diff --git a/core/math/matrix3.cpp b/core/math/matrix3.cpp
index b64f34d9779..f2f6ff93cf5 100644
--- a/core/math/matrix3.cpp
+++ b/core/math/matrix3.cpp
@@ -338,7 +338,7 @@ void Basis::set_rotation_axis_angle(const Vector3 &p_axis, real_t p_angle) {
rotate(p_axis, p_angle);
}
-// get_euler returns a vector containing the Euler angles in the format
+// 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).
//
@@ -348,7 +348,7 @@ void Basis::set_rotation_axis_angle(const Vector3 &p_axis, real_t p_angle) {
// 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() const {
+Vector3 Basis::get_euler_xyz() const {
// Euler angles in XYZ convention.
// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
@@ -366,6 +366,9 @@ Vector3 Basis::get_euler() const {
if (euler.y > -Math_PI * 0.5) {
//if rotation is Y-only, return a proper -pi,pi range like in x or z for the same case.
if (elements[1][0] == 0.0 && elements[0][1] == 0.0 && elements[0][0] < 0.0) {
+ euler.x = 0;
+ euler.z = 0;
+
if (euler.y > 0.0)
euler.y = Math_PI - euler.y;
else
@@ -389,10 +392,11 @@ Vector3 Basis::get_euler() const {
return euler;
}
-// set_euler expects a vector containing the Euler angles in the format
-// (c,b,a), where a is the angle of the first rotation, and c is the last.
+// 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(const Vector3 &p_euler) {
+void Basis::set_euler_xyz(const Vector3 &p_euler) {
real_t c, s;
@@ -412,6 +416,78 @@ void Basis::set_euler(const Vector3 &p_euler) {
*this = xmat * (ymat * zmat);
}
+// 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;
+#ifdef MATH_CHECKS
+ ERR_FAIL_COND_V(is_rotation() == false, euler);
+#endif
+ real_t m12 = elements[1][2];
+
+ if (m12 < 1) {
+ if (m12 > -1) {
+ if (elements[1][0] == 0 && elements[0][1] == 0 && elements[2][2] < 0) { // use pure x rotation
+ real_t x = asin(-m12);
+ euler.y = 0;
+ euler.z = 0;
+
+ if (x > 0.0)
+ euler.x = Math_PI - x;
+ else
+ euler.x = -(Math_PI + x);
+ } 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;
+ }
+
+ return euler;
+}
+
+// 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) {
+
+ 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 = ymat * xmat * zmat;
+}
+
bool Basis::is_equal_approx(const Basis &a, const Basis &b) const {
for (int i = 0; i < 3; i++) {
diff --git a/core/math/matrix3.h b/core/math/matrix3.h
index 8897c692f7c..74e65645780 100644
--- a/core/math/matrix3.h
+++ b/core/math/matrix3.h
@@ -84,8 +84,13 @@ public:
void set_rotation_euler(const Vector3 &p_euler);
void set_rotation_axis_angle(const Vector3 &p_axis, real_t p_angle);
- Vector3 get_euler() const;
- void set_euler(const Vector3 &p_euler);
+ Vector3 get_euler_xyz() const;
+ void set_euler_xyz(const Vector3 &p_euler);
+ Vector3 get_euler_yxz() const;
+ void set_euler_yxz(const Vector3 &p_euler);
+
+ Vector3 get_euler() const { return get_euler_yxz(); };
+ void set_euler(const Vector3 &p_euler) { set_euler_yxz(p_euler); };
void get_axis_angle(Vector3 &r_axis, real_t &r_angle) const;
void set_axis_angle(const Vector3 &p_axis, real_t p_phi);
diff --git a/core/math/quat.cpp b/core/math/quat.cpp
index 0bea97c2e89..5984cdf6577 100644
--- a/core/math/quat.cpp
+++ b/core/math/quat.cpp
@@ -31,10 +31,11 @@
#include "matrix3.h"
#include "print_string.h"
-// set_euler expects a vector containing the Euler angles in the format
-// (c,b,a), where a is the angle of the first rotation, and c is the last.
-// The current implementation uses XYZ convention (Z is the first rotation).
-void Quat::set_euler(const Vector3 &p_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.
+// This implementation uses XYZ convention (Z is the first rotation).
