis Basis::lerp(const Basis &p_to, const real_t &p_weight) const { return b; } -Basis Basis::slerp(const Basis &p_to, const real_t &p_weight) const { +Basis Basis::slerp(const Basis &p_to, real_t p_weight) const { //consider scale Quaternion from(*this); Quaternion to(p_to); |