diff options
Diffstat (limited to 'src/variant/basis.cpp')
-rw-r--r-- | src/variant/basis.cpp | 887 |
1 files changed, 399 insertions, 488 deletions
diff --git a/src/variant/basis.cpp b/src/variant/basis.cpp index 0385214..27212c0 100644 --- a/src/variant/basis.cpp +++ b/src/variant/basis.cpp @@ -38,16 +38,16 @@ namespace godot { void Basis::from_z(const Vector3 &p_z) { - if (Math::abs(p_z.z) > Math_SQRT12) { + if (Math::abs(p_z.z) > (real_t)Math_SQRT12) { // choose p in y-z plane real_t a = p_z[1] * p_z[1] + p_z[2] * p_z[2]; - real_t k = 1.0 / Math::sqrt(a); + real_t k = 1.0f / Math::sqrt(a); rows[0] = Vector3(0, -p_z[2] * k, p_z[1] * k); rows[1] = Vector3(a * k, -p_z[0] * rows[0][2], p_z[0] * rows[0][1]); } else { // choose p in x-y plane real_t a = p_z.x * p_z.x + p_z.y * p_z.y; - real_t k = 1.0 / Math::sqrt(a); + real_t k = 1.0f / Math::sqrt(a); rows[0] = Vector3(-p_z.y * k, p_z.x * k, 0); rows[1] = Vector3(-p_z.z * rows[0].y, p_z.z * rows[0].x, a * k); } @@ -59,12 +59,12 @@ void Basis::invert() { cofac(1, 1, 2, 2), cofac(1, 2, 2, 0), cofac(1, 0, 2, 1) }; real_t det = rows[0][0] * co[0] + - rows[0][1] * co[1] + - rows[0][2] * co[2]; + rows[0][1] * co[1] + + rows[0][2] * co[2]; #ifdef MATH_CHECKS ERR_FAIL_COND(det == 0); #endif - real_t s = 1.0 / det; + real_t s = 1.0f / det; set(co[0] * s, cofac(0, 2, 2, 1) * s, cofac(0, 1, 1, 2) * s, co[1] * s, cofac(0, 0, 2, 2) * s, cofac(0, 2, 1, 0) * s, @@ -74,9 +74,9 @@ void Basis::invert() { void Basis::orthonormalize() { // Gram-Schmidt Process - Vector3 x = get_axis(0); - Vector3 y = get_axis(1); - Vector3 z = get_axis(2); + Vector3 x = get_column(0); + Vector3 y = get_column(1); + Vector3 z = get_column(2); x.normalize(); y = (y - x * (x.dot(y))); @@ -84,9 +84,9 @@ void Basis::orthonormalize() { z = (z - x * (x.dot(z)) - y * (y.dot(z))); z.normalize(); - set_axis(0, x); - set_axis(1, y); - set_axis(2, z); + set_column(0, x); + set_column(1, y); + set_column(2, z); } Basis Basis::orthonormalized() const { @@ -95,6 +95,18 @@ Basis Basis::orthonormalized() const { return c; } +void Basis::orthogonalize() { + Vector3 scl = get_scale(); + orthonormalize(); + scale_local(scl); +} + +Basis Basis::orthogonalized() const { + Basis c = *this; + c.orthogonalize(); + return c; +} + bool Basis::is_orthogonal() const { Basis identity; Basis m = (*this) * transposed(); @@ -132,7 +144,7 @@ bool Basis::is_symmetric() const { Basis Basis::diagonalize() { // NOTE: only implemented for symmetric matrices -// with the Jacobi iterative method method +// with the Jacobi iterative method #ifdef MATH_CHECKS ERR_FAIL_COND_V(!is_symmetric(), Basis()); #endif @@ -142,7 +154,7 @@ Basis Basis::diagonalize() { int ite = 0; Basis acc_rot; - while (off_matrix_norm_2 > CMP_EPSILON2 && ite++ < ite_max) { + while (off_matrix_norm_2 > (real_t)CMP_EPSILON2 && ite++ < ite_max) { real_t el01_2 = rows[0][1] * rows[0][1]; real_t el02_2 = rows[0][2] * rows[0][2]; real_t el12_2 = rows[1][2] * rows[1][2]; @@ -171,7 +183,7 @@ Basis Basis::diagonalize() { if (Math::is_equal_approx(rows[j][j], rows[i][i])) { angle = Math_PI / 4; } else { - angle = 0.5 * Math::atan(2 * rows[i][j] / (rows[j][j] - rows[i][i])); + angle = 0.5f * Math::atan(2 * rows[i][j] / (rows[j][j] - rows[i][i])); } // Compute the rotation matrix @@ -208,6 +220,10 @@ Basis Basis::transposed() const { return tr; } +Basis Basis::from_scale(const Vector3 &p_scale) { + return Basis(p_scale.x, 0, 0, 0, p_scale.y, 0, 0, 0, p_scale.z); +} + // Multiplies the matrix from left by the scaling matrix: M -> S.M // See the comment for Basis::rotated for further explanation. void Basis::scale(const Vector3 &p_scale) { @@ -234,12 +250,30 @@ void Basis::scale_local(const Vector3 &p_scale) { *this = scaled_local(p_scale); } +void Basis::scale_orthogonal(const Vector3 &p_scale) { + *this = scaled_orthogonal(p_scale); +} + +Basis Basis::scaled_orthogonal(const Vector3 &p_scale) const { + Basis m = *this; + Vector3 s = Vector3(-1, -1, -1) + p_scale; + Vector3 dots; + Basis b; + for (int i = 0; i < 3; i++) { + for (int j = 0; j < 3; j++) { + dots[j] += s[i] * abs(m.get_column(i).normalized().dot(b.get_column(j))); + } + } + m.scale_local(Vector3(1, 1, 1) + dots); + return m; +} + float Basis::get_uniform_scale() const { - return (rows[0].length() + rows[1].length() + rows[2].length()) / 3.0; + return (rows[0].length() + rows[1].length() + rows[2].length()) / 3.0f; } void Basis::make_scale_uniform() { - float l = (rows[0].length() + rows[1].length() + rows[2].length()) / 3.0; + float l = (rows[0].length() + rows[1].length() + rows[2].length()) / 3.0f; for (int i = 0; i < 3; i++) { rows[i].normalize(); rows[i] *= l; @@ -247,10 +281,7 @@ void