function quat_slerp(QUATERNION *q, QUATERNION *u, QUATERNION *v, double t) {
	QUATERNION qa, qb;
	quat_set(&qa, u);
	quat_set(&qb, v);
	double cosHalfTheta=qa.w*qb.w + qa.x*qb.x + qa.y*qb.y + qa.z*qb.z;
	if(abs(cosHalfTheta)>=1.0)
		quat_set(&q,&qa);
	else
	{
		double halfTheta=acos(cosHalfTheta);
		double sinHalfTheta=sqrt(1.0 - cosHalfTheta*cosHalfTheta);
		if (abs(sinHalfTheta) < 0.001)
		{ 
			q.w = (qa.w * 0.5 + qb.w * 0.5);
			q.x = (qa.x * 0.5 + qb.x * 0.5);
			q.y = (qa.y * 0.5 + qb.y * 0.5);
			q.z = (qa.z * 0.5 + qb.z * 0.5);
		}
		else
		{
			double ratioA = sin((1 - t) * halfTheta) / sinHalfTheta;
			double ratioB = sin(t * halfTheta) / sinHalfTheta; 
			//calculate Quaternion.
			q.w = (qa.w * ratioA + qb.w * ratioB);
			q.x = (qa.x * ratioA + qb.x * ratioB);
			q.y = (qa.y * ratioA + qb.y * ratioB);
			q.z = (qa.z * ratioA + qb.z * ratioB);
		}
	}
}