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-rw-r--r--core/math/basis.cpp631
1 files changed, 282 insertions, 349 deletions
diff --git a/core/math/basis.cpp b/core/math/basis.cpp
index 50299902eb..566300c716 100644
--- a/core/math/basis.cpp
+++ b/core/math/basis.cpp
@@ -58,8 +58,8 @@ void Basis::invert() {
cofac(1, 1, 2, 2), cofac(1, 2, 2, 0), cofac(1, 0, 2, 1)
};
real_t det = elements[0][0] * co[0] +
- elements[0][1] * co[1] +
- elements[0][2] * co[2];
+ elements[0][1] * co[1] +
+ elements[0][2] * co[2];
#ifdef MATH_CHECKS
ERR_FAIL_COND(det == 0);
#endif
@@ -109,7 +109,7 @@ bool Basis::is_diagonal() const {
}
bool Basis::is_rotation() const {
- return Math::is_equal_approx(determinant(), 1, UNIT_EPSILON) && is_orthogonal();
+ return Math::is_equal_approx(determinant(), 1, (real_t)UNIT_EPSILON) && is_orthogonal();
}
#ifdef MATH_CHECKS
@@ -207,6 +207,10 @@ 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) {
@@ -246,10 +250,7 @@ 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 {
@@ -260,7 +261,7 @@ Vector3 Basis::get_scale_abs() const {
}
Vector3 Basis::get_scale_local() const {
- real_t det_sign = SGN(determinant());
+ real_t det_sign = SIGN(determinant());
return det_sign * Vector3(elements[0].length(), elements[1].length(), elements[2].length());
}
@@ -286,11 +287,8 @@ Vector3 Basis::get_scale() const {
// matrix elements.
//
// The rotation part of this decomposition is returned by get_rotation* functions.
- real_t det_sign = SGN(determinant());
- return det_sign * Vector3(
- Vector3(elements[0][0], elements[1][0], elements[2][0]).length(),
- Vector3(elements[0][1], elements[1][1], elements[2][1]).length(),
- Vector3(elements[0][2], elements[1][2], elements[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.
@@ -345,15 +343,15 @@ void Basis::rotate(const Vector3 &p_euler) {
*this = rotated(p_euler);
}
-Basis Basis::rotated(const Quat &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 Quat &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.
@@ -364,10 +362,10 @@ Vector3 Basis::get_rotation_euler() const {
m.scale(Vector3(-1, -1, -1));
}
- return m.get_euler();
+ return m.get_euler(p_order);
}
-Quat Basis::get_rotation_quat() const {
+Quaternion Basis::get_rotation_quaternion() 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.
@@ -378,7 +376,19 @@ Quat Basis::get_rotation_quat() const {
m.scale(Vector3(-1, -1, -1));
}
- return m.get_quat();
+ 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, -1.0, 1.0);
+ 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 {
@@ -411,218 +421,203 @@ 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 = elements[0][2];
- if (sy < (1.0 - CMP_EPSILON)) {
- if (sy > -(1.0 - CMP_EPSILON)) {
- // is this a pure Y rotation?
- if (elements[1][0] == 0.0 && elements[0][1] == 0.0 && elements[1][2] == 0 && elements[2][1] == 0 && elements[1][1] == 1) {
- // return the simplest form (human friendlier in editor and scripts)
- euler.x = 0;
- euler.y = atan2(elements[0][2], elements[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 = elements[0][2];
+ if (sy < (1.0 - CMP_EPSILON)) {
+ if (sy > -(1.0 - CMP_EPSILON)) {
+ // is this a pure Y rotation?