Basis::make_scale_uniform() { } Basis Basis::scaled_local(const Vector3 &p_scale) const { - Basis b; - b.set_diagonal(p_scale); - - return (*this) * b; + return (*this) * Basis::from_scale(p_scale); } Vector3 Basis::get_scale_abs() const { @@ -261,7 +292,7 @@ Vector3 Basis::get_scale_abs() const { } Vector3 Basis::get_scale_local() const { - real_t det_sign = Math::sign(determinant()); + real_t det_sign = SIGN(determinant()); return det_sign * Vector3(rows[0].length(), rows[1].length(), rows[2].length()); } @@ -287,11 +318,8 @@ Vector3 Basis::get_scale() const { // matrix rows. // // The rotation part of this decomposition is returned by get_rotation* functions. - real_t det_sign = Math::sign(determinant()); - return det_sign * Vector3( - Vector3(rows[0][0], rows[1][0], rows[2][0]).length(), - Vector3(rows[0][1], rows[1][1], rows[2][1]).length(), - Vector3(rows[0][2], rows[1][2], rows[2][2]).length()); + real_t det_sign = SIGN(determinant()); + return det_sign * get_scale_abs(); } // Decomposes a Basis into a rotation-reflection matrix (an element of the group O(3)) and a positive scaling matrix as B = O.S. @@ -317,44 +345,44 @@ Vector3 Basis::rotref_posscale_decomposition(Basis &rotref) const { // Multiplies the matrix from left by the rotation matrix: M -> R.M // Note that this does *not* rotate the matrix itself. // -// The main use of Basis is as Transform3D.basis, which is used a the transformation matrix +// The main use of Basis is as Transform.basis, which is used by the transformation matrix // of 3D object. Rotate here refers to rotation of the object (which is R * (*this)), // not the matrix itself (which is R * (*this) * R.transposed()). -Basis Basis::rotated(const Vector3 &p_axis, real_t p_phi) const { - return Basis(p_axis, p_phi) * (*this); +Basis Basis::rotated(const Vector3 &p_axis, real_t p_angle) const { + return Basis(p_axis, p_angle) * (*this); } -void Basis::rotate(const Vector3 &p_axis, real_t p_phi) { - *this = rotated(p_axis, p_phi); +void Basis::rotate(const Vector3 &p_axis, real_t p_angle) { + *this = rotated(p_axis, p_angle); } -void Basis::rotate_local(const Vector3 &p_axis, real_t p_phi) { +void Basis::rotate_local(const Vector3 &p_axis, real_t p_angle) { // performs a rotation in object-local coordinate system: // M -> (M.R.Minv).M = M.R. - *this = rotated_local(p_axis, p_phi); + *this = rotated_local(p_axis, p_angle); } -Basis Basis::rotated_local(const Vector3 &p_axis, real_t p_phi) const { - return (*this) * Basis(p_axis, p_phi); +Basis Basis::rotated_local(const Vector3 &p_axis, real_t p_angle) const { + return (*this) * Basis(p_axis, p_angle); } -Basis Basis::rotated(const Vector3 &p_euler) const { - return Basis(p_euler) * (*this); +Basis Basis::rotated(const Vector3 &p_euler, EulerOrder p_order) const { + return Basis::from_euler(p_euler, p_order) * (*this); } -void Basis::rotate(const Vector3 &p_euler) { - *this = rotated(p_euler); +void Basis::rotate(const Vector3 &p_euler, EulerOrder p_order) { + *this = rotated(p_euler, p_order); } -Basis Basis::rotated(const Quaternion &p_quat) const { - return Basis(p_quat) * (*this); +Basis Basis::rotated(const Quaternion &p_quaternion) const { + return Basis(p_quaternion) * (*this); } -void Basis::rotate(const Quaternion &p_quat) { - *this = rotated(p_quat); +void Basis::rotate(const Quaternion &p_quaternion) { + *this = rotated(p_quaternion); } -Vector3 Basis::get_rotation_euler() const { +Vector3 Basis::get_euler_normalized(EulerOrder p_order) const { // Assumes that the matrix can be decomposed into a proper rotation and scaling matrix as M = R.S, // and returns the Euler angles corresponding to the rotation part, complementing get_scale(). // See the comment in get_scale() for further information. @@ -365,7 +393,7 @@ Vector3 Basis::get_rotation_euler() const { m.scale(Vector3(-1, -1, -1)); } - return m.get_euler(); + return m.get_euler(p_order); } Quaternion Basis::get_rotation_quaternion() const { @@ -382,6 +410,18 @@ Quaternion Basis::get_rotation_quaternion() const { return m.get_quaternion(); } +void Basis::rotate_to_align(Vector3 p_start_direction, Vector3 p_end_direction) { + // Takes two vectors and rotates the basis from the first vector to the second vector. + // Adopted from: https://gist.github.com/kevinmoran/b45980723e53edeb8a5a43c49f134724 + const Vector3 axis = p_start_direction.cross(p_end_direction).normalized(); + if (axis.length_squared() != 0) { + real_t dot = p_start_direction.dot(p_end_direction); + dot = CLAMP(dot, -1.0f, 1.0f); + const real_t angle_rads = Math::acos(dot); + set_axis_angle(axis, angle_rads); + } +} + void Basis::get_rotation_axis_angle(Vector3 &p_axis, real_t &p_angle) const { // Assumes that the matrix can be decomposed into a proper rotation and scaling matrix as M = R.S, // and returns the Euler angles corresponding to the rotation part, complementing get_scale(). @@ -412,328 +452,240 @@ void Basis::get_rotation_axis_angle_local(Vector3 &p_axis, real_t &p_angle) cons p_angle = -p_angle; } -// get_euler_xyz returns a vector containing the Euler angles in the format -// (a1,a2,a3), where a3 is the angle of the first rotation, and a1 is the last -// (following the convention they are commonly defined in the literature). -// -// The current implementation uses XYZ convention (Z is the first rotation), -// so euler.z is the angle of the (first) rotation around Z axis and so on, -// -// And thus, assuming the matrix is a rotation matrix, this function returns -// the angles in the decomposition R = X(a1).Y(a2).Z(a3) where Z(a) rotates -// around the z-axis by a and so on. -Vector3 Basis::get_euler_xyz() const { - // Euler angles in XYZ convention. - // See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix - // - // rot = cy*cz -cy*sz sy - // cz*sx*sy+cx*sz cx*cz-sx*sy*sz -cy*sx - // -cx*cz*sy+sx*sz cz*sx+cx*sy*sz cx*cy - - Vector3 euler; - real_t sy = rows[0][2]; - if (sy < (1.0 - CMP_EPSILON)) { - if (sy > -(1.0 - CMP_EPSILON)) { - // is this a pure Y rotation? - if (rows[1][0] == 0.0 && rows[0][1] == 0.0 && rows[1][2] == 0 && rows[2][1] == 0 && rows[1][1] == 1) { - // return the simplest form (human friendlier in editor and scripts) - euler.x = 0; - euler.y = atan2(rows[0][2], rows[0][0]); - euler.z = 0; +Vector3 Basis::get_euler(EulerOrder p_order) const { + switch (p_order) { + case EULER_ORDER_XYZ: { + // Euler angles in XYZ convention. + // See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix + // + // rot = cy*cz -cy*sz sy + // cz*sx*sy+cx*sz cx*cz-sx*sy*sz -cy*sx + // -cx*cz*sy+sx*sz cz*sx+cx*sy*sz cx*cy + + Vector3 euler; + real_t sy = rows[0][2]; + if (sy < (1.0f - (real_t)CMP_EPSILON)) { + if (sy > -(1.0f - (real_t)CMP_EPSILON)) { + // is this a pure Y rotation? + if (rows[1][0] == 0 && rows[0][1] == 0 && rows[1][2] == 0 && rows[2][1] == 0 && rows[1][1] == 1) { + // return the simplest form (human friendlier in editor and scripts) + euler.x = 0; + euler.y = atan2(rows[0][2], rows[0][0]); + euler.z = 0; + } else { + euler.x = Math::atan2(-rows[1][2], rows[2][2]); + euler.y = Math::asin(sy); + euler.z = Math::atan2(-rows[0][1], rows[0][0]); + } + } else { + euler.x = Math::atan2(rows[2][1], rows[1][1]); + euler.y = -Math_PI / 2.0f; + euler.z = 0.0f; + } } else { - euler.x = Math::atan2(-rows[1][2], rows[2][2]); - euler.y = Math::asin(sy); - euler.z = Math::atan2(-rows[0][1], rows[0][0]); + euler.x = Math::atan2(rows[2][1], rows[1][1]); + euler.y = Math_PI / 2.0f; + euler.z = 0.0f; + } + return euler; + } break; + case EULER_ORDER_XZY: { + // Euler angles in XZY convention. + // See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix + // + // rot = cz*cy -sz cz*sy + // sx*sy+cx*cy*sz cx*cz cx*sz*sy-cy*sx + // cy*sx*sz cz*sx cx*cy+sx*sz*sy + + Vector3 euler; + real_t sz = rows[0][1]; + if (sz < (1.0f - (real_t)CMP_EPSILON)) { + if (sz > -(1.0f - (real_t)CMP_EPSILON)) { + euler.x = Math::atan2(rows[2][1], rows[1][1]); + euler.y = Math::atan2(rows[0][2], rows[0][0]); + euler.z = Math::asin(-sz); + } else { + // It's -1 + euler.x = -Math::atan2(rows[1][2], rows[2][2]); + euler.y = 0.0f; + euler.z = Math_PI / 2.0f; + } + } else { + // It's 1 + euler.x = -Math::atan2(rows[1][2], rows[2][2]); + euler.y = 0.0f; + euler.z = -Math_PI / 2.0f; + } + return euler; + } break; + case EULER_ORDER_YXZ: { + // Euler angles in YXZ convention. + // See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix + // + // rot = cy*cz+sy*sx*sz cz*sy*sx-cy*sz cx*sy + // cx*sz cx*cz -sx + // cy*sx*sz-cz*sy cy*cz*sx+sy*sz cy*cx + + Vector3 euler; + + real_t m12 = rows[1][2]; + + if (m12 < (1 - (real_t)CMP_EPSILON)) { + if (m12 > -(1 - (real_t)CMP_EPSILON)) { + // is this a pure X rotation? + if (rows[1][0] == 0 && rows[0][1] == 0 && rows[0][2] == 0 && rows[2][0] == 0 && rows[0][0] == 1) { + // return the simplest form (human friendlier in editor and scripts) + euler.x = atan2(-m12, rows[1][1]); + euler.y = 0; + euler.z = 0; + } else { + euler.x = asin(-m12); + euler.y = atan2(rows[0][2], rows[2][2]); + euler.z = atan2(rows[1][0], rows[1][1]); + } + } else { // m12 == -1 + euler.x = Math_PI * 0.5f; + euler.y = atan2(rows[0][1], rows[0][0]); + euler.z = 0; + } + } else { // m12 == 1 + euler.x = -Math_PI * 0.5f; + euler.y = -atan2(rows[0][1], rows[0][0]); + euler.z = 0; } - } else { - euler.x = Math::atan2(rows[2][1], rows[1][1]); - euler.y = -Math_PI / 2.0; - euler.z = 