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basis.h
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basis.h
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/**************************************************************************/
/* basis.h */
/**************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/**************************************************************************/
/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */
/* */
/* Permission is hereby granted, free of charge, to any person obtaining */
/* a copy of this software and associated documentation files (the */
/* "Software"), to deal in the Software without restriction, including */
/* without limitation the rights to use, copy, modify, merge, publish, */
/* distribute, sublicense, and/or sell copies of the Software, and to */
/* permit persons to whom the Software is furnished to do so, subject to */
/* the following conditions: */
/* */
/* The above copyright notice and this permission notice shall be */
/* included in all copies or substantial portions of the Software. */
/* */
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. */
/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
/**************************************************************************/
#ifndef BASIS_H
#define BASIS_H
#include "core/math/quaternion.h"
#include "core/math/vector3.h"
struct _NO_DISCARD_ Basis {
Vector3 rows[3] = {
Vector3(1, 0, 0),
Vector3(0, 1, 0),
Vector3(0, 0, 1)
};
_FORCE_INLINE_ const Vector3 &operator[](int p_axis) const {
return rows[p_axis];
}
_FORCE_INLINE_ Vector3 &operator[](int p_axis) {
return rows[p_axis];
}
void invert();
void transpose();
Basis inverse() const;
Basis transposed() const;
_FORCE_INLINE_ real_t determinant() const;
void rotate(const Vector3 &p_axis, real_t p_angle);
Basis rotated(const Vector3 &p_axis, real_t p_angle) const;
void rotate_local(const Vector3 &p_axis, real_t p_angle);
Basis rotated_local(const Vector3 &p_axis, real_t p_angle) const;
void rotate(const Vector3 &p_euler, EulerOrder p_order = EulerOrder::YXZ);
Basis rotated(const Vector3 &p_euler, EulerOrder p_order = EulerOrder::YXZ) const;
void rotate(const Quaternion &p_quaternion);
Basis rotated(const Quaternion &p_quaternion) const;
Vector3 get_euler_normalized(EulerOrder p_order = EulerOrder::YXZ) const;
void get_rotation_axis_angle(Vector3 &p_axis, real_t &p_angle) const;
void get_rotation_axis_angle_local(Vector3 &p_axis, real_t &p_angle) const;
Quaternion get_rotation_quaternion() const;
void rotate_to_align(Vector3 p_start_direction, Vector3 p_end_direction);
Vector3 rotref_posscale_decomposition(Basis &rotref) const;
Vector3 get_euler(EulerOrder p_order = EulerOrder::YXZ) const;
void set_euler(const Vector3 &p_euler, EulerOrder p_order = EulerOrder::YXZ);
static Basis from_euler(const Vector3 &p_euler, EulerOrder p_order = EulerOrder::YXZ) {
Basis b;
b.set_euler(p_euler, p_order);
return b;
}
Quaternion get_quaternion() const;
void set_quaternion(const Quaternion &p_quaternion);
void get_axis_angle(Vector3 &r_axis, real_t &r_angle) const;
void set_axis_angle(const Vector3 &p_axis, real_t p_angle);
void scale(const Vector3 &p_scale);
Basis scaled(const Vector3 &p_scale) const;
void scale_local(const Vector3 &p_scale);
Basis scaled_local(const Vector3 &p_scale) const;
void scale_orthogonal(const Vector3 &p_scale);
Basis scaled_orthogonal(const Vector3 &p_scale) const;
real_t get_uniform_scale() const;
Vector3 get_scale() const;
Vector3 get_scale_abs() const;
Vector3 get_scale_global() const;
void set_axis_angle_scale(const Vector3 &p_axis, real_t p_angle, const Vector3 &p_scale);
void set_euler_scale(const Vector3 &p_euler, const Vector3 &p_scale, EulerOrder p_order = EulerOrder::YXZ);
void set_quaternion_scale(const Quaternion &p_quaternion, const Vector3 &p_scale);
// transposed dot products
_FORCE_INLINE_ real_t tdotx(const Vector3 &p_v) const {
return rows[0][0] * p_v[0] + rows[1][0] * p_v[1] + rows[2][0] * p_v[2];
}
_FORCE_INLINE_ real_t tdoty(const Vector3 &p_v) const {
return rows[0][1] * p_v[0] + rows[1][1] * p_v[1] + rows[2][1] * p_v[2];
}
_FORCE_INLINE_ real_t tdotz(const Vector3 &p_v) const {