+ if (elements[1][0] == 0.0 && elements[0][1] == 0.0 && elements[1][2] == 0 && elements[2][1] == 0 && elements[1][1] == 1) {
+ // return the simplest form (human friendlier in editor and scripts)
+ euler.x = 0;
+ euler.y = atan2(elements[0][2], elements[0][0]);
+ euler.z = 0;
+ } else {
+ euler.x = Math::atan2(-elements[1][2], elements[2][2]);
+ euler.y = Math::asin(sy);
+ euler.z = Math::atan2(-elements[0][1], elements[0][0]);
+ }
+ } else {
+ euler.x = Math::atan2(elements[2][1], elements[1][1]);
+ euler.y = -Math_PI / 2.0;
+ euler.z = 0.0;
+ }
} else {
- euler.x = Math::atan2(-elements[1][2], elements[2][2]);
- euler.y = Math::asin(sy);
- euler.z = Math::atan2(-elements[0][1], elements[0][0]);
+ euler.x = Math::atan2(elements[2][1], elements[1][1]);
+ euler.y = Math_PI / 2.0;
+ euler.z = 0.0;
+ }
+ 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 = elements[0][1];
+ if (sz < (1.0 - CMP_EPSILON)) {
+ if (sz > -(1.0 - CMP_EPSILON)) {
+ euler.x = Math::atan2(elements[2][1], elements[1][1]);
+ euler.y = Math::atan2(elements[0][2], elements[0][0]);
+ euler.z = Math::asin(-sz);
+ } else {
+ // It's -1
+ euler.x = -Math::atan2(elements[1][2], elements[2][2]);
+ euler.y = 0.0;
+ euler.z = Math_PI / 2.0;
+ }
+ } else {
+ // It's 1
+ euler.x = -Math::atan2(elements[1][2], elements[2][2]);
+ euler.y = 0.0;
+ euler.z = -Math_PI / 2.0;
+ }
+ 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 = elements[1][2];
+
+ if (m12 < (1 - CMP_EPSILON)) {
+ if (m12 > -(1 - CMP_EPSILON)) {
+ // is this a pure X rotation?
+ if (elements[1][0] == 0 && elements[0][1] == 0 && elements[0][2] == 0 && elements[2][0] == 0 && elements[0][0] == 1) {
+ // return the simplest form (human friendlier in editor and scripts)
+ euler.x = atan2(-m12, elements[1][1]);
+ euler.y = 0;
+ euler.z = 0;
+ } else {
+ euler.x = asin(-m12);
+ euler.y = atan2(elements[0][2], elements[2][2]);
+ euler.z = atan2(elements[1][0], elements[1][1]);
+ }
+ } else { // m12 == -1
+ euler.x = Math_PI * 0.5;
+ euler.y = atan2(elements[0][1], elements[0][0]);
+ euler.z = 0;
+ }
+ } else { // m12 == 1
+ euler.x = -Math_PI * 0.5;
+ euler.y = -atan2(elements[0][1], elements[0][0]);
+ euler.z = 0;
}
- } else {
- euler.x = Math::atan2(elements[2][1], elements[1][1]);
- euler.y = -Math_PI / 2.0;
- euler.z = 0.0;
- }
- } else {
- euler.x = Math::atan2(elements[2][1], elements[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 = elements[0][1];
- if (sz < (1.0 - CMP_EPSILON)) {
- if (sz > -(1.0 - CMP_EPSILON)) {
- euler.x = Math::atan2(elements[2][1], elements[1][1]);
- euler.y = Math::atan2(elements[0][2], elements[0][0]);
- euler.z = Math::asin(-sz);
- } else {
- // It's -1
- euler.x = -Math::atan2(elements[1][2], elements[2][2]);
- euler.y = 0.0;
- euler.z = Math_PI / 2.0;
- }
- } else {
- // It's 1
- euler.x = -Math::atan2(elements[1][2], elements[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 = elements[1][0];
- if (sz < (1.0 - CMP_EPSILON)) {
- if (sz > -(1.0 - CMP_EPSILON)) {
- euler.x = Math::atan2(-elements[1][2], elements[1][1]);
- euler.y = Math::atan2(-elements[2][0], elements[0][0]);
- euler.z = Math::asin(sz);
- } else {
- // It's -1
- euler.x = Math::atan2(elements[2][1], elements[2][2]);
- euler.y = 0.0;
- euler.z = -Math_PI / 2.0;
- }
- } else {
- // It's 1
- euler.x = Math::atan2(elements[2][1], elements[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 = elements[1][2];
- if (m12 < (1 - CMP_EPSILON)) {
- if (m12 > -(1 - CMP_EPSILON)) {
- // is this a pure X rotation?
