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-rw-r--r--core/math/basis.cpp471
1 files changed, 255 insertions, 216 deletions
diff --git a/core/math/basis.cpp b/core/math/basis.cpp
index 566300c716..65353d8118 100644
--- a/core/math/basis.cpp
+++ b/core/math/basis.cpp
@@ -5,8 +5,8 @@
/* GODOT ENGINE */
/* https://godotengine.org */
/*************************************************************************/
-/* Copyright (c) 2007-2021 Juan Linietsky, Ariel Manzur. */
-/* Copyright (c) 2014-2021 Godot Engine contributors (cf. AUTHORS.md). */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur. */
+/* Copyright (c) 2014-2022 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 */
@@ -34,36 +34,36 @@
#include "core/string/print_string.h"
#define cofac(row1, col1, row2, col2) \
- (elements[row1][col1] * elements[row2][col2] - elements[row1][col2] * elements[row2][col1])
+ (rows[row1][col1] * rows[row2][col2] - rows[row1][col2] * rows[row2][col1])
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);
- 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]);
+ 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);
- elements[0] = Vector3(-p_z.y * k, p_z.x * k, 0);
- elements[1] = Vector3(-p_z.z * elements[0].y, p_z.z * elements[0].x, a * k);
+ 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);
}
- elements[2] = p_z;
+ rows[2] = p_z;
}
void Basis::invert() {
real_t co[3] = {
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];
+ real_t det = rows[0][0] * co[0] +
+ 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,
@@ -73,9 +73,9 @@ 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)));
@@ -83,9 +83,9 @@ 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 {
@@ -94,6 +94,18 @@ 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();
@@ -103,9 +115,9 @@ bool Basis::is_orthogonal() const {
bool Basis::is_diagonal() const {
return (
- Math::is_zero_approx(elements[0][1]) && Math::is_zero_approx(elements[0][2]) &&
- Math::is_zero_approx(elements[1][0]) && Math::is_zero_approx(elements[1][2]) &&
- Math::is_zero_approx(elements[2][0]) && Math::is_zero_approx(elements[2][1]));
+ Math::is_zero_approx(rows[0][1]) && Math::is_zero_approx(rows[0][2]) &&
+ Math::is_zero_approx(rows[1][0]) && Math::is_zero_approx(rows[1][2]) &&
+ Math::is_zero_approx(rows[2][0]) && Math::is_zero_approx(rows[2][1]));
}
bool Basis::is_rotation() const {
@@ -115,13 +127,13 @@ bool Basis::is_rotation() const {
#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(elements[0][1], elements[1][0])) {
+ if (!Math::is_equal_approx(rows[0][1], rows[1][0])) {
return false;
}
- if (!Math::is_equal_approx(elements[0][2], elements[2][0])) {
+ if (!Math::is_equal_approx(rows[0][2], rows[2][0])) {
return false;
}
- if (!Math::is_equal_approx(elements[1][2], elements[2][1])) {
+ if (!Math::is_equal_approx(rows[1][2], rows[2][1])) {
return false;
}
@@ -137,14 +149,14 @@ Basis Basis::diagonalize() {
#endif
const int ite_max = 1024;
- real_t off_matrix_norm_2 = elements[0][1] * elements[0][1] + elements[0][2] * elements[0][2] + elements[1][2] * elements[1][2];
+ real_t off_matrix_norm_2 = rows[0][1] * rows[0][1] + rows[0][2] * rows[0][2] + rows[1][2] * rows[1][2];
int ite = 0;
Basis acc_rot;