0.0; - } - } else { - euler.x = Math::atan2(rows[2][1], rows[1][1]); - euler.y = Math_PI / 2.0; - euler.z = 0.0; - } - return euler; -} - -// set_euler_xyz expects a vector containing the Euler angles in the format -// (ax,ay,az), where ax is the angle of rotation around x axis, -// and similar for other axes. -// The current implementation uses XYZ convention (Z is the first rotation). -void Basis::set_euler_xyz(const Vector3 &p_euler) { - real_t c, s; - - c = Math::cos(p_euler.x); - s = Math::sin(p_euler.x); - Basis xmat(1.0, 0.0, 0.0, 0.0, c, -s, 0.0, s, c); - - c = Math::cos(p_euler.y); - s = Math::sin(p_euler.y); - Basis ymat(c, 0.0, s, 0.0, 1.0, 0.0, -s, 0.0, c); - - c = Math::cos(p_euler.z); - s = Math::sin(p_euler.z); - Basis zmat(c, -s, 0.0, s, c, 0.0, 0.0, 0.0, 1.0); - - // optimizer will optimize away all this anyway - *this = xmat * (ymat * zmat); -} - -Vector3 Basis::get_euler_xzy() const { - // Euler angles in XZY convention. - // See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix - // - // rot = cz*cy -sz cz*sy - // sx*sy+cx*cy*sz cx*cz cx*sz*sy-cy*sx - // cy*sx*sz cz*sx cx*cy+sx*sz*sy - - Vector3 euler; - real_t sz = rows[0][1]; - if (sz < (1.0 - CMP_EPSILON)) { - if (sz > -(1.0 - CMP_EPSILON)) { - euler.x = Math::atan2(rows[2][1], rows[1][1]); - euler.y = Math::atan2(rows[0][2], rows[0][0]); - euler.z = Math::asin(-sz); - } else { - // It's -1 - euler.x = -Math::atan2(rows[1][2], rows[2][2]); - euler.y = 0.0; - euler.z = Math_PI / 2.0; - } - } else { - // It's 1 - euler.x = -Math::atan2(rows[1][2], rows[2][2]); - euler.y = 0.0; - euler.z = -Math_PI / 2.0; - } - return euler; -} - -void Basis::set_euler_xzy(const Vector3 &p_euler) { - real_t c, s; - - c = Math::cos(p_euler.x); - s = Math::sin(p_euler.x); - Basis xmat(1.0, 0.0, 0.0, 0.0, c, -s, 0.0, s, c); - - c = Math::cos(p_euler.y); - s = Math::sin(p_euler.y); - Basis ymat(c, 0.0, s, 0.0, 1.0, 0.0, -s, 0.0, c); - - c = Math::cos(p_euler.z); - s = Math::sin(p_euler.z); - Basis zmat(c, -s, 0.0, s, c, 0.0, 0.0, 0.0, 1.0); - - *this = xmat * zmat * ymat; -} - -Vector3 Basis::get_euler_yzx() const { - // Euler angles in YZX convention. - // See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix - // - // rot = cy*cz sy*sx-cy*cx*sz cx*sy+cy*sz*sx - // sz cz*cx -cz*sx - // -cz*sy cy*sx+cx*sy*sz cy*cx-sy*sz*sx - - Vector3 euler; - real_t sz = rows[1][0]; - if (sz < (1.0 - CMP_EPSILON)) { - if (sz > -(1.0 - CMP_EPSILON)) { - euler.x = Math::atan2(-rows[1][2], rows[1][1]); - euler.y = Math::atan2(-rows[2][0], rows[0][0]); - euler.z = Math::asin(sz); - } else { - // It's -1 - euler.x = Math::atan2(rows[2][1], rows[2][2]); - euler.y = 0.0; - euler.z = -Math_PI / 2.0; - } - } else { - // It's 1 - euler.x = Math::atan2(rows[2][1], rows[2][2]); - euler.y = 0.0; - euler.z = Math_PI / 2.0; - } - return euler; -} - -void Basis::set_euler_yzx(const Vector3 &p_euler) { - real_t c, s; - - c = Math::cos(p_euler.x); - s = Math::sin(p_euler.x); - Basis xmat(1.0, 0.0, 0.0, 0.0, c, -s, 0.0, s, c); - - c = Math::cos(p_euler.y); - s = Math::sin(p_euler.y); - Basis ymat(c, 0.0, s, 0.0, 1.0, 0.0, -s, 0.0, c); - - c = Math::cos(p_euler.z); - s = Math::sin(p_euler.z); - Basis zmat(c, -s, 0.0, s, c, 0.0, 0.0, 0.0, 1.0); - - *this = ymat * zmat * xmat; -} - -// get_euler_yxz returns a vector containing the Euler angles in the YXZ convention, -// as in first-Z, then-X, last-Y. The angles for X, Y, and Z rotations are returned -// as the x, y, and z components of a Vector3 respectively. -Vector3 Basis::get_euler_yxz() const { - // Euler angles in YXZ convention. - // See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix - // - // rot = cy*cz+sy*sx*sz cz*sy*sx-cy*sz cx*sy - // cx*sz cx*cz -sx - // cy*sx*sz-cz*sy cy*cz*sx+sy*sz cy*cx - - Vector3 euler; - - real_t m12 = rows[1][2]; - if (m12 < (1 - CMP_EPSILON)) { - if (m12 > -(1 - CMP_EPSILON)) { - // is this a pure X rotation? - if (rows[1][0] == 0 && rows[0][1] == 0 && rows[0][2] == 0 && rows[2][0] == 0 && rows[0][0] == 1) { - // return the simplest form (human friendlier in editor and scripts) - euler.x = atan2(-m12, rows[1][1]); - euler.y = 0; + return euler; + } break; + case EULER_ORDER_YZX: { + // Euler angles in YZX convention. + // See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix + // + // rot = cy*cz sy*sx-cy*cx*sz cx*sy+cy*sz*sx + // sz cz*cx -cz*sx + // -cz*sy cy*sx+cx*sy*sz cy*cx-sy*sz*sx + + Vector3 euler; + real_t sz = rows[1][0]; + if (sz < (1.0f - (real_t)CMP_EPSILON)) { + if (sz > -(1.0f - (real_t)CMP_EPSILON)) { + euler.x = Math::atan2(-rows[1][2], rows[1][1]); + euler.y = Math::atan2(-rows[2][0], rows[0][0]); + euler.z = Math::asin(sz); + } else { + // It's -1 + euler.x = Math::atan2(rows[2][1], rows[2][2]); + euler.y = 0.0f; + euler.z = -Math_PI / 2.0f; + } + } else { + // It's 1 + euler.x = Math::atan2(rows[2][1], rows[2][2]); + euler.y = 0.0f; + euler.z = Math_PI / 2.0f; + } + return euler; + } break; + case EULER_ORDER_ZXY: { + // Euler angles in ZXY convention. + // See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix + // + // rot = cz*cy-sz*sx*sy -cx*sz cz*sy+cy*sz*sx + // cy*sz+cz*sx*sy cz*cx sz*sy-cz*cy*sx + // -cx*sy sx cx*cy + Vector3 euler; + real_t sx = rows[2][1]; + if (sx < (1.0f - (real_t)CMP_EPSILON)) { + if (sx > -(1.0f - (real_t)CMP_EPSILON)) { + euler.x = Math::asin(sx); + euler.y = Math::atan2(-rows[2][0], rows[2][2]); + euler.z = Math::atan2(-rows[0][1], rows[1][1]); + } else { + // It's -1 + euler.x = -Math_PI / 2.0f; + euler.y = Math::atan2(rows[0][2], rows[0][0]); + euler.z = 0; + } + } else { + // It's 1 + euler.x = Math_PI / 2.0f; + euler.y = Math::atan2(rows[0][2], rows[0][0]); euler.z = 0; + } + return euler; + } break; + case EULER_ORDER_ZYX: { + // Euler angles in ZYX convention. + // See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix + // + // rot = cz*cy cz*sy*sx-cx*sz sz*sx+cz*cx*cy + // cy*sz cz*cx+sz*sy*sx cx*sz*sy-cz*sx + // -sy cy*sx cy*cx + Vector3 euler; + real_t sy = rows[2][0]; + if (sy < (1.0f - (real_t)CMP_EPSILON)) { + if (sy > -(1.0f - (real_t)CMP_EPSILON)) { + euler.x = Math::atan2(rows[2][1], rows[2][2]); + euler.y = Math::asin(-sy); + euler.z = Math::atan2(rows[1][0], rows[0][0]); + } else { + // It's -1 + euler.x = 0; + euler.y = Math_PI / 2.0f; + euler.z = -Math::atan2(rows[0][1], rows[1][1]); + } } else { - euler.x = asin(-m12); - euler.y = atan2(rows[0][2], rows[2][2]); - euler.z = atan2(rows[1][0], rows[1][1]); + // It's 1 + euler.x = 0; + euler.y = -Math_PI / 2.0f; + euler.z = -Math::atan2(rows[0][1], rows[1][1]); } - } else { // m12 == -1 - euler.x = Math_PI * 0.5; - euler.y = atan2(rows[0][1], rows[0][0]); - euler.z = 0; + return euler; + } break; + default: { + ERR_FAIL_V_MSG(Vector3(), "Invalid parameter for get_euler(order)"); } - } else { // m12 == 1 - euler.x = -Math_PI * 0.5; - euler.y = -atan2(rows[0][1], rows[0][0]); - euler.z = 0; } - - return euler; + return Vector3(); } -// set_euler_yxz expects a vector containing the Euler angles in the format -// (ax,ay,az), where ax is the angle of rotation around x axis, -// and similar for other axes. -// The current implementation uses YXZ convention (Z is the first rotation). -void Basis::set_euler_yxz(const Vector3 &p_euler) { +void Basis::set_euler(const Vector3 &p_euler, EulerOrder p_order) { real_t c, s; c = Math::cos(p_euler.x); s = Math::sin(p_euler.x); - Basis xmat(1.0, 0.0, 0.0, 0.0, c, -s, 0.0, s, c); + Basis xmat(1, 0, 0, 0, c, -s, 0, s, c); c = Math::cos(p_euler.y); s = Math::sin(p_euler.y); - Basis ymat(c, 0.0, s, 0.0, 1.0, 0.0, -s, 0.0, c); + Basis ymat(c, 0, s, 0, 1, 0, -s, 0, c); c = Math::cos(p_euler.z); s = Math::sin(p_euler.z); - Basis zmat(c, -s, 0.0, s, c, 0.0, 0.0, 0.0, 1.0); - - // optimizer will optimize away all this anyway - *this = ymat * xmat * zmat; -} - -Vector3 Basis::get_euler_zxy() const { - // Euler angles in ZXY convention. - // See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix - // - // rot = cz*cy-sz*sx*sy -cx*sz cz*sy+cy*sz*sx - // cy*sz+cz*sx*sy cz*cx sz*sy-cz*cy*sx - // -cx*sy sx cx*cy - Vector3 euler; - real_t sx = rows[2][1]; - if (sx < (1.0 - CMP_EPSILON)) { - if (sx > -(1.0 - CMP_EPSILON)) { - euler.x = Math::asin(sx); - euler.y = Math::atan2(-rows[2][0], rows[2][2]); - euler.z = Math::atan2(-rows[0][1], rows[1][1]); - } else { - // It's -1 - euler.x = -Math_PI / 2.0; - euler.y = Math::atan2(rows[0][2], rows[0][0]); - euler.z = 0; + Basis zmat(c, -s, 0, s, c, 0, 0, 0, 1); + + switch (p_order) { + case EULER_ORDER_XYZ: { + *this = xmat * (ymat * zmat); + } break; + case EULER_ORDER_XZY: { + *this = xmat * zmat * ymat; + } break; + case EULER_ORDER_YXZ: { + *this = ymat * xmat * zmat; + } break; + case EULER_ORDER_YZX: { + *this = ymat * zmat * xmat; + } break; + case EULER_ORDER_ZXY: { + *this = zmat * xmat * ymat; + } break; + case EULER_ORDER_ZYX: { + *this = zmat * ymat * xmat; + } break; + default: { + ERR_FAIL_MSG("Invalid order parameter for set_euler(vec3,order)"); } - } else { - // It's 1 - euler.x = Math_PI / 2.0; - euler.y = Math::atan2(rows[0][2], rows[0][0]); - euler.z = 0; } - return euler; -} - -void Basis::set_euler_zxy(const Vector3 &p_euler) { - real_t c, s; - - c = Math::cos(p_euler.x); - s = Math::sin(p_euler.x); - Basis xmat(1.0, 0.0, 0.0, 0.0, c, -s, 0.0, s, c); - - c = Math::cos(p_euler.y); - s = Math::sin(p_euler.y); - Basis ymat(c, 0.0, s, 0.0, 1.0, 0.0, -s, 