- if (elements[1][0] == 0 && elements[0][1] == 0 && elements[0][2] == 0 && elements[2][0] == 0 && elements[0][0] == 1) {
- // return the simplest form (human friendlier in editor and scripts)
- euler.x = atan2(-m12, elements[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 = elements[1][0];
+ if (sz < (1.0 - CMP_EPSILON)) {
+ if (sz > -(1.0 - CMP_EPSILON)) {
+ euler.x = Math::atan2(-elements[1][2], elements[1][1]);
+ euler.y = Math::atan2(-elements[2][0], elements[0][0]);
+ euler.z = Math::asin(sz);
+ } else {
+ // It's -1
+ euler.x = Math::atan2(elements[2][1], elements[2][2]);
+ euler.y = 0.0;
+ euler.z = -Math_PI / 2.0;
+ }
+ } else {
+ // It's 1
+ euler.x = Math::atan2(elements[2][1], elements[2][2]);
+ euler.y = 0.0;
+ euler.z = Math_PI / 2.0;
+ }
+ 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 = elements[2][1];
+ if (sx < (1.0 - CMP_EPSILON)) {
+ if (sx > -(1.0 - CMP_EPSILON)) {
+ euler.x = Math::asin(sx);
+ euler.y = Math::atan2(-elements[2][0], elements[2][2]);
+ euler.z = Math::atan2(-elements[0][1], elements[1][1]);
+ } else {
+ // It's -1
+ euler.x = -Math_PI / 2.0;
+ euler.y = Math::atan2(elements[0][2], elements[0][0]);
+ euler.z = 0;
+ }
+ } else {
+ // It's 1
+ euler.x = Math_PI / 2.0;
+ euler.y = Math::atan2(elements[0][2], elements[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 = elements[2][0];
+ if (sy < (1.0 - CMP_EPSILON)) {
+ if (sy > -(1.0 - CMP_EPSILON)) {
+ euler.x = Math::atan2(elements[2][1], elements[2][2]);
+ euler.y = Math::asin(-sy);
+ euler.z = Math::atan2(elements[1][0], elements[0][0]);
+ } else {
+ // It's -1
+ euler.x = 0;
+ euler.y = Math_PI / 2.0;
+ euler.z = -Math::atan2(elements[0][1], elements[1][1]);
+ }
} else {
- euler.x = asin(-m12);
- euler.y = atan2(elements[0][2], elements[2][2]);
- euler.z = atan2(elements[1][0], elements[1][1]);
+ // It's 1
+ euler.x = 0;
+ euler.y = -Math_PI / 2.0;
+ euler.z = -Math::atan2(elements[0][1], elements[1][1]);
}
- } else { // m12 == -1
- euler.x = Math_PI * 0.5;
- euler.y = atan2(elements[0][1], elements[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(elements[0][1], elements[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);
@@ -637,102 +632,29 @@ void Basis::set_euler_yxz(const Vector3 &p_euler) {
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 = elements[2][1];
- if (sx < (1.0 - CMP_EPSILON)) {
- if (sx > -(1.0 - CMP_EPSILON)) {
- euler.x = Math::asin(sx);
- euler.y = Math::atan2(-elements[2][0], elements[2][2]);
- euler.z = Math::atan2(-elements[0][1], elements[1][1]);
- } else {
- // It's -1
- euler.x = -Math_PI / 2.0;
- euler.y = Math::atan2(elements[0][2], elements[0][0]);
- euler.z = 0;
+ 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(elements[0][2], elements[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 = elements[2][0];
- if (sy < (1.0 - CMP_EPSILON)) {
- if (sy > -(1.0 - CMP_EPSILON)) {
- euler.x = Math::atan2(elements[2][1], elements[2][2]);
- euler.y = Math::asin(-sy);
- euler.z = Math::atan2(elements[1][0], elements[0][0]);
- } else {
- // It's -1
- euler.x = 0;
- euler.y = Math_PI / 2.0;
- euler.z = -Math::atan2(elements[0][1], elements[1][1]);
- }
- } else {
- // It's 1
- euler.x = 0;
- euler.y = -Math_PI / 2.0;
- euler.z = -Math::atan2(elements[0][1], elements[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 {
@@ -756,23 +678,14 @@ 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 += rtos(elements[j][i]); //matrix is stored transposed for performance, so print it transposed
- }
- }
-
- return mtx;
+ return "[X: " + get_axis(0).operator String() +
+ ", Y: " + get_axis(1).operator String() +
+ ", Z: " + get_axis(2).operator String() + "]";
}
-Quat Basis::get_quat() const {
+Quaternion Basis::get_quaternion() const {
#ifdef MATH_CHECKS
- ERR_FAIL_COND_V_MSG(!is_rotation(), Quat(), "Basis must be normalized in order to be casted to a Quaternion. Use get_rotation_quat() or call orthonormalized() instead.");
+ 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;
@@ -788,9 +701,9 @@ Quat Basis::get_quat() const {
temp[1] = ((m.elements[0][2] - m.elements[2][0]) * s);
temp[2] = ((m.elements[1][0] - m.elements[0][1]) * s);
} else {
- int i = m.elements[0][0] < m.elements[1][1] ?
