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/*************************************************************************/
/* quaternion.h */
/*************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/*************************************************************************/
/* 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 */
/* "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 QUATERNION_H
#define QUATERNION_H
#include "core/math/math_defs.h"
#include "core/math/math_funcs.h"
#include "core/math/vector3.h"
#include "core/string/ustring.h"
struct _NO_DISCARD_ Quaternion {
union {
struct {
real_t x;
real_t y;
real_t z;
real_t w;
};
real_t components[4] = { 0, 0, 0, 1.0 };
};
_FORCE_INLINE_ real_t &operator[](int idx) {
return components[idx];
}
_FORCE_INLINE_ const real_t &operator[](int idx) const {
return components[idx];
}
_FORCE_INLINE_ real_t length_squared() const;
bool is_equal_approx(const Quaternion &p_quaternion) const;
real_t length() const;
void normalize();
Quaternion normalized() const;
bool is_normalized() const;
Quaternion inverse() const;
_FORCE_INLINE_ real_t dot(const Quaternion &p_q) const;
real_t angle_to(const Quaternion &p_to) const;
Vector3 get_euler_xyz() const;
Vector3 get_euler_yxz() const;
Vector3 get_euler() const { return get_euler_yxz(); };
Quaternion slerp(const Quaternion &p_to, const real_t &p_weight) const;
Quaternion slerpni(const Quaternion &p_to, const real_t &p_weight) const;
Quaternion cubic_slerp(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &p_post_b, const real_t &p_weight) const;
Vector3 get_axis() const;
float get_angle() const;
_FORCE_INLINE_ void get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
r_angle = 2 * Math::acos(w);
real_t r = ((real_t)1) / Math::sqrt(1 - w * w);
r_axis.x = x * r;
r_axis.y = y * r;
r_axis.z = z * r;
}
void operator*=(const Quaternion &p_q);
Quaternion operator*(const Quaternion &p_q) const;
_FORCE_INLINE_ Vector3 xform(const Vector3 &v) const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V_MSG(!is_normalized(), v, "The quaternion must be normalized.");
#endif
Vector3 u(x, y, z);
Vector3 uv = u.cross(v);
return v + ((uv * w) + u.cross(uv)) * ((real_t)2);
}
_FORCE_INLINE_ Vector3 xform_inv(const Vector3 &v) const {
return inverse().xform(v);
}
_FORCE_INLINE_ void operator+=(const Quaternion &p_q);
_FORCE_INLINE_ void operator-=(const Quaternion &p_q);
_FORCE_INLINE_ void operator*=(const real_t &s);
_FORCE_INLINE_ void operator/=(const real_t &s);
_FORCE_INLINE_ Quaternion operator+(const Quaternion &q2) const;
_FORCE_INLINE_ Quaternion operator-(const Quaternion &q2) const;
_FORCE_INLINE_ Quaternion operator-() const;
_FORCE_INLINE_ Quaternion operator*(const real_t &s) const;
_FORCE_INLINE_ Quaternion operator/(const real_t &s) const;
_FORCE_INLINE_ bool operator==(const Quaternion &p_quaternion) const;
_FORCE_INLINE_ bool operator!=(const Quaternion &p_quaternion) const;
operator String() const;
_FORCE_INLINE_ Quaternion() {}
_FORCE_INLINE_ Quaternion(real_t p_x, real_t p_y, real_t p_z, real_t p_w) :
x(p_x),
y(p_y),
z(p_z),
w(p_w) {
}
Quaternion(const Vector3 &p_axis, real_t p_angle);
Quaternion(const Vector3 &p_euler);
Quaternion(const Quaternion &p_q) :
x(p_q.x),
y(p_q.y),
z(p_q.z),
w(p_q.w) {
}
void operator=(const Quaternion &p_q) {
x = p_q.x;
y = p_q.y;
z = p_q.z;
w = p_q.w;
}
Quaternion(const Vector3 &v0, const Vector3 &v1) // shortest arc
{
Vector3 c = v0.cross(v1);
real_t d = v0.dot(v1);
if (d < -1.0 + CMP_EPSILON) {
x = 0;
y = 1;
z = 0;
w = 0;
} else {
real_t s = Math::sqrt((1.0 + d) * 2.0);
real_t rs = 1.0 / s;
x = c.x * rs;
y = c.y * rs;
z = c.z * rs;
w = s * 0.5;
}
}
};
real_t Quaternion::dot(const Quaternion &p_q) const {
return x * p_q.x + y * p_q.y + z * p_q.z + w * p_q.w;
}
real_t Quaternion::length_squared() const {
return dot(*this);
}
void Quaternion::operator+=(const Quaternion &p_q) {
x += p_q.x;
y += p_q.y;
z += p_q.z;
w += p_q.w;
}
void Quaternion::operator-=(const Quaternion &p_q) {
x -= p_q.x;
y -= p_q.y;
z -= p_q.z;
w -= p_q.w;
}
void Quaternion::operator*=(const real_t &s) {
x *= s;
y *= s;
z *= s;
w *= s;
}
void Quaternion::operator/=(const real_t &s) {
*this *= 1.0 / s;
}
Quaternion Quaternion::operator+(const Quaternion &q2) const {
const Quaternion &q1 = *this;
return Quaternion(q1.x + q2.x, q1.y + q2.y, q1.z + q2.z, q1.w + q2.w);
}
Quaternion Quaternion::operator-(const Quaternion &q2) const {
const Quaternion &q1 = *this;
return Quaternion(q1.x - q2.x, q1.y - q2.y, q1.z - q2.z, q1.w - q2.w);
}
Quaternion Quaternion::operator-() const {
const Quaternion &q2 = *this;
return Quaternion(-q2.x, -q2.y, -q2.z, -q2.w);
}
Quaternion Quaternion::operator*(const real_t &s) const {
return Quaternion(x * s, y * s, z * s, w * s);
}
Quaternion Quaternion::operator/(const real_t &s) const {
return *this * (1.0 / s);
}
bool Quaternion::operator==(const Quaternion &p_quaternion) const {
return x == p_quaternion.x && y == p_quaternion.y && z == p_quaternion.z && w == p_quaternion.w;
}
bool Quaternion::operator!=(const Quaternion &p_quaternion) const {
return x != p_quaternion.x || y != p_quaternion.y || z != p_quaternion.z || w != p_quaternion.w;
}
_FORCE_INLINE_ Quaternion operator*(const real_t &p_real, const Quaternion &p_quaternion) {
return p_quaternion * p_real;
}
#endif // QUATERNION_H
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