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-rw-r--r--core/math/basis.cpp253
1 files changed, 213 insertions, 40 deletions
diff --git a/core/math/basis.cpp b/core/math/basis.cpp
index cbfd09810c..cbdd8a8c9f 100644
--- a/core/math/basis.cpp
+++ b/core/math/basis.cpp
@@ -5,8 +5,8 @@
/* GODOT ENGINE */
/* https://godotengine.org */
/*************************************************************************/
-/* Copyright (c) 2007-2020 Juan Linietsky, Ariel Manzur. */
-/* Copyright (c) 2014-2020 Godot Engine contributors (cf. AUTHORS.md). */
+/* Copyright (c) 2007-2021 Juan Linietsky, Ariel Manzur. */
+/* Copyright (c) 2014-2021 Godot Engine contributors (cf. AUTHORS.md). */
/* */
/* Permission is hereby granted, free of charge, to any person obtaining */
/* a copy of this software and associated documentation files (the */
@@ -32,7 +32,7 @@
#include "core/math/math_funcs.h"
#include "core/os/copymem.h"
-#include "core/print_string.h"
+#include "core/string/print_string.h"
#define cofac(row1, col1, row2, col2) \
(elements[row1][col1] * elements[row2][col2] - elements[row1][col2] * elements[row2][col1])
@@ -113,19 +113,22 @@ bool Basis::is_rotation() const {
return Math::is_equal_approx(determinant(), 1, UNIT_EPSILON) && is_orthogonal();
}
+#ifdef MATH_CHECKS
+// This method is only used once, in diagonalize. If it's desired elsewhere, feel free to remove the #ifdef.
bool Basis::is_symmetric() const {
- if (!Math::is_equal_approx_ratio(elements[0][1], elements[1][0], UNIT_EPSILON)) {
+ if (!Math::is_equal_approx(elements[0][1], elements[1][0])) {
return false;
}
- if (!Math::is_equal_approx_ratio(elements[0][2], elements[2][0], UNIT_EPSILON)) {
+ if (!Math::is_equal_approx(elements[0][2], elements[2][0])) {
return false;
}
- if (!Math::is_equal_approx_ratio(elements[1][2], elements[2][1], UNIT_EPSILON)) {
+ if (!Math::is_equal_approx(elements[1][2], elements[2][1])) {
return false;
}
return true;
}
+#endif
Basis Basis::diagonalize() {
//NOTE: only implemented for symmetric matrices
@@ -428,12 +431,9 @@ 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)
@@ -446,12 +446,12 @@ 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;
}
@@ -481,15 +481,106 @@ 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
//
@@ -501,8 +592,8 @@ 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)
@@ -516,12 +607,12 @@ 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;
}
@@ -551,20 +642,102 @@ void Basis::set_euler_yxz(const Vector3 &p_euler) {
*this = ymat * xmat * zmat;
}
-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]);
+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;
}
-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)) {
- return false;
- }
+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;
+}
- return true;
+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::operator==(const Basis &p_matrix) const {
@@ -591,7 +764,7 @@ Basis::operator String() const {
mtx += ", ";
}
- mtx += rtos(elements[i][j]);
+ mtx += rtos(elements[j][i]); //matrix is stored transposed for performance, so print it transposed
}
}
@@ -617,8 +790,8 @@ Quat Basis::get_quat() const {
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);
+ (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;
@@ -844,15 +1017,15 @@ void Basis::set_diagonal(const Vector3 &p_diag) {
elements[2][2] = p_diag.z;
}
-Basis Basis::slerp(const Basis &target, const real_t &t) const {
+Basis Basis::slerp(const Basis &p_to, const real_t &p_weight) const {
//consider scale
Quat from(*this);
- Quat to(target);
+ Quat to(p_to);
- Basis b(from.slerp(to, t));
- b.elements[0] *= Math::lerp(elements[0].length(), target.elements[0].length(), t);
- b.elements[1] *= Math::lerp(elements[1].length(), target.elements[1].length(), t);
- b.elements[2] *= Math::lerp(elements[2].length(), target.elements[2].length(), t);
+ Basis b(from.slerp(to, p_weight));
+ b.elements[0] *= Math::lerp(elements[0].length(), p_to.elements[0].length(), p_weight);
+ b.elements[1] *= Math::lerp(elements[1].length(), p_to.elements[1].length(), p_weight);
+ b.elements[2] *= Math::lerp(elements[2].length(), p_to.elements[2].length(), p_weight);
return b;
}
generated by cgit v1.2.3 (git 2.25.1) at 2025-02-21 22:42:01 +0000