src/third_party/glm/glm/gtx/quaternion.inl

/// @ref gtx_quaternion
/// @file glm/gtx/quaternion.inl

#include <limits>
#include "../gtc/constants.hpp"

namespace glm
{
	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec3<T, P> cross(tvec3<T, P> const& v, tquat<T, P> const& q)
	{
		return inverse(q) * v;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec3<T, P> cross(tquat<T, P> const& q, tvec3<T, P> const& v)
	{
		return q * v;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> squad
	(
		tquat<T, P> const & q1,
		tquat<T, P> const & q2,
		tquat<T, P> const & s1,
		tquat<T, P> const & s2,
		T const & h)
	{
		return mix(mix(q1, q2, h), mix(s1, s2, h), static_cast<T>(2) * (static_cast<T>(1) - h) * h);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> intermediate
	(
		tquat<T, P> const & prev,
		tquat<T, P> const & curr,
		tquat<T, P> const & next
	)
	{
		tquat<T, P> invQuat = inverse(curr);
		return exp((log(next + invQuat) + log(prev + invQuat)) / static_cast<T>(-4)) * curr;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> exp(tquat<T, P> const& q)
	{
		tvec3<T, P> u(q.x, q.y, q.z);
		T const Angle = glm::length(u);
		if (Angle < epsilon<T>())
			return tquat<T, P>();

		tvec3<T, P> const v(u / Angle);
		return tquat<T, P>(cos(Angle), sin(Angle) * v);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> log(tquat<T, P> const& q)
	{
		tvec3<T, P> u(q.x, q.y, q.z);
		T Vec3Len = length(u);

		if (Vec3Len < epsilon<T>())
		{
			if(q.w > static_cast<T>(0))
				return tquat<T, P>(log(q.w), static_cast<T>(0), static_cast<T>(0), static_cast<T>(0));
			else if(q.w < static_cast<T>(0))
				return tquat<T, P>(log(-q.w), pi<T>(), static_cast<T>(0), static_cast<T>(0));
			else
				return tquat<T, P>(std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity());
		}
		else
		{
			T t = atan(Vec3Len, T(q.w)) / Vec3Len;
			T QuatLen2 = Vec3Len * Vec3Len + q.w * q.w;
			return tquat<T, P>(static_cast<T>(0.5) * log(QuatLen2), t * q.x, t * q.y, t * q.z);
		}
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> pow(tquat<T, P> const & x, T const & y)
	{
		//Raising to the power of 0 should yield 1
		//Needed to prevent a division by 0 error later on
		if(y > -epsilon<T>() && y < epsilon<T>())
			return tquat<T, P>(1,0,0,0);

		//To deal with non-unit quaternions
		T magnitude = sqrt(x.x * x.x + x.y * x.y + x.z * x.z + x.w *x.w);

		//Equivalent to raising a real number to a power
		//Needed to prevent a division by 0 error later on
		if(abs(x.w / magnitude) > static_cast<T>(1) - epsilon<T>() && abs(x.w / magnitude) < static_cast<T>(1) + epsilon<T>())
			return tquat<T, P>(pow(x.w, y),0,0,0);

		T Angle = acos(x.w / magnitude);
		T NewAngle = Angle * y;
		T Div = sin(NewAngle) / sin(Angle);
		T Mag = pow(magnitude, y - static_cast<T>(1));

		return tquat<T, P>(cos(NewAngle) * magnitude * Mag, x.x * Div * Mag, x.y * Div * Mag, x.z * Div * Mag);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec3<T, P> rotate(tquat<T, P> const& q, tvec3<T, P> const& v)
	{
		return q * v;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec4<T, P> rotate(tquat<T, P> const& q, tvec4<T, P> const& v)
	{
		return q * v;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER T extractRealComponent(tquat<T, P> const& q)
	{
		T w = static_cast<T>(1) - q.x * q.x - q.y * q.y - q.z * q.z;
		if(w < T(0))
			return T(0);
		else
			return -sqrt(w);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER T length2(tquat<T, P> const& q)
	{
		return q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> shortMix(tquat<T, P> const& x, tquat<T, P> const& y, T const& a)
	{
		if(a <= static_cast<T>(0)) return x;
		if(a >= static_cast<T>(1)) return y;

		T fCos = dot(x, y);
		tquat<T, P> y2(y); //BUG!!! tquat<T> y2;
		if(fCos < static_cast<T>(0))
		{
			y2 = -y;
			fCos = -fCos;
		}

		//if(fCos > 1.0f) // problem
		T k0, k1;
		if(fCos > (static_cast<T>(1) - epsilon<T>()))
		{
			k0 = static_cast<T>(1) - a;
			k1 = static_cast<T>(0) + a; //BUG!!! 1.0f + a;
		}
		else
		{
			T fSin = sqrt(T(1) - fCos * fCos);
			T fAngle = atan(fSin, fCos);
			T fOneOverSin = static_cast<T>(1) / fSin;
			k0 = sin((static_cast<T>(1) - a) * fAngle) * fOneOverSin;
			k1 = sin((static_cast<T>(0) + a) * fAngle) * fOneOverSin;
		}

		return tquat<T, P>(
			k0 * x.w + k1 * y2.w,
			k0 * x.x + k1 * y2.x,
			k0 * x.y + k1 * y2.y,
			k0 * x.z + k1 * y2.z);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> fastMix(tquat<T, P> const& x, tquat<T, P> const& y, T const & a)
	{
		return glm::normalize(x * (static_cast<T>(1) - a) + (y * a));
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> rotation(tvec3<T, P> const& orig, tvec3<T, P> const& dest)
	{
		T cosTheta = dot(orig, dest);
		tvec3<T, P> rotationAxis;

		if(cosTheta >= static_cast<T>(1) - epsilon<T>())
			return quat();

		if(cosTheta < static_cast<T>(-1) + epsilon<T>())
		{
			// special case when vectors in opposite directions :
			// there is no "ideal" rotation axis
			// So guess one; any will do as long as it's perpendicular to start
			// This implementation favors a rotation around the Up axis (Y),
			// since it's often what you want to do.
			rotationAxis = cross(tvec3<T, P>(0, 0, 1), orig);
			if(length2(rotationAxis) < epsilon<T>()) // bad luck, they were parallel, try again!
				rotationAxis = cross(tvec3<T, P>(1, 0, 0), orig);

			rotationAxis = normalize(rotationAxis);
			return angleAxis(pi<T>(), rotationAxis);
		}

		// Implementation from Stan Melax's Game Programming Gems 1 article
		rotationAxis = cross(orig, dest);

		T s = sqrt((T(1) + cosTheta) * static_cast<T>(2));
		T invs = static_cast<T>(1) / s;

		return tquat<T, P>(
			s * static_cast<T>(0.5f), 
			rotationAxis.x * invs,
			rotationAxis.y * invs,
			rotationAxis.z * invs);
	}

}//namespace glm