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/*************************************************************************/
/* basis.h */
/*************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/*************************************************************************/
/* 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 */
/* "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"
class Basis {
private:
void _set_diagonal(const Vector3 &p_diag);
public:
Vector3 elements[3] = {
Vector3(1, 0, 0),
Vector3(0, 1, 0),
Vector3(0, 0, 1)
};
_FORCE_INLINE_ const Vector3 &operator[](int axis) const {
return elements[axis];
}
_FORCE_INLINE_ Vector3 &operator[](int axis) {
return elements[axis];
}
void invert();
void transpose();
Basis inverse() const;
Basis transposed() const;
_FORCE_INLINE_ real_t determinant() const;
void from_z(const Vector3 &p_z);
_FORCE_INLINE_ Vector3 get_axis(int p_axis) const {
// get actual basis axis (elements is transposed for performance)
return Vector3(elements[0][p_axis], elements[1][p_axis], elements[2][p_axis]);
}
_FORCE_INLINE_ void set_axis(int p_axis, const Vector3 &p_value) {
// get actual basis axis (elements is transposed for performance)
elements[0][p_axis] = p_value.x;
elements[1][p_axis] = p_value.y;
elements[2][p_axis] = p_value.z;
}
void rotate(const Vector3 &p_axis, real_t p_phi);
Basis rotated(const Vector3 &p_axis, real_t p_phi) const;
void rotate_local(const Vector3 &p_axis, real_t p_phi);
Basis rotated_local(const Vector3 &p_axis, real_t p_phi) const;
void rotate(const Vector3 &p_euler);
Basis rotated(const Vector3 &p_euler) const;
void rotate(const Quaternion &p_quaternion);
Basis rotated(const Quaternion &p_quaternion) const;
enum EulerOrder {
EULER_ORDER_XYZ,
EULER_ORDER_XZY,
EULER_ORDER_YXZ,
EULER_ORDER_YZX,
EULER_ORDER_ZXY,
EULER_ORDER_ZYX
};
Vector3 get_euler_normalized(EulerOrder p_order = EULER_ORDER_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 = EULER_ORDER_YXZ) const;
void set_euler(const Vector3 &p_euler, EulerOrder p_order = EULER_ORDER_YXZ);
static Basis from_euler(const Vector3 &p_euler, EulerOrder p_order = EULER_ORDER_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_phi);
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 make_scale_uniform();
float get_uniform_scale() const;
Vector3 get_scale() const;
Vector3 get_scale_abs() const;
Vector3 get_scale_local() const;
void set_axis_angle_scale(const Vector3 &p_axis, real_t p_phi, const Vector3 &p_scale);
void set_euler_scale(const Vector3 &p_euler, const Vector3 &p_scale);
void set_quaternion_scale(const Quaternion &p_quaternion, const Vector3 &p_scale);
// transposed dot products
_FORCE_INLINE_ real_t tdotx(const Vector3 &v) const {
return elements[0][0] * v[0] + elements[1][0] * v[1] + elements[2][0] * v[2];
}
_FORCE_INLINE_ real_t tdoty(const Vector3 &v) const {
return elements[0][1] * v[0] + elements[1][1] * v[1] + elements[2][1] * v[2];
}
_FORCE_INLINE_ real_t tdotz(const Vector3 &v) const {
return elements[0][2] * v[0] + elements[1][2] * v[1] + elements[2][2] * v[2];
}
bool is_equal_approx(const Basis &p_basis) 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*=(const real_t p_val);
_FORCE_INLINE_ Basis operator*(const real_t p_val) const;
int get_orthogonal_index() const;
void set_orthogonal_index(int p_index);
bool is_orthogonal() const;
bool is_diagonal() const;
bool is_rotation() const;
Basis slerp(const Basis &p_to, const real_t &p_weight) const;
void rotate_sh(real_t *p_values);
operator String() const;
/* create / set */
_FORCE_INLINE_ void set(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) {
elements[0][0] = xx;
elements[0][1] = xy;
elements[0][2] = xz;
elements[1][0] = yx;
elements[1][1] = yy;
elements[1][2] = yz;
elements[2][0] = zx;
elements[2][1] = zy;
elements[2][2] = zz;
}
_FORCE_INLINE_ void set(const Vector3 &p_x, const Vector3 &p_y, const Vector3 &p_z) {
set_axis(0, p_x);
set_axis(1, p_y);
set_axis(2, p_z);
}
_FORCE_INLINE_ Vector3 get_column(int i) const {
return Vector3(elements[0][i], elements[1][i], elements[2][i]);