- while (off_matrix_norm_2 > CMP_EPSILON2 && ite++ < ite_max) {
- real_t el01_2 = elements[0][1] * elements[0][1];
- real_t el02_2 = elements[0][2] * elements[0][2];
- real_t el12_2 = elements[1][2] * elements[1][2];
+ 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];
// Find the pivot element
int i, j;
if (el01_2 > el02_2) {
@@ -167,19 +179,19 @@ Basis Basis::diagonalize() {
// Compute the rotation angle
real_t angle;
- if (Math::is_equal_approx(elements[j][j], elements[i][i])) {
+ if (Math::is_equal_approx(rows[j][j], rows[i][i])) {
angle = Math_PI / 4;
} else {
- angle = 0.5 * Math::atan(2 * elements[i][j] / (elements[j][j] - elements[i][i]));
+ angle = 0.5f * Math::atan(2 * rows[i][j] / (rows[j][j] - rows[i][i]));
}
// Compute the rotation matrix
Basis rot;
- rot.elements[i][i] = rot.elements[j][j] = Math::cos(angle);
- rot.elements[i][j] = -(rot.elements[j][i] = Math::sin(angle));
+ rot.rows[i][i] = rot.rows[j][j] = Math::cos(angle);
+ rot.rows[i][j] = -(rot.rows[j][i] = Math::sin(angle));
// Update the off matrix norm
- off_matrix_norm_2 -= elements[i][j] * elements[i][j];
+ off_matrix_norm_2 -= rows[i][j] * rows[i][j];
// Apply the rotation
*this = rot * *this * rot.transposed();
@@ -196,9 +208,9 @@ Basis Basis::inverse() const {
}
void Basis::transpose() {
- SWAP(elements[0][1], elements[1][0]);
- SWAP(elements[0][2], elements[2][0]);
- SWAP(elements[1][2], elements[2][1]);
+ SWAP(rows[0][1], rows[1][0]);
+ SWAP(rows[0][2], rows[2][0]);
+ SWAP(rows[1][2], rows[2][1]);
}
Basis Basis::transposed() const {
@@ -214,15 +226,15 @@ Basis Basis::from_scale(const Vector3 &p_scale) {
// 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;
- elements[1][0] *= p_scale.y;
- elements[1][1] *= p_scale.y;
- elements[1][2] *= p_scale.y;
- elements[2][0] *= p_scale.z;
- elements[2][1] *= p_scale.z;
- elements[2][2] *= p_scale.z;
+ rows[0][0] *= p_scale.x;
+ rows[0][1] *= p_scale.x;
+ rows[0][2] *= p_scale.x;
+ rows[1][0] *= p_scale.y;
+ rows[1][1] *= p_scale.y;
+ rows[1][2] *= p_scale.y;
+ rows[2][0] *= p_scale.z;
+ rows[2][1] *= p_scale.z;
+ rows[2][2] *= p_scale.z;
}
Basis Basis::scaled(const Vector3 &p_scale) const {
@@ -237,15 +249,33 @@ 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 (elements[0].length() + elements[1].length() + elements[2].length()) / 3.0;
+ return (rows[0].length() + rows[1].length() + rows[2].length()) / 3.0f;
}
void Basis::make_scale_uniform() {
- float l = (elements[0].length() + elements[1].length() + elements[2].length()) / 3.0;
+ float l = (rows[0].length() + rows[1].length() + rows[2].length()) / 3.0f;
for (int i = 0; i < 3; i++) {
- elements[i].normalize();
- elements[i] *= l;
+ rows[i].normalize();
+ rows[i] *= l;
}
}
@@ -255,14 +285,14 @@ 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(),
- Vector3(elements[0][2], elements[1][2], elements[2][2]).length());
+ 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());
}
Vector3 Basis::get_scale_local() const {
real_t det_sign = SIGN(determinant());
- return det_sign * Vector3(elements[0].length(), elements[1].length(), elements[2].length());
+ return det_sign * Vector3(rows[0].length(), rows[1].length(), rows[2].length());
}
// get_scale works with get_rotation, use get_scale_abs if you need to enforce positive signature.