return rows[0][2] * p_v[0] + rows[1][2] * p_v[1] + rows[2][2] * p_v[2];
}
bool is_equal_approx(const Basis &p_basis) const;
bool is_finite() const;
bool operator==(const Basis &p_matrix) const;
bool operator!=(const Basis &p_matrix) const;
_FORCE_INLINE_ Vector3 xform(const Vector3 &p_vector) const;
_FORCE_INLINE_ Vector3 xform_inv(const Vector3 &p_vector) const;
_FORCE_INLINE_ void operator*=(const Basis &p_matrix);
_FORCE_INLINE_ Basis operator*(const Basis &p_matrix) const;
_FORCE_INLINE_ void operator+=(const Basis &p_matrix);
_FORCE_INLINE_ Basis operator+(const Basis &p_matrix) const;
_FORCE_INLINE_ void operator-=(const Basis &p_matrix);
_FORCE_INLINE_ Basis operator-(const Basis &p_matrix) const;
_FORCE_INLINE_ void operator*=(real_t p_val);
_FORCE_INLINE_ Basis operator*(real_t p_val) const;
_FORCE_INLINE_ void operator/=(real_t p_val);
_FORCE_INLINE_ Basis operator/(real_t p_val) const;
bool is_orthogonal() const;
bool is_orthonormal() const;
bool is_conformal() const;
bool is_diagonal() const;
bool is_rotation() const;
Basis lerp(const Basis &p_to, real_t p_weight) const;
Basis slerp(const Basis &p_to, real_t p_weight) const;
void rotate_sh(real_t *p_values);
operator String() const;
/* create / set */
_FORCE_INLINE_ void set(real_t p_xx, real_t p_xy, real_t p_xz, real_t p_yx, real_t p_yy, real_t p_yz, real_t p_zx, real_t p_zy, real_t p_zz) {
rows[0][0] = p_xx;
rows[0][1] = p_xy;
rows[0][2] = p_xz;
rows[1][0] = p_yx;
rows[1][1] = p_yy;
rows[1][2] = p_yz;
rows[2][0] = p_zx;
rows[2][1] = p_zy;
rows[2][2] = p_zz;
}
_FORCE_INLINE_ void set_columns(const Vector3 &p_x, const Vector3 &p_y, const Vector3 &p_z) {
set_column(0, p_x);
set_column(1, p_y);
set_column(2, p_z);
}
_FORCE_INLINE_ Vector3 get_column(int p_index) const {
// Get actual basis axis column (we store transposed as rows for performance).
return Vector3(rows[0][p_index], rows[1][p_index], rows[2][p_index]);
}
_FORCE_INLINE_ void set_column(int p_index, const Vector3 &p_value) {
// Set actual basis axis column (we store transposed as rows for performance).
rows[0][p_index] = p_value.x;
rows[1][p_index] = p_value.y;
rows[2][p_index] = p_value.z;
}
_FORCE_INLINE_ Vector3 get_main_diagonal() const {
return Vector3(rows[0][0], rows[1][1], rows[2][2]);
}
_FORCE_INLINE_ void set_zero() {
rows[0].zero();
rows[1].zero();
rows[2].zero();
}
_FORCE_INLINE_ Basis transpose_xform(const Basis &p_m) const {
return Basis(
rows[0].x * p_m[0].x + rows[1].x * p_m[1].x + rows[2].x * p_m[2].x,
rows[0].x * p_m[0].y + rows[1].x * p_m[1].y + rows[2].x * p_m[2].y,
rows[0].x * p_m[0].z + rows[1].x * p_m[1].z + rows[2].x * p_m[2].z,
rows[0].y * p_m[0].x + rows[1].y * p_m[1].x + rows[2].y * p_m[2].x,
rows[0].y * p_m[0].y + rows[1].y * p_m[1].y + rows[2].y * p_m[2].y,
rows[0].y * p_m[0].z + rows[1].y * p_m[1].z + rows[2].y * p_m[2].z,
rows[0].z * p_m[0].x + rows[1].z * p_m[1].x + rows[2].z * p_m[2].x,
rows[0].z * p_m[0].y + rows[1].z * p_m[1].y + rows[2].z * p_m[2].y,
rows[0].z * p_m[0].z + rows[1].z * p_m[1].z + rows[2].z * p_m[2].z);
}
Basis(real_t p_xx, real_t p_xy, real_t p_xz, real_t p_yx, real_t p_yy, real_t p_yz, real_t p_zx, real_t p_zy, real_t p_zz) {
set(p_xx, p_xy, p_xz, p_yx, p_yy, p_yz, p_zx, p_zy, p_zz);
}
void orthonormalize();
Basis orthonormalized() const;
void orthogonalize();
Basis orthogonalized() const;
#ifdef MATH_CHECKS
bool is_symmetric() const;
#endif
Basis diagonalize();
operator Quaternion() const { return get_quaternion(); }
static Basis looking_at(const Vector3 &p_target, const Vector3 &p_up = Vector3(0, 1, 0), bool p_use_model_front = false);
Basis(const Quaternion &p_quaternion) { set_quaternion(p_quaternion); };
Basis(const Quaternion &p_quaternion, const Vector3 &p_scale) { set_quaternion_scale(p_quaternion, p_scale); }
Basis(const Vector3 &p_axis, real_t p_angle) { set_axis_angle(p_axis, p_angle); }
Basis(const Vector3 &p_axis, real_t p_angle, const Vector3 &p_scale) { set_axis_angle_scale(p_axis, p_angle, p_scale); }
static Basis from_scale(const Vector3 &p_scale);
_FORCE_INLINE_ Basis(const Vector3 &p_x_axis, const Vector3 &p_y_axis, const Vector3 &p_z_axis) {
set_columns(p_x_axis, p_y_axis, p_z_axis);
}
_FORCE_INLINE_ Basis() {}
private:
// Helper method.