0.0, c); - - c = Math::cos(p_euler.z); - s = Math::sin(p_euler.z); - Basis zmat(c, -s, 0.0, s, c, 0.0, 0.0, 0.0, 1.0); - - *this = zmat * xmat * ymat; -} - -Vector3 Basis::get_euler_zyx() const { - // Euler angles in ZYX convention. - // See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix - // - // rot = cz*cy cz*sy*sx-cx*sz sz*sx+cz*cx*cy - // cy*sz cz*cx+sz*sy*sx cx*sz*sy-cz*sx - // -sy cy*sx cy*cx - Vector3 euler; - real_t sy = rows[2][0]; - if (sy < (1.0 - CMP_EPSILON)) { - if (sy > -(1.0 - CMP_EPSILON)) { - euler.x = Math::atan2(rows[2][1], rows[2][2]); - euler.y = Math::asin(-sy); - euler.z = Math::atan2(rows[1][0], rows[0][0]); - } else { - // It's -1 - euler.x = 0; - euler.y = Math_PI / 2.0; - euler.z = -Math::atan2(rows[0][1], rows[1][1]); - } - } else { - // It's 1 - euler.x = 0; - euler.y = -Math_PI / 2.0; - euler.z = -Math::atan2(rows[0][1], rows[1][1]); - } - return euler; -} - -void Basis::set_euler_zyx(const Vector3 &p_euler) { - real_t c, s; - - c = Math::cos(p_euler.x); - s = Math::sin(p_euler.x); - Basis xmat(1.0, 0.0, 0.0, 0.0, c, -s, 0.0, s, c); - - c = Math::cos(p_euler.y); - s = Math::sin(p_euler.y); - Basis ymat(c, 0.0, s, 0.0, 1.0, 0.0, -s, 0.0, c); - - c = Math::cos(p_euler.z); - s = Math::sin(p_euler.z); - Basis zmat(c, -s, 0.0, s, c, 0.0, 0.0, 0.0, 1.0); - - *this = zmat * ymat * xmat; } bool Basis::is_equal_approx(const Basis &p_basis) const { @@ -757,47 +709,38 @@ bool Basis::operator!=(const Basis &p_matrix) const { } Basis::operator String() const { - String mtx; - for (int i = 0; i < 3; i++) { - for (int j = 0; j < 3; j++) { - if (i != 0 || j != 0) { - mtx = mtx + ", "; - } - - mtx = mtx + String::num(rows[j][i]); // matrix is stored transposed for performance, so print it transposed - } - } - - return mtx; + return "[X: " + get_column(0).operator String() + + ", Y: " + get_column(1).operator String() + + ", Z: " + get_column(2).operator String() + "]"; } Quaternion Basis::get_quaternion() const { #ifdef MATH_CHECKS - ERR_FAIL_COND_V(!is_rotation(), Quaternion()); + 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."); #endif /* Allow getting a quaternion from an unnormalized transform */ Basis m = *this; real_t trace = m.rows[0][0] + m.rows[1][1] + m.rows[2][2]; real_t temp[4]; - if (trace > 0.0) { - real_t s = Math::sqrt(trace + 1.0); - temp[3] = (s * 0.5); - s = 0.5 / s; + if (trace > 0.0f) { + real_t s = Math::sqrt(trace + 1.0f); + temp[3] = (s * 0.5f); + s = 0.5f / s; temp[0] = ((m.rows[2][1] - m.rows[1][2]) * s); temp[1] = ((m.rows[0][2] - m.rows[2][0]) * s); temp[2] = ((m.rows[1][0] - m.rows[0][1]) * s); } else { - int i = m.rows[0][0] < m.rows[1][1] ? - (m.rows[1][1] < m.rows[2][2] ? 2 : 1) : - (m.rows[0][0] < m.rows[2][2] ? 2 : 0); + int i = m.rows[0][0] < m.rows[1][1] + ? (m.rows[1][1] < m.rows[2][2] ? 2 : 1) + : (m.rows[0][0] < m.rows[2][2] ? 2 : 0); int j = (i + 1) % 3; int k = (i + 2) % 3; - real_t s = Math::sqrt(m.rows[i][i] - m.rows[j][j] - m.rows[k][k] + 1.0); - temp[i] = s * 0.5; - s = 0.5 / s; + real_t s = Math::sqrt(m.rows[i][i] - m.rows[j][j] - m.rows[k][k] + 1.0f); + temp[i] = s * 0.5f; + s = 0.5f / s; temp[3] = (m.rows[k][j] - m.rows[j][k]) * s; temp[j] = (m.rows[j][i] + m.rows[i][j]) * s; @@ -807,97 +750,34 @@ Quaternion Basis::get_quaternion() const { return Quaternion(temp[0], temp[1], temp[2], temp[3]); } -static const Basis _ortho_bases[24] = { - Basis(1, 0, 0, 0, 1, 0, 0, 0, 1), - Basis(0, -1, 0, 1, 0, 0, 0, 0, 1), - Basis(-1, 0, 0, 0, -1, 0, 0, 0, 1), - Basis(0, 1, 0, -1, 0, 0, 0, 0, 1), - Basis(1, 0, 0, 0, 0, -1, 0, 1, 0), - Basis(0, 0, 1, 1, 0, 0, 0, 1, 0), - Basis(-1, 0, 0, 0, 0, 1, 0, 1, 0), - Basis(0, 0, -1, -1, 0, 0, 0, 1, 0), - Basis(1, 0, 0, 0, -1, 0, 0, 0, -1), - Basis(0, 1, 0, 1, 0, 0, 0, 0, -1), - Basis(-1, 0, 0, 0, 1, 0, 0, 0, -1), - Basis(0, -1, 0, -1, 0, 0, 0, 0, -1), - Basis(1, 0, 0, 0, 0, 1, 0, -1, 0), - Basis(0, 0, -1, 1, 0, 0, 0, -1, 0), - Basis(-1, 0, 0, 0, 0, -1, 0, -1, 0), - Basis(0, 0, 1, -1, 0, 0, 0, -1, 0), - Basis(0, 0, 1, 0, 1, 0, -1, 0, 0), - Basis(0, -1, 0, 0, 0, 1, -1, 0, 0), - Basis(0, 0, -1, 0, -1, 0, -1, 0, 0), - Basis(0, 1, 0, 0, 0, -1, -1, 0, 0), - Basis(0, 0, 1, 0, -1, 0, 1, 0, 0), - Basis(0, 1, 0, 0, 0, 1, 1, 0, 0), - Basis(0, 0, -1, 0, 1, 0, 1, 0, 0), - Basis(0, -1, 0, 0, 0, -1, 1, 0, 0) -}; - -int Basis::get_orthogonal_index() const { - // could be sped up if i come up with a way - Basis orth = *this; - for (int i = 0; i < 3; i++) { - for (int j = 0; j < 3; j++) { - real_t v = orth[i][j]; - if (v > 0.5) { - v = 1.0; - } else if (v < -0.5) { - v = -1.0; - } else { - v = 0; - } - - orth[i][j] = v; - } - } - - for (int i = 0; i < 24; i++) { - if (_ortho_bases[i] == orth) { - return