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

#include "Quat.hpp"


#include <cmath>

#include "Defs.hpp"

#include "Vector3.hpp"

#include "Basis.hpp"

namespace godot {

real_t Quat::length() const
{
	return ::sqrt(length_squared());
}

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

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

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

void Quat::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);
}

Quat 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 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 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 Quat::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);
}



Quat 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 Quat::xform(const Vector3& v) const {

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


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


Quat::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::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;
	}
}


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 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;
}


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

}