void _set_diagonal(const Vector3 &p_diag);
};
_FORCE_INLINE_ void Basis::operator*=(const Basis &p_matrix) {
set(
p_matrix.tdotx(rows[0]), p_matrix.tdoty(rows[0]), p_matrix.tdotz(rows[0]),
p_matrix.tdotx(rows[1]), p_matrix.tdoty(rows[1]), p_matrix.tdotz(rows[1]),
p_matrix.tdotx(rows[2]), p_matrix.tdoty(rows[2]), p_matrix.tdotz(rows[2]));
}
_FORCE_INLINE_ Basis Basis::operator*(const Basis &p_matrix) const {
return Basis(
p_matrix.tdotx(rows[0]), p_matrix.tdoty(rows[0]), p_matrix.tdotz(rows[0]),
p_matrix.tdotx(rows[1]), p_matrix.tdoty(rows[1]), p_matrix.tdotz(rows[1]),
p_matrix.tdotx(rows[2]), p_matrix.tdoty(rows[2]), p_matrix.tdotz(rows[2]));
}
_FORCE_INLINE_ void Basis::operator+=(const Basis &p_matrix) {
rows[0] += p_matrix.rows[0];
rows[1] += p_matrix.rows[1];
rows[2] += p_matrix.rows[2];
}
_FORCE_INLINE_ Basis Basis::operator+(const Basis &p_matrix) const {
Basis ret(*this);
ret += p_matrix;
return ret;
}
_FORCE_INLINE_ void Basis::operator-=(const Basis &p_matrix) {
rows[0] -= p_matrix.rows[0];
rows[1] -= p_matrix.rows[1];
rows[2] -= p_matrix.rows[2];
}
_FORCE_INLINE_ Basis Basis::operator-(const Basis &p_matrix) const {
Basis ret(*this);
ret -= p_matrix;
return ret;
}
_FORCE_INLINE_ void Basis::operator*=(real_t p_val) {
rows[0] *= p_val;
rows[1] *= p_val;
rows[2] *= p_val;
}
_FORCE_INLINE_ Basis Basis::operator*(real_t p_val) const {
Basis ret(*this);
ret *= p_val;
return ret;
}
_FORCE_INLINE_ void Basis::operator/=(real_t p_val) {
rows[0] /= p_val;
rows[1] /= p_val;
rows[2] /= p_val;
}
_FORCE_INLINE_ Basis Basis::operator/(real_t p_val) const {
Basis ret(*this);
ret /= p_val;
return ret;
}
Vector3 Basis::xform(const Vector3 &p_vector) const {
return Vector3(
rows[0].dot(p_vector),
rows[1].dot(p_vector),
rows[2].dot(p_vector));
}
Vector3 Basis::xform_inv(const Vector3 &p_vector) const {
return Vector3(
(rows[0][0] * p_vector.x) + (rows[1][0] * p_vector.y) + (rows[2][0] * p_vector.z),
(rows[0][1] * p_vector.x) + (rows[1][1] * p_vector.y) + (rows[2][1] * p_vector.z),
(rows[0][2] * p_vector.x) + (rows[1][2] * p_vector.y) + (rows[2][2] * p_vector.z));
}
real_t Basis::determinant() const {
return rows[0][0] * (rows[1][1] * rows[2][2] - rows[2][1] * rows[1][2]) -
rows[1][0] * (rows[0][1] * rows[2][2] - rows[2][1] * rows[0][2]) +
rows[2][0] * (rows[0][1] * rows[1][2] - rows[1][1] * rows[0][2]);
}
#endif // BASIS_H