+void Quat::set_euler_xyz(const Vector3 &p_euler) {
real_t half_a1 = p_euler.x * 0.5;
real_t half_a2 = p_euler.y * 0.5;
real_t half_a3 = p_euler.z * 0.5;
@@ -56,12 +57,48 @@ void Quat::set_euler(const Vector3 &p_euler) {
-sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3);
}
-// get_euler 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.
-// The current implementation uses XYZ convention (Z is the first rotation).
-Vector3 Quat::get_euler() const {
+// get_euler_xyz returns 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.
+// This implementation uses XYZ convention (Z is the first rotation).
+Vector3 Quat::get_euler_xyz() const {
Basis m(*this);
- return m.get_euler();
+ return m.get_euler_xyz();
+}
+
+// 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.
+// This implementation uses YXZ convention (Z is the first rotation).
+void Quat::set_euler_yxz(const Vector3 &p_euler) {
+ real_t half_a1 = p_euler.y * 0.5;
+ real_t half_a2 = p_euler.x * 0.5;
+ real_t half_a3 = p_euler.z * 0.5;
+
+ // R = Y(a1).X(a2).Z(a3) convention for Euler angles.
+ // Conversion to quaternion as listed in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf (page A-6)
+ // a3 is the angle of the first rotation, following the notation in this reference.
+
+ real_t cos_a1 = Math::cos(half_a1);
+ real_t sin_a1 = Math::sin(half_a1);
+ real_t cos_a2 = Math::cos(half_a2);
+ real_t sin_a2 = Math::sin(half_a2);
+ real_t cos_a3 = Math::cos(half_a3);
+ real_t sin_a3 = Math::sin(half_a3);
+
+ set(sin_a1 * cos_a2 * sin_a3 + cos_a1 * sin_a2 * cos_a3,
+ sin_a1 * cos_a2 * cos_a3 - cos_a1 * sin_a2 * sin_a3,
+ -sin_a1 * sin_a2 * cos_a3 + cos_a1 * sin_a2 * sin_a3,
+ sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3);
+}
+
+// get_euler_yxz returns 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.
+// This implementation uses YXZ convention (Z is the first rotation).
+Vector3 Quat::get_euler_yxz() const {
+ Basis m(*this);
+ return m.get_euler_yxz();
}
void Quat::operator*=(const Quat &q) {
diff --git a/core/math/quat.h b/core/math/quat.h
index f22275b457f..0e378eb4e48 100644
--- a/core/math/quat.h
+++ b/core/math/quat.h
@@ -51,8 +51,15 @@ public:
bool is_normalized() const;
Quat inverse() const;
_FORCE_INLINE_ real_t dot(const Quat &q) const;
- void set_euler(const Vector3 &p_euler);
- Vector3 get_euler() const;
+
+ void set_euler_xyz(const Vector3 &p_euler);
+ Vector3 get_euler_xyz() const;
+ void set_euler_yxz(const Vector3 &p_euler);
+ Vector3 get_euler_yxz() const;
+
+ void set_euler(const Vector3 &p_euler) { set_euler_yxz(p_euler); };
+ Vector3 get_euler() const { return get_euler_yxz(); };
+
Quat slerp(const Quat &q, const real_t &t) const;
Quat slerpni(const Quat &q, const real_t &t) const;
Quat cubic_slerp(const Quat &q, const Quat &prep, const Quat &postq, const real_t &t) const;
diff --git a/doc/base/classes.xml b/doc/base/classes.xml
index 7dd22d7cb06..db758d9197d 100644
--- a/doc/base/classes.xml
+++ b/doc/base/classes.xml
@@ -7652,7 +7652,7 @@
- Create a rotation matrix (in the XYZ convention: first Z, then Y, and X last) from the specified Euler angles, given in the vector format as (third, second, first).
+ Create a rotation matrix (in the YXZ convention: first Z, then X, and Y last) from the specified Euler angles, given in the vector format as (X-angle, Y-angle, Z-angle).
@@ -7690,7 +7690,7 @@
- Assuming that the matrix is a proper rotation matrix (orthonormal matrix with determinant +1), return Euler angles (in the XYZ convention: first Z, then Y, and X last). Returned vector contains the rotation angles in the format (third,second,first).
+ Assuming that the matrix is a proper rotation matrix (orthonormal matrix with determinant +1), return Euler angles (in the YXZ convention: first Z, then X, and Y last). Returned vector contains the rotation angles in the format (X-angle, Y-angle, Z-angle).