}
_FORCE_INLINE_ Vector3 get_row(int i) const {
return Vector3(elements[i][0], elements[i][1], elements[i][2]);
}
_FORCE_INLINE_ Vector3 get_main_diagonal() const {
return Vector3(elements[0][0], elements[1][1], elements[2][2]);
}
_FORCE_INLINE_ void set_row(int i, const Vector3 &p_row) {
elements[i][0] = p_row.x;
elements[i][1] = p_row.y;
elements[i][2] = p_row.z;
}
_FORCE_INLINE_ void set_zero() {
elements[0].zero();
elements[1].zero();
elements[2].zero();
}
_FORCE_INLINE_ Basis transpose_xform(const Basis &m) const {
return Basis(
elements[0].x * m[0].x + elements[1].x * m[1].x + elements[2].x * m[2].x,
elements[0].x * m[0].y + elements[1].x * m[1].y + elements[2].x * m[2].y,
elements[0].x * m[0].z + elements[1].x * m[1].z + elements[2].x * m[2].z,
elements[0].y * m[0].x + elements[1].y * m[1].x + elements[2].y * m[2].x,
elements[0].y * m[0].y + elements[1].y * m[1].y + elements[2].y * m[2].y,
elements[0].y * m[0].z + elements[1].y * m[1].z + elements[2].y * m[2].z,
elements[0].z * m[0].x + elements[1].z * m[1].x + elements[2].z * m[2].x,
elements[0].z * m[0].y + elements[1].z * m[1].y + elements[2].z * m[2].y,
elements[0].z * m[0].z + elements[1].z * m[1].z + elements[2].z * m[2].z);
}
Basis(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) {
set(xx, xy, xz, yx, yy, yz, zx, zy, zz);
}
void orthonormalize();
Basis orthonormalized() 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));
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_phi) { set_axis_angle(p_axis, p_phi); }
Basis(const Vector3 &p_axis, real_t p_phi, const Vector3 &p_scale) { set_axis_angle_scale(p_axis, p_phi, p_scale); }
static Basis from_scale(const Vector3 &p_scale);
_FORCE_INLINE_ Basis(const Vector3 &row0, const Vector3 &row1, const Vector3 &row2) {
elements[0] = row0;
elements[1] = row1;
elements[2] = row2;
}
_FORCE_INLINE_ Basis() {}
};
_FORCE_INLINE_ void Basis::operator*=(const Basis &p_matrix) {
set(
p_matrix.tdotx(elements[0]), p_matrix.tdoty(elements[0]), p_matrix.tdotz(elements[0]),
p_matrix.tdotx(elements[1]), p_matrix.tdoty(elements[1]), p_matrix.tdotz(elements[1]),
p_matrix.tdotx(elements[2]), p_matrix.tdoty(elements[2]), p_matrix.tdotz(elements[2]));
}
_FORCE_INLINE_ Basis Basis::operator*(const Basis &p_matrix) const {
return Basis(
p_matrix.tdotx(elements[0]), p_matrix.tdoty(elements[0]), p_matrix.tdotz(elements[0]),
p_matrix.tdotx(elements[1]), p_matrix.tdoty(elements[1]), p_matrix.tdotz(elements[1]),
p_matrix.tdotx(elements[2]), p_matrix.tdoty(elements[2]), p_matrix.tdotz(elements[2]));
}
_FORCE_INLINE_ void Basis::operator+=(const Basis &p_matrix) {
elements[0] += p_matrix.elements[0];
elements[1] += p_matrix.elements[1];
elements[2] += p_matrix.elements[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) {
elements[0] -= p_matrix.elements[0];
elements[1] -= p_matrix.elements[1];
elements[2] -= p_matrix.elements[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 real_t p_val) {
elements[0] *= p_val;
elements[1] *= p_val;
elements[2] *= p_val;
}
_FORCE_INLINE_ Basis Basis::operator*(const real_t p_val) const {
Basis ret(*this);
ret *= p_val;
return ret;
}
Vector3 Basis::xform(const Vector3 &p_vector) const {
return Vector3(
elements[0].dot(p_vector),
elements[1].dot(p_vector),
elements[2].dot(p_vector));
}
Vector3 Basis::xform_inv(const Vector3 &p_vector) const {
return Vector3(
(elements[0][0] * p_vector.x) + (elements[1][0] * p_vector.y) + (elements[2][0] * p_vector.z),
(elements[0][1] * p_vector.x) + (elements[1][1] * p_vector.y) + (elements[2][1] * p_vector.z),
(elements[0][2] * p_vector.x) + (elements[1][2] * p_vector.y) + (elements[2][2] * p_vector.z));
}
real_t Basis::determinant() const {
return elements[0][0] * (elements[1][1] * elements[2][2] - elements[2][1] * elements[1][2]) -
elements[1][0] * (elements[0][1] * elements[2][2] - elements[2][1] * elements[0][2]) +
elements[2][0] * (elements[0][1] * elements[1][2] - elements[1][1] * elements[0][2]);
}
#endif // BASIS_H
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