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-rw-r--r--src/variant/basis.cpp887
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