@@ -317,22 +347,22 @@ Vector3 Basis::rotref_posscale_decomposition(Basis &rotref) const {
// 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 {
@@ -385,7 +415,7 @@ void Basis::rotate_to_align(Vector3 p_start_direction, Vector3 p_end_direction)
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);
+ dot = CLAMP(dot, -1.0f, 1.0f);
const real_t angle_rads = Math::acos(dot);
set_axis_angle(axis, angle_rads);
}
@@ -432,29 +462,29 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
// -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)) {
+ 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 (elements[1][0] == 0.0 && elements[0][1] == 0.0 && elements[1][2] == 0 && elements[2][1] == 0 && elements[1][1] == 1) {
+ 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(elements[0][2], elements[0][0]);
+ euler.y = atan2(rows[0][2], rows[0][0]);
euler.z = 0;
} else {
- euler.x = Math::atan2(-elements[1][2], elements[2][2]);
+ euler.x = Math::atan2(-rows[1][2], rows[2][2]);
euler.y = Math::asin(sy);
- euler.z = Math::atan2(-elements[0][1], elements[0][0]);
+ euler.z = Math::atan2(-rows[0][1], rows[0][0]);
}
} else {
- euler.x = Math::atan2(elements[2][1], elements[1][1]);
- euler.y = -Math_PI / 2.0;
- euler.z = 0.0;
+ 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(elements[2][1], elements[1][1]);
- euler.y = Math_PI / 2.0;
- euler.z = 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;
@@ -467,23 +497,23 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
// 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]);
+ 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(elements[1][2], elements[2][2]);
- euler.y = 0.0;
- euler.z = Math_PI / 2.0;
+ 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(elements[1][2], elements[2][2]);
- euler.y = 0.0;
- euler.z = -Math_PI / 2.0;
+ euler.x = -Math::atan2(rows[1][2], rows[2][2]);
+ euler.y = 0.0f;
+ euler.z = -Math_PI / 2.0f;
}
return euler;
} break;
@@ -497,29 +527,29 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
Vector3 euler;
- real_t m12 = elements[1][2];
+ real_t m12 = rows[1][2];
- if (m12 < (1 - CMP_EPSILON)) {
- if (m12 > -(1 - CMP_EPSILON)) {
+ if (m12 < (1 - (real_t)CMP_EPSILON)) {
+ if (m12 > -(1 - (real_t)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) {
+ 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, elements[1][1]);
+ euler.x = atan2(-m12, rows[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]);
+ 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 * 0.5;
- euler.y = atan2(elements[0][1], elements[0][0]);
+ 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 * 0.5;
- euler.y = -atan2(elements[0][1], elements[0][0]);
+ euler.x = -Math_PI * 0.5f;
+ euler.y = -atan2(rows[0][1], rows[0][0]);
euler.z = 0;
}
@@ -534,23 +564,23 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
// -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]);
+ 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(elements[2][1], elements[2][2]);
- euler.y = 0.0;
- euler.z = -Math_PI / 2.0;
+ 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(elements[2][1], elements[2][2]);
- euler.y = 0.0;
- euler.z = Math_PI / 2.0;
+ euler.x = Math::atan2(rows[2][1], rows[2][2]);
+ euler.y = 0.0f;
+ euler.z = Math_PI / 2.0f;
}
return euler;
} break;
@@ -562,22 +592,22 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
// 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)) {
+ 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(-elements[2][0], elements[2][2]);
- euler.z = Math::atan2(-elements[0][1], elements[1][1]);
+ 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(elements[0][2], elements[0][0]);
+ 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 / 2.0;
- euler.y = Math::atan2(elements[0][2], elements[0][0]);
+ euler.x = Math_PI / 2.0f;
+ euler.y = Math::atan2(rows[0][2], rows[0][0]);
euler.z = 0;
}
return euler;
@@ -590,23 +620,23 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
// 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]);
+ 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(elements[1][0], elements[0][0]);
+ 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(elements[0][1], elements[1][1]);