i; - } - } - - return 0; -} - -void Basis::set_orthogonal_index(int p_index) { - // there only exist 24 orthogonal bases in r3 - ERR_FAIL_INDEX(p_index, 24); - - *this = _ortho_bases[p_index]; -} - void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const { /* checking this is a bad idea, because obtaining from scaled transform is a valid use case #ifdef MATH_CHECKS ERR_FAIL_COND(!is_rotation()); #endif -*/ - real_t angle, x, y, z; // variables for result - real_t epsilon = 0.01; // margin to allow for rounding errors - real_t epsilon2 = 0.1; // margin to distinguish between 0 and 180 degrees - - if ((Math::abs(rows[1][0] - rows[0][1]) < epsilon) && (Math::abs(rows[2][0] - rows[0][2]) < epsilon) && (Math::abs(rows[2][1] - rows[1][2]) < epsilon)) { - // singularity found - // first check for identity matrix which must have +1 for all terms - // in leading diagonaland zero in other terms - if ((Math::abs(rows[1][0] + rows[0][1]) < epsilon2) && (Math::abs(rows[2][0] + rows[0][2]) < epsilon2) && (Math::abs(rows[2][1] + rows[1][2]) < epsilon2) && (Math::abs(rows[0][0] + rows[1][1] + rows[2][2] - 3) < epsilon2)) { - // this singularity is identity matrix so angle = 0 + */ + + // https://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToAngle/index.htm + real_t x, y, z; // Variables for result. + if (Math::is_zero_approx(rows[0][1] - rows[1][0]) && Math::is_zero_approx(rows[0][2] - rows[2][0]) && Math::is_zero_approx(rows[1][2] - rows[2][1])) { + // Singularity found. + // First check for identity matrix which must have +1 for all terms in leading diagonal and zero in other terms. + if (is_diagonal() && (Math::abs(rows[0][0] + rows[1][1] + rows[2][2] - 3) < 3 * CMP_EPSILON)) { + // This singularity is identity matrix so angle = 0. r_axis = Vector3(0, 1, 0); r_angle = 0; return; } - // otherwise this singularity is angle = 180 - angle = Math_PI; + // Otherwise this singularity is angle = 180. real_t xx = (rows[0][0] + 1) / 2; real_t yy = (rows[1][1] + 1) / 2; real_t zz = (rows[2][2] + 1) / 2; - real_t xy = (rows[1][0] + rows[0][1]) / 4; - real_t xz = (rows[2][0] + rows[0][2]) / 4; - real_t yz = (rows[2][1] + rows[1][2]) / 4; - if ((xx > yy) && (xx > zz)) { // rows[0][0] is the largest diagonal term - if (xx < epsilon) { + real_t xy = (rows[0][1] + rows[1][0]) / 4; + real_t xz = (rows[0][2] + rows[2][0]) / 4; + real_t yz = (rows[1][2] + rows[2][1]) / 4; + + if ((xx > yy) && (xx > zz)) { // rows[0][0] is the largest diagonal term. + if (xx < CMP_EPSILON) { x = 0; y = Math_SQRT12; z = Math_SQRT12; @@ -906,8 +786,8 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const { y = xy / x; z = xz / x; } - } else if (yy > zz) { // rows[1][1] is the largest diagonal term - if (yy < epsilon) { + } else if (yy > zz) { // rows[1][1] is the largest diagonal term. + if (yy < CMP_EPSILON) { x = Math_SQRT12; y = 0; z = Math_SQRT12; @@ -916,8 +796,8 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const { x = xy / y; z = yz / y; } - } else { // rows[2][2] is the largest diagonal term so base result on this - if (zz < epsilon) { + } else { // rows[2][2] is the largest diagonal term so base result on this. + if (zz < CMP_EPSILON) { x = Math_SQRT12; y = Math_SQRT12; z = 0; @@ -928,48 +808,50 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const { } } r_axis = Vector3(x, y, z); - r_angle = angle; + r_angle = Math_PI; return; } - // as we have reached here there are no singularities so we can handle normally - real_t s = Math::sqrt((rows[1][2] - rows[2][1]) * (rows[1][2] - rows[2][1]) + (rows[2][0] - rows[0][2]) * (rows[2][0] - rows[0][2]) + (rows[0][1] - rows[1][0]) * (rows[0][1] - rows[1][0])); // s=|axis||sin(angle)|, used to normalise + // As we have reached here there are no singularities so we can handle normally. + double s = Math::sqrt((rows[2][1] - rows[1][2]) * (rows[2][1] - rows[1][2]) + (rows[0][2] - rows[2][0]) * (rows[0][2] - rows[2][0]) + (rows[1][0] - rows[0][1]) * (rows[1][0] - rows[0][1])); // Used to normalise. - angle = Math::acos((rows[0][0] + rows[1][1] + rows[2][2] - 1) / 2); - if (angle < 0) { - s = -s; + if (Math::abs(s) < CMP_EPSILON) { + // Prevent divide by zero, should not happen if matrix is orthogonal and should be caught by singularity test above. + s = 1; } + x = (rows[2][1] - rows[1][2]) / s; y = (rows[0][2] - rows[2][0]) / s; z = (rows[1][0] - rows[0][1]) / s; r_axis = Vector3(x, y, z); - r_angle = angle; + // CLAMP to avoid NaN if the value passed to acos is not in [0,1]. + r_angle = Math::acos(CLAMP((rows[0][0] + rows[1][1] + rows[2][2] - 1) / 2, (real_t)0.0, (real_t)1.0)); } -void Basis::set_quaternion(const Quaternion &p_quat) { - real_t d = p_quat.length_squared(); - real_t