godot-cpp/include/godot/core/Quat.h

#ifndef QUAT_H
#define QUAT_H

#include <cmath>

#include "Vector3.h"

// #include "Basis.h"

namespace godot {

#define CMP_EPSILON 0.00001

typedef float real_t;

class Quat{
public:

	real_t x,y,z,w;

	real_t length_squared() const; // down below
	real_t length() const
	{
		return ::sqrt(length_squared());
	}

	void normalize()
	{
		*this /= length();
	}

	Quat normalized() const
	{
		return *this / length();
	}

	Quat inverse() const
	{
		return Quat( -x, -y, -z, w );
	}

	real_t dot(const Quat& q) const; // down below
	void set_euler(const Vector3& p_euler)
	{
		real_t half_a1 = p_euler.x * 0.5;
		real_t half_a2 = p_euler.y * 0.5;
		real_t half_a3 = p_euler.z * 0.5;

		// R = X(a1).Y(a2).Z(a3) convention for Euler angles.
		// Conversion to quaternion as listed in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf (page A-2)
		// a3 is the angle of the first rotation, following the notation in this reference.

		real_t cos_a1 = ::cos(half_a1);
		real_t sin_a1 = ::sin(half_a1);
		real_t cos_a2 = ::cos(half_a2);
		real_t sin_a2 = ::sin(half_a2);
		real_t cos_a3 = ::cos(half_a3);
		real_t sin_a3 = ::sin(half_a3);

		set(sin_a1*cos_a2*cos_a3 + sin_a2*sin_a3*cos_a1,
			-sin_a1*sin_a3*cos_a2 + sin_a2*cos_a1*cos_a3,
			sin_a1*sin_a2*cos_a3 + sin_a3*cos_a1*cos_a2,
			-sin_a1*sin_a2*sin_a3 + cos_a1*cos_a2*cos_a3);
	}

	Vector3 get_euler() const; // down below

	Quat slerp(const Quat& q, const real_t& t) const {

		Quat          to1;
		real_t        omega, cosom, sinom, scale0, scale1;


		// calc cosine
		cosom = dot(q);

		// adjust signs (if necessary)
		if ( cosom <0.0 ) {
			cosom = -cosom;
			to1.x = - q.x;
			to1.y = - q.y;
			to1.z = - q.z;
			to1.w = - q.w;
		} else  {
			to1.x = q.x;
			to1.y = q.y;
			to1.z = q.z;
			to1.w = q.w;
		}


		// calculate coefficients

		if ( (1.0 - cosom) > CMP_EPSILON ) {
			// standard case (slerp)
			omega = ::acos(cosom);
			sinom = ::sin(omega);
			scale0 = ::sin((1.0 - t) * omega) / sinom;
			scale1 = ::sin(t * omega) / sinom;
		} else {
			// "from" and "to" quaternions are very close
			//  ... so we can do a linear interpolation
			scale0 = 1.0 - t;
			scale1 = t;
		}
		// calculate final values
		return Quat(
			scale0 * x + scale1 * to1.x,
			scale0 * y + scale1 * to1.y,
			scale0 * z + scale1 * to1.z,
			scale0 * w + scale1 * to1.w
		);
	}

	Quat slerpni(const Quat& q, const real_t& t) const {

		const Quat &from = *this;

		real_t dot = from.dot(q);

		if (::fabs(dot) > 0.9999) return from;

		real_t	theta		= ::acos(dot),
			sinT		= 1.0 / ::sin(theta),
			newFactor	= ::sin(t * theta) * sinT,
			invFactor	= ::sin((1.0 - t) * theta) * sinT;

		return Quat(invFactor * from.x + newFactor * q.x,
					invFactor * from.y + newFactor * q.y,
					invFactor * from.z + newFactor * q.z,
					invFactor * from.w + newFactor * q.w);
	}

	Quat cubic_slerp(const Quat& q, const Quat& prep, const Quat& postq,const real_t& t) const
	{
		//the only way to do slerp :|
		real_t t2 = (1.0-t)*t*2;
		Quat sp = this->slerp(q,t);
		Quat sq = prep.slerpni(postq,t);
		return sp.slerpni(sq,t2);
	}

	void get_axis_and_angle(Vector3& r_axis, real_t &r_angle) const {
		r_angle = 2 * ::acos(w);
		r_axis.x = x / ::sqrt(1-w*w);
		r_axis.y = y / ::sqrt(1-w*w);
		r_axis.z = z / ::sqrt(1-w*w);
	}

	void operator*=(const Quat& q); // down below
	Quat operator*(const Quat& q) const; // down below



	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);
	}

	Vector3 xform(const Vector3& v) const {

		Quat q = *this * v;
		q *= this->inverse();
		return Vector3(q.x,q.y,q.z);
	}

	// everything's down
	void operator+=(const Quat& q);
	void operator-=(const Quat& q);
	void operator*=(const real_t& s);
	void operator/=(const real_t& s);
	Quat operator+(const Quat& q2) const;
	Quat operator-(const Quat& q2) const;
	Quat operator-() const;
	Quat operator*(const real_t& s) const;
	Quat operator/(const real_t& s) const;


	bool operator==(const Quat& p_quat) const;
	bool operator!=(const Quat& p_quat) const;

	operator String() const
	{
		return String(); // @Todo
	}

	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)
	{
		real_t d = axis.length();
		if (d==0)
			set(0,0,0,0);
		else {
			real_t sin_angle = ::sin(angle * 0.5);
			real_t cos_angle = ::cos(angle * 0.5);
			real_t s = sin_angle / d;
			set(axis.x * s, axis.y * s, axis.z * s,
				cos_angle);
		}
	}

	Quat(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 = ::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;
		}
	}

	inline Quat() {x=y=z=0; w=1; }


};


real_t Quat::dot(const Quat& q) const {
	return x * q.x+y * q.y+z * q.z+w * q.w;
}

real_t Quat::length_squared() const {
	return dot(*this);
}

void Quat::operator+=(const Quat& q) {
	x += q.x; y += q.y; z += q.z; w += q.w;
}

void Quat::operator-=(const Quat& q) {
	x -= q.x; y -= q.y; z -= q.z; w -= 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 *= 1.0 / 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 Quat& q2) const {
	Quat q1 = *this;
	q1 *= q2;
	return q1;
}


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 * (1.0 / 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;
}


}

#include "Basis.h"

namespace godot {

Vector3 Quat::get_euler() const
{
	Basis m(*this);
	return m.get_euler();
}

}

#endif // QUAT_H