+ euler.y = Math_PI / 2.0f;
+ 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(elements[0][1], elements[1][1]);
+ euler.y = -Math_PI / 2.0f;
+ euler.z = -Math::atan2(rows[0][1], rows[1][1]);
}
return euler;
} break;
@@ -622,15 +652,15 @@ void Basis::set_euler(const Vector3 &p_euler, EulerOrder p_order) {
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);
+ Basis zmat(c, -s, 0, s, c, 0, 0, 0, 1);
switch (p_order) {
case EULER_ORDER_XYZ: {
@@ -658,13 +688,13 @@ void Basis::set_euler(const Vector3 &p_euler, EulerOrder p_order) {
}
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]);
+ return rows[0].is_equal_approx(p_basis.rows[0]) && rows[1].is_equal_approx(p_basis.rows[1]) && rows[2].is_equal_approx(p_basis.rows[2]);
}
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 (rows[i][j] != p_matrix.rows[i][j]) {
return false;
}
}
@@ -678,9 +708,9 @@ bool Basis::operator!=(const Basis &p_matrix) const {
}
Basis::operator String() const {
- return "[X: " + get_axis(0).operator String() +
- ", Y: " + get_axis(1).operator String() +
- ", Z: " + get_axis(2).operator String() + "]";
+ return "[X: " + get_column(0).operator String() +
+ ", Y: " + get_column(1).operator String() +
+ ", Z: " + get_column(2).operator String() + "]";
}
Quaternion Basis::get_quaternion() const {
@@ -689,31 +719,31 @@ Quaternion Basis::get_quaternion() const {
#endif
/* Allow getting a quaternion from an unnormalized transform */
Basis m = *this;
- real_t trace = m.elements[0][0] + m.elements[1][1] + m.elements[2][2];
+ 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.elements[2][1] - m.elements[1][2]) * s);
- temp[1] = ((m.elements[0][2] - m.elements[2][0]) * s);
- temp[2] = ((m.elements[1][0] - m.elements[0][1]) * 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.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.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.elements[i][i] - m.elements[j][j] - m.elements[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.elements[k][j] - m.elements[j][k]) * s;
- temp[j] = (m.elements[j][i] + m.elements[i][j]) * s;
- temp[k] = (m.elements[k][i] + m.elements[i][k]) * s;
+ temp[3] = (m.rows[k][j] - m.rows[j][k]) * s;
+ temp[j] = (m.rows[j][i] + m.rows[i][j]) * s;
+ temp[k] = (m.rows[k][i] + m.rows[i][k]) * s;
}
return Quaternion(temp[0], temp[1], temp[2], temp[3]);
@@ -752,10 +782,10 @@ int Basis::get_orthogonal_index() const {
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;
+ if (v > 0.5f) {
+ v = 1.0f;
+ } else if (v < -0.5f) {
+ v = -1.0f;
} else {
v = 0;
}
@@ -790,11 +820,11 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
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(elements[1][0] - elements[0][1]) < epsilon) && (Math::abs(elements[2][0] - elements[0][2]) < epsilon) && (Math::abs(elements[2][1] - elements[1][2]) < epsilon)) {
+ 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 diagonal and zero in other terms
- if ((Math::abs(elements[1][0] + elements[0][1]) < epsilon2) && (Math::abs(elements[2][0] + elements[0][2]) < epsilon2) && (Math::abs(elements[2][1] + elements[1][2]) < epsilon2) && (Math::abs(elements[0][0] + elements[1][1] + elements[2][2] - 3) < epsilon2)) {
+ 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
r_axis = Vector3(0, 1, 0);
r_angle = 0;
@@ -802,13 +832,13 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
}
// otherwise this singularity is angle = 180
angle = Math_PI;
- real_t xx = (elements[0][0] + 1) / 2;
- real_t yy = (elements[1][1] + 1) / 2;
- real_t zz = (elements[2][2] + 1) / 2;
- real_t xy = (elements[1][0] + elements[0][1]) / 4;
- real_t xz = (elements[2][0] + elements[0][2]) / 4;
- real_t yz = (elements[2][1] + elements[1][2]) / 4;
- if ((xx > yy) && (xx > zz)) { // elements[0][0] is the largest diagonal term
+ 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) {
x = 0;
y = Math_SQRT12;
@@ -818,7 +848,7 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
y = xy / x;
z = xz / x;
}
- } else if (yy > zz) { // elements[1][1] is the largest diagonal term
+ } else if (yy > zz) { // rows[1][1] is the largest diagonal term
if (yy < epsilon) {
x = Math_SQRT12;
y = 0;
