text: /*************************************************************************/
  /*  quat.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).   */
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  /*************************************************************************/
  
  #ifndef QUAT_H
  #define QUAT_H
  
  #include "core/math/math_defs.h"
  #include "core/math/math_funcs.h"
  #include "core/math/vector3.h"
  #include "core/ustring.h"
  
  class _NO_DISCARD_CLASS_ Quat {
  public:
  	real_t x, y, z, w;
  
  	_FORCE_INLINE_ real_t length_squared() const;
  	bool is_equal_approx(const Quat &p_quat) const;
  	real_t length() const;
  	void normalize();
  	Quat normalized() const;
  	bool is_normalized() const;
  	Quat inverse() const;
  	_FORCE_INLINE_ real_t dot(const Quat &p_q) const;
  	real_t angle_to(const Quat &p_to) const;
  
  	void set_euler_xyz(const Vector3 &p_euler);
  	Vector3 get_euler_xyz() const;
  	void set_euler_yxz(const Vector3 &p_euler);
  	Vector3 get_euler_yxz() const;
  
  	void set_euler(const Vector3 &p_euler) { set_euler_yxz(p_euler); };
  	Vector3 get_euler() const { return get_euler_yxz(); };
  
  	Quat slerp(const Quat &p_to, const real_t &p_weight) const;
  	Quat slerpni(const Quat &p_to, const real_t &p_weight) const;
  	Quat cubic_slerp(const Quat &p_b, const Quat &p_pre_a, const Quat &p_post_b, const real_t &p_weight) const;
  
  	void set_axis_angle(const Vector3 &axis, const real_t &angle);
  	_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 Quat &p_q);
  	Quat operator*(const Quat &p_q) const;
  
  	Quat operator*(const Vector3 &v) const {
  		return Quat(w * v.x + y * v.z - z * v.y,
  				w * v.y + z * v.x - x * v.z,
  				w * v.z + x * v.y - y * v.x,
  				-x * v.x - y * v.y - z * v.z);
  	}
  
  	_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_ void operator+=(const Quat &p_q);
  	_FORCE_INLINE_ void operator-=(const Quat &p_q);
  	_FORCE_INLINE_ void operator*=(const real_t &s);
  	_FORCE_INLINE_ void operator/=(const real_t &s);
  	_FORCE_INLINE_ Quat operator+(const Quat &q2) const;
  	_FORCE_INLINE_ Quat operator-(const Quat &q2) const;
  	_FORCE_INLINE_ Quat operator-() const;
  	_FORCE_INLINE_ Quat operator*(const real_t &s) const;
  	_FORCE_INLINE_ Quat operator/(const real_t &s) const;
  
  	_FORCE_INLINE_ bool operator==(const Quat &p_quat) const;
  	_FORCE_INLINE_ bool operator!=(const Quat &p_quat) const;
  
  	operator String() const;
  
  	inline void set(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;
  	}
  	inline Quat(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) {
  	}
  	Quat(const Vector3 &axis, const real_t &angle) { set_axis_angle(axis, angle); }
  
  	Quat(const Vector3 &euler) { set_euler(euler); }
  	Quat(const Quat &p_q) :
  			x(p_q.x),
  			y(p_q.y),
  			z(p_q.z),
  			w(p_q.w) {
  	}
  
  	Quat &operator=(const Quat &p_q) {
  		x = p_q.x;
  		y = p_q.y;
  		z = p_q.z;
  		w = p_q.w;
  		return *this;
  	}
  
  	Quat(const Vector3 &v0, const Vector3 &v1) // shortest arc
  	{
  		Vector3 c = v0.cross(v1);
  		real_t d = v0.dot(v1);
  
  		if (d < -1 + (real_t)CMP_EPSILON) {
  			x = 0;
  			y = 1;
  			z = 0;
  			w = 0;
  		} else {
  			real_t s = Math::sqrt((1 + d) * 2);
  			real_t rs = 1 / s;
  
  			x = c.x * rs;
  			y = c.y * rs;
  			z = c.z * rs;
  			w = s * 0.5f;
  		}
  	}
  
  	inline Quat() :
  			x(0),
  			y(0),
  			z(0),
  			w(1) {
  	}
  };
  
  real_t Quat::dot(const Quat &p_q) const {
  	return x * p_q.x + y * p_q.y + z * p_q.z + w * p_q.w;
  }
  
  real_t Quat::length_squared() const {
  	return dot(*this);
  }
  
  void Quat::operator+=(const Quat &p_q) {
  	x += p_q.x;
  	y += p_q.y;
  	z += p_q.z;
  	w += p_q.w;
  }
  
  void Quat::operator-=(const Quat &p_q) {
  	x -= p_q.x;
  	y -= p_q.y;
  	z -= p_q.z;
  	w -= p_q.w;
  }
  
  void Quat::operator*=(const real_t &s) {
  	x *= s;
  	y *= s;
  	z *= s;
  	w *= s;
  }
  
  void Quat::operator/=(const real_t &s) {
  	*this *= 1 / s;
  }
  
  Quat Quat::operator+(const Quat &q2) const {
  	const Quat &q1 = *this;
  	return Quat(q1.x + q2.x, q1.y + q2.y, q1.z + q2.z, q1.w + q2.w);
  }
  
  Quat Quat::operator-(const Quat &q2) const {
  	const Quat &q1 = *this;
  	return Quat(q1.x - q2.x, q1.y - q2.y, q1.z - q2.z, q1.w - q2.w);
  }
  
  Quat Quat::operator-() const {
  	const Quat &q2 = *this;
  	return Quat(-q2.x, -q2.y, -q2.z, -q2.w);
  }
  
  Quat Quat::operator*(const real_t &s) const {
  	return Quat(x * s, y * s, z * s, w * s);
  }
  
  Quat Quat::operator/(const real_t &s) const {
  	return *this * (1 / s);
  }
  
  bool Quat::operator==(const Quat &p_quat) const {
  	return x == p_quat.x && y == p_quat.y && z == p_quat.z && w == p_quat.w;
  }
  
  bool Quat::operator!=(const Quat &p_quat) const {
  	return x != p_quat.x || y != p_quat.y || z != p_quat.z || w != p_quat.w;
  }
  
  #endif
  