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-rw-r--r--core/math/basis.cpp279
1 files changed, 219 insertions, 60 deletions
diff --git a/core/math/basis.cpp b/core/math/basis.cpp
index 6218b7e248..df5199b0f9 100644
--- a/core/math/basis.cpp
+++ b/core/math/basis.cpp
@@ -38,16 +38,13 @@
(elements[row1][col1] * elements[row2][col2] - elements[row1][col2] * elements[row2][col1])
void Basis::from_z(const Vector3 &p_z) {
-
if (Math::abs(p_z.z) > 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);
elements[0] = Vector3(0, -p_z[2] * k, p_z[1] * k);
elements[1] = Vector3(a * k, -p_z[0] * elements[0][2], p_z[0] * elements[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);
@@ -58,7 +55,6 @@ void Basis::from_z(const Vector3 &p_z) {
}
void Basis::invert() {
-
real_t co[3] = {
cofac(1, 1, 2, 2), cofac(1, 2, 2, 0), cofac(1, 0, 2, 1)
};
@@ -76,7 +72,6 @@ void Basis::invert() {
}
void Basis::orthonormalize() {
-
// Gram-Schmidt Process
Vector3 x = get_axis(0);
@@ -95,7 +90,6 @@ void Basis::orthonormalize() {
}
Basis Basis::orthonormalized() const {
-
Basis c = *this;
c.orthonormalize();
return c;
@@ -120,19 +114,20 @@ bool Basis::is_rotation() const {
}
bool Basis::is_symmetric() const {
-
- if (!Math::is_equal_approx_ratio(elements[0][1], elements[1][0], UNIT_EPSILON))
+ if (!Math::is_equal_approx_ratio(elements[0][1], elements[1][0], UNIT_EPSILON)) {
return false;
- if (!Math::is_equal_approx_ratio(elements[0][2], elements[2][0], UNIT_EPSILON))
+ }
+ if (!Math::is_equal_approx_ratio(elements[0][2], elements[2][0], UNIT_EPSILON)) {
return false;
- if (!Math::is_equal_approx_ratio(elements[1][2], elements[2][1], UNIT_EPSILON))
+ }
+ if (!Math::is_equal_approx_ratio(elements[1][2], elements[2][1], UNIT_EPSILON)) {
return false;
+ }
return true;
}
Basis Basis::diagonalize() {
-
//NOTE: only implemented for symmetric matrices
//with the Jacobi iterative method method
#ifdef MATH_CHECKS
@@ -193,21 +188,18 @@ Basis Basis::diagonalize() {
}
Basis Basis::inverse() const {
-
Basis inv = *this;
inv.invert();
return inv;
}
void Basis::transpose() {
-
SWAP(elements[0][1], elements[1][0]);
SWAP(elements[0][2], elements[2][0]);
SWAP(elements[1][2], elements[2][1]);
}
Basis Basis::transposed() const {
-
Basis tr = *this;
tr.transpose();
return tr;
@@ -216,7 +208,6 @@ Basis Basis::transposed() const {
// 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) {
-
elements[0][0] *= p_scale.x;
elements[0][1] *= p_scale.x;
elements[0][2] *= p_scale.x;
@@ -260,7 +251,6 @@ Basis Basis::scaled_local(const Vector3 &p_scale) const {
}
Vector3 Basis::get_scale_abs() const {
-
return Vector3(
Vector3(elements[0][0], elements[1][0], elements[2][0]).length(),
Vector3(elements[0][1], elements[1][1], elements[2][1]).length(),
@@ -340,8 +330,8 @@ void Basis::rotate_local(const Vector3 &p_axis, real_t p_phi) {
// M -> (M.R.Minv).M = M.R.
*this = rotated_local(p_axis, p_phi);
}
-Basis Basis::rotated_local(const Vector3 &p_axis, real_t p_phi) const {
+Basis Basis::rotated_local(const Vector3 &p_axis, real_t p_phi) const {
return (*this) * Basis(p_axis, p_phi);
}
@@ -430,7 +420,6 @@ void Basis::get_rotation_axis_angle_local(Vector3 &p_axis, real_t &p_angle) cons
// 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
//
@@ -439,12 +428,9 @@ Vector3 Basis::get_euler_xyz() const {
// -cx*cz*sy+sx*sz cz*sx+cx*sy*sz cx*cy
Vector3 euler;
-#ifdef MATH_CHECKS
- ERR_FAIL_COND_V(!is_rotation(), euler);
-#endif
real_t sy = elements[0][2];
- if (sy < 1.0) {
- if (sy > -1.0) {
+ 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)
@@ -457,12 +443,12 @@ Vector3 Basis::get_euler_xyz() const {
euler.z = Math::atan2(-elements[0][1], elements[0][0]);
}
} else {
- euler.x = -Math::atan2(elements[0][1], elements[1][1]);
+ 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[0][1], elements[1][1]);
+ euler.x = Math::atan2(elements[2][1], elements[1][1]);
euler.y = Math_PI / 2.0;
euler.z = 0.0;
}
@@ -474,7 +460,6 @@ Vector3 Basis::get_euler_xyz() const {
// 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);
@@ -493,16 +478,106 @@ void Basis::set_euler_xyz(const Vector3 &p_euler) {
*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 {
-
- /* 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
-*/
// Euler angles in YXZ convention.
// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
//
@@ -514,8 +589,8 @@ Vector3 Basis::get_euler_yxz() const {
real_t m12 = elements[1][2];
- if (m12 < 1) {
- if (m12 > -1) {
+ 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)
@@ -529,12 +604,12 @@ Vector3 Basis::get_euler_yxz() const {
}
} else { // m12 == -1
euler.x = Math_PI * 0.5;
- euler.y = -atan2(-elements[0][1], elements[0][0]);
+ 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.y = -atan2(elements[0][1], elements[0][0]);
euler.z = 0;
}
@@ -546,7 +621,6 @@ Vector3 Basis::get_euler_yxz() const {
// 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);
@@ -565,17 +639,110 @@ void Basis::set_euler_yxz(const Vector3 &p_euler) {
*this = ymat * xmat * zmat;
}
-bool Basis::is_equal_approx(const Basis &p_basis) const {
+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;
+ }
+ } 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 {
return elements[0].is_equal_approx(p_basis.elements[0]) && elements[1].is_equal_approx(p_basis.elements[1]) && elements[2].is_equal_approx(p_basis.elements[2]);
}
bool Basis::is_equal_approx_ratio(const Basis &a, const Basis &b, real_t p_epsilon) const {
-
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
- if (!Math::is_equal_approx_ratio(a.elements[i][j], b.elements[i][j], p_epsilon))
+ if (!Math::is_equal_approx_ratio(a.elements[i][j], b.elements[i][j], p_epsilon)) {
return false;
+ }
}
}
@@ -583,11 +750,11 @@ bool Basis::is_equal_approx_ratio(const Basis &a, const Basis &b, real_t p_epsil
}
bool Basis::operator==(const Basis &p_matrix) const {
-
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
- if (elements[i][j] != p_matrix.elements[i][j])
+ if (elements[i][j] != p_matrix.elements[i][j]) {
return false;
+ }
}
}
@@ -595,19 +762,16 @@ bool Basis::operator==(const Basis &p_matrix) const {
}
bool Basis::operator!=(const Basis &p_matrix) const {
-
return (!(*this == p_matrix));
}
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)
+ if (i != 0 || j != 0) {
mtx += ", ";
+ }
mtx += rtos(elements[i][j]);
}
@@ -617,7 +781,6 @@ Basis::operator String() const {
}
Quat Basis::get_quat() 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.");
#endif
@@ -681,35 +844,33 @@ static const Basis _ortho_bases[24] = {
};
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)
+ if (v > 0.5) {
v = 1.0;
- else if (v < -0.5)
+ } else if (v < -0.5) {
v = -1.0;
- else
+ } else {
v = 0;
+ }
orth[i][j] = v;
}
}
for (int i = 0; i < 24; i++) {
-
- if (_ortho_bases[i] == orth)
+ 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);
@@ -783,8 +944,9 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
real_t s = Math::sqrt((elements[1][2] - elements[2][1]) * (elements[1][2] - elements[2][1]) + (elements[2][0] - elements[0][2]) * (elements[2][0] - elements[0][2]) + (elements[0][1] - elements[1][0]) * (elements[0][1] - elements[1][0])); // s=|axis||sin(angle)|, used to normalise
angle = Math::acos((elements[0][0] + elements[1][1] + elements[2][2] - 1) / 2);
- if (angle < 0)
+ if (angle < 0) {
s = -s;
+ }
x = (elements[2][1] - elements[1][2]) / s;
y = (elements[0][2] - elements[2][0]) / s;
z = (elements[1][0] - elements[0][1]) / s;
@@ -794,7 +956,6 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
}
void Basis::set_quat(const Quat &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;
@@ -866,7 +1027,6 @@ void Basis::set_diagonal(const Vector3 &p_diag) {
}
Basis Basis::slerp(const Basis &target, const real_t &t) const {
-
//consider scale
Quat from(*this);
Quat to(target);
@@ -880,7 +1040,6 @@ Basis Basis::slerp(const Basis &target, const real_t &t) const {
}
void Basis::rotate_sh(real_t *p_values) {
-
// code by John Hable
// http://filmicworlds.com/blog/simple-and-fast-spherical-harmonic-rotation/
// this code is Public Domain
generated by cgit v1.2.3 (git 2.25.1) at 2025-04-16 17:21:13 +0000