@@ -828,7 +858,7 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
x = xy / y;
z = yz / y;
}
- } else { // elements[2][2] is the largest diagonal term so base result on this
+ } else { // rows[2][2] is the largest diagonal term so base result on this
if (zz < epsilon) {
x = Math_SQRT12;
y = Math_SQRT12;
@@ -844,15 +874,15 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
return;
}
// as we have reached here there are no singularities so we can handle normally
- 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
+ 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
- angle = Math::acos((elements[0][0] + elements[1][1] + elements[2][2] - 1) / 2);
+ angle = Math::acos((rows[0][0] + rows[1][1] + rows[2][2] - 1) / 2);
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;
+ 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;
@@ -860,49 +890,49 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
void Basis::set_quaternion(const Quaternion &p_quaternion) {
real_t d = p_quaternion.length_squared();
- real_t s = 2.0 / d;
+ 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(1.0 - (yy + zz), xy - wz, xz + wy,
- xy + wz, 1.0 - (xx + zz), yz - wx,
- xz - wy, yz + wx, 1.0 - (xx + yy));
+ 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_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);
- elements[0][0] = axis_sq.x + cosine * (1.0 - axis_sq.x);
- elements[1][1] = axis_sq.y + cosine * (1.0 - axis_sq.y);
- elements[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;
real_t zyxs = p_axis.z * sine;
- elements[0][1] = xyzt - zyxs;
- elements[1][0] = xyzt + zyxs;
+ rows[0][1] = xyzt - zyxs;
+ rows[1][0] = xyzt + zyxs;
xyzt = p_axis.x * p_axis.z * t;
zyxs = p_axis.y * sine;
- elements[0][2] = xyzt + zyxs;
- elements[2][0] = xyzt - zyxs;
+ rows[0][2] = xyzt + zyxs;
+ rows[2][0] = xyzt - zyxs;
xyzt = p_axis.y * p_axis.z * t;
zyxs = p_axis.x * sine;
- elements[1][2] = xyzt - zyxs;
- elements[2][1] = xyzt + zyxs;
+ rows[1][2] = xyzt - zyxs;
+ rows[2][1] = xyzt + zyxs;
}
-void Basis::set_axis_angle_scale(const Vector3 &p_axis, real_t p_phi, const Vector3 &p_scale) {
+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_phi);
+ rotate(p_axis, p_angle);
}
void Basis::set_euler_scale(const Vector3 &p_euler, const Vector3 &p_scale) {
@@ -918,17 +948,26 @@ void Basis::set_quaternion_scale(const Quaternion &p_quaternion, const Vector3 &
// 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;
+ rows[0][0] = p_diag.x;
+ rows[0][1] = 0;
+ rows[0][2] = 0;
+
+ rows[1][0] = 0;
+ rows[1][1] = p_diag.y;
+ rows[1][2] = 0;
- elements[1][0] = 0;
- elements[1][1] = p_diag.y;
- elements[1][2] = 0;
+ rows[2][0] = 0;
+ rows[2][1] = 0;
+ rows[2][2] = p_diag.z;
+}
- elements[2][0] = 0;
- elements[2][1] = 0;
- elements[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 {
@@ -937,9 +976,9 @@ Basis Basis::slerp(const Basis &p_to, const real_t &p_weight) const {
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);
- 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);
+ b.rows[0] *= Math::lerp(rows[0].length(), p_to.rows[0].length(), p_weight);
+ b.rows[1] *= Math::lerp(rows[1].length(), p_to.rows[1].length(), p_weight);
+ b.rows[2] *= Math::lerp(rows[2].length(), p_to.rows[2].length(), p_weight);
return b;
}
@@ -963,17 +1002,17 @@ 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 = elements[0][0];
- real_t m01 = elements[0][1];
- real_t m02 = elements[0][2];
- real_t m10 = elements[1][0];
- real_t m11 = elements[1][1];
- real_t m12 = elements[1][2];
- real_t m20 = elements[2][0];
- real_t m21 = elements[2][1];
- real_t m22 = elements[2][2];
+ real_t m00 = rows[0][0];
+ real_t m01 = rows[0][1];
+ real_t m02 = rows[0][2];
+ real_t m10 = rows[1][0];
+ real_t m11 = rows[1][1];
+ real_t m12 = rows[1][2];
+ real_t m20 = rows[2][0];
+ real_t m21 = rows[2][1];
+ real_t m22 = rows[2][2];
p_values[0] = src[0];
p_values[1] = m11 * src[1] - m12 * src[2] + m10 * src[3];
@@ -1068,6 +1107,6 @@ Basis Basis::looking_at(const Vector3 &p_target, const Vector3 &p_up) {
Vector3 v_y = v_z.cross(v_x);
Basis basis;
- basis.set(v_x, v_y, v_z);
+ basis.set_columns(v_x, v_y, v_z);
return basis;
}
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-29 07:27:53 +0000