- (m.elements[1][1] < m.elements[2][2] ? 2 : 1) :
- (m.elements[0][0] < m.elements[2][2] ? 2 : 0);
+ int i = m.elements[0][0] < m.elements[1][1]
+ ? (m.elements[1][1] < m.elements[2][2] ? 2 : 1)
+ : (m.elements[0][0] < m.elements[2][2] ? 2 : 0);
int j = (i + 1) % 3;
int k = (i + 2) % 3;
@@ -803,7 +716,7 @@ Quat Basis::get_quat() const {
temp[k] = (m.elements[k][i] + m.elements[i][k]) * s;
}
- return Quat(temp[0], temp[1], temp[2], temp[3]);
+ return Quaternion(temp[0], temp[1], temp[2], temp[3]);
}
static const Basis _ortho_bases[24] = {
@@ -945,13 +858,13 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
r_angle = angle;
}
-void Basis::set_quat(const Quat &p_quat) {
- real_t d = p_quat.length_squared();
+void Basis::set_quaternion(const Quaternion &p_quaternion) {
+ real_t d = p_quaternion.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;
+ 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(1.0 - (yy + zz), xy - wz, xz + wy,
xy + wz, 1.0 - (xx + zz), yz - wx,
xz - wy, yz + wx, 1.0 - (xx + yy));
@@ -988,21 +901,23 @@ void Basis::set_axis_angle(const Vector3 &p_axis, real_t p_phi) {
}
void Basis::set_axis_angle_scale(const Vector3 &p_axis, real_t p_phi, const Vector3 &p_scale) {
- set_diagonal(p_scale);
+ _set_diagonal(p_scale);
rotate(p_axis, p_phi);
}
void Basis::set_euler_scale(const Vector3 &p_euler, const Vector3 &p_scale) {
- set_diagonal(p_scale);
+ _set_diagonal(p_scale);
rotate(p_euler);
}
-void Basis::set_quat_scale(const Quat &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) {
elements[0][0] = p_diag.x;
elements[0][1] = 0;
elements[0][2] = 0;
@@ -1018,8 +933,8 @@ void Basis::set_diagonal(const Vector3 &p_diag) {
Basis Basis::slerp(const Basis &p_to, const real_t &p_weight) const {
//consider scale
- Quat from(*this);
- Quat to(p_to);
+ Quaternion from(*this);
+ Quaternion to(p_to);
Basis b(from.slerp(to, p_weight));
b.elements[0] *= Math::lerp(elements[0].length(), p_to.elements[0].length(), p_weight);
@@ -1138,3 +1053,21 @@ void Basis::rotate_sh(real_t *p_values) {
p_values[7] = -d3;
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_equal_approx(Vector3()), Basis(), "The target vector can't be zero.");
+ ERR_FAIL_COND_V_MSG(p_up.is_equal_approx(Vector3()), 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_equal_approx(Vector3()), 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(v_x, v_y, v_z);
+ return basis;
+}
generated by cgit v1.2.3 (git 2.25.1) at 2025-02-02 13:50:08 +0000