s = 2.0 / d; - real_t xs = p_quat.x * s, ys = p_quat.y * s, zs = p_quat.z * s; - real_t wx = p_quat.w * xs, wy = p_quat.w * ys, wz = p_quat.w * zs; - real_t xx = p_quat.x * xs, xy = p_quat.x * ys, xz = p_quat.x * zs; - real_t yy = p_quat.y * ys, yz = p_quat.y * zs, zz = p_quat.z * zs; - set(1.0 - (yy + zz), xy - wz, xz + wy, - xy + wz, 1.0 - (xx + zz), yz - wx, - xz - wy, yz + wx, 1.0 - (xx + yy)); +void Basis::set_quaternion(const Quaternion &p_quaternion) { + real_t d = p_quaternion.length_squared(); + real_t s = 2.0f / d; + real_t xs = p_quaternion.x * s, ys = p_quaternion.y * s, zs = p_quaternion.z * s; + real_t wx = p_quaternion.w * xs, wy = p_quaternion.w * ys, wz = p_quaternion.w * zs; + real_t xx = p_quaternion.x * xs, xy = p_quaternion.x * ys, xz = p_quaternion.x * zs; + real_t yy = p_quaternion.y * ys, yz = p_quaternion.y * zs, zz = p_quaternion.z * zs; + set(1.0f - (yy + zz), xy - wz, xz + wy, + xy + wz, 1.0f - (xx + zz), yz - wx, + xz - wy, yz + wx, 1.0f - (xx + yy)); } -void Basis::set_axis_angle(const Vector3 &p_axis, real_t p_phi) { +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(!p_axis.is_normalized()); + ERR_FAIL_COND_MSG(!p_axis.is_normalized(), "The axis Vector3 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_phi); - rows[0][0] = axis_sq.x + cosine * (1.0 - axis_sq.x); - rows[1][1] = axis_sq.y + cosine * (1.0 - axis_sq.y); - rows[2][2] = axis_sq.z + cosine * (1.0 - axis_sq.z); + real_t cosine = Math::cos(p_angle); + rows[0][0] = axis_sq.x + cosine * (1.0f - axis_sq.x); + rows[1][1] = axis_sq.y + cosine * (1.0f - axis_sq.y); + rows[2][2] = axis_sq.z + cosine * (1.0f - axis_sq.z); - real_t sine = Math::sin(p_phi); + real_t sine = Math::sin(p_angle); real_t t = 1 - cosine; real_t xyzt = p_axis.x * p_axis.y * t; @@ -988,22 +870,24 @@ void Basis::set_axis_angle(const Vector3 &p_axis, real_t p_phi) { rows[2][1] = xyzt + zyxs; } -void Basis::set_axis_angle_scale(const Vector3 &p_axis, real_t p_phi, const Vector3 &p_scale) { - set_diagonal(p_scale); - rotate(p_axis, p_phi); +void Basis::set_axis_angle_scale(const Vector3 &p_axis, real_t p_angle, const Vector3 &p_scale) { + _set_diagonal(p_scale); + rotate(p_axis, p_angle); } -void Basis::set_euler_scale(const Vector3 &p_euler, const Vector3 &p_scale) { - set_diagonal(p_scale); - rotate(p_euler); +void Basis::set_euler_scale(const Vector3 &p_euler, const Vector3 &p_scale, EulerOrder p_order) { + _set_diagonal(p_scale); + rotate(p_euler, p_order); } -void Basis::set_quaternion_scale(const Quaternion &p_quat, const Vector3 &p_scale) { - set_diagonal(p_scale); - rotate(p_quat); +void Basis::set_quaternion_scale(const Quaternion &p_quaternion, const Vector3 &p_scale) { + _set_diagonal(p_scale); + rotate(p_quaternion); } -void Basis::set_diagonal(const Vector3 &p_diag) { +// This also sets the non-diagonal elements to 0, which is misleading from the +// name, so we want this method to be private. Use `from_scale` externally. +void Basis::_set_diagonal(const Vector3 &p_diag) { rows[0][0] = p_diag.x; rows[0][1] = 0; rows[0][2] = 0; @@ -1017,8 +901,17 @@ 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 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); + b.rows[2] = rows[2].lerp(p_to.rows[2], p_weight); + + return b; +} + Basis Basis::slerp(const Basis &p_to, const real_t &p_weight) const { - // consider scale + //consider scale Quaternion from(*this); Quaternion to(p_to); @@ -1049,7 +942,7 @@ void Basis::rotate_sh(real_t *p_values) { const static real_t s_scale_dst2 = s_c3 * s_c_scale_inv; const static real_t s_scale_dst4 = s_c5 * s_c_scale_inv; - real_t src[9] = { p_values[0], p_values[1], p_values[2], p_values[3], p_values[4], p_values[5], p_values[6], p_values[7], p_values[8] }; + const real_t src[9] = { p_values[0], p_values[1], p_values[2], p_values[3], p_values[4], p_values[5], p_values[6], p_values[7], p_values[8] }; real_t m00 = rows[0][0]; real_t m01 = rows[0][1]; @@ -1140,4 +1033,22 @@ void Basis::rotate_sh(real_t *p_values) { p_values[8] = d4 * s_scale_dst4; } +Basis Basis::looking_at(const Vector3 &p_target, const Vector3 &p_up) { +#ifdef MATH_CHECKS + ERR_FAIL_COND_V_MSG(p_target.is_zero_approx(), Basis(), "The target vector can't be zero."); + ERR_FAIL_COND_V_MSG(p_up.is_zero_approx(), Basis(), "The up vector can't be zero."); +#endif + Vector3 v_z = -p_target.normalized(); + Vector3 v_x = p_up.cross(v_z); +#ifdef MATH_CHECKS + ERR_FAIL_COND_V_MSG(v_x.is_zero_approx(), Basis(), "The target vector and up vector can't be parallel to each other."); +#endif + v_x.normalize(); + Vector3 v_y = v_z.cross(v_x); + + Basis basis; + basis.set_columns(v_x, v_y, v_z); + return basis; +} + } // namespace godot |