///////////////////////////////////////////////////////////////////////////////////////////////////
// OpenGL Mathematics Copyright (c) 2005 - 2011 G-Truc Creation (www.g-truc.net)
///////////////////////////////////////////////////////////////////////////////////////////////////
// Created : 2005-12-21
// Updated : 2009-05-21
// Licence : This source is under MIT License
// File    : glm/gtx/quaternion.hpp
///////////////////////////////////////////////////////////////////////////////////////////////////
// Dependency:
// - GLM core
///////////////////////////////////////////////////////////////////////////////////////////////////
// ToDo:
// - Study constructors with angles and axis
// - Study constructors with vec3 that are the imaginary component of quaternion
///////////////////////////////////////////////////////////////////////////////////////////////////

#ifndef glm_gtx_quaternion
#define glm_gtx_quaternion

// Dependency:
#include "../glm.hpp"
#include "../gtc/quaternion.hpp"

#if(defined(GLM_MESSAGES) && !defined(glm_ext))
#	pragma message("GLM: GLM_GTX_quaternion extension included")
#endif

namespace glm{
namespace gtx{
namespace quaternion ///< GLM_GTX_quaternion extension: Quaternion types and functions
{
	using namespace gtc::quaternion;

	/// \addtogroup gtx_quaternion
	///@{

	//! Compute a cross product between a quaternion and a vector. 
	//! From GLM_GTX_quaternion extension.
	template <typename valType> 
	detail::tvec3<valType> cross(
		detail::tquat<valType> const & q, 
		detail::tvec3<valType> const & v);

	//! Compute a cross product between a vector and a quaternion.
	//! From GLM_GTX_quaternion extension.
	template <typename valType> 
	detail::tvec3<valType> cross(
		detail::tvec3<valType> const & v, 
		detail::tquat<valType> const & q);

	//! Compute a point on a path according squad equation. 
	//! q1 and q2 are control points; s1 and s2 are intermediate control points.
	//! From GLM_GTX_quaternion extension.
	template <typename valType> 
	detail::tquat<valType> squad(
		detail::tquat<valType> const & q1, 
		detail::tquat<valType> const & q2, 
		detail::tquat<valType> const & s1, 
		detail::tquat<valType> const & s2, 
		valType const & h);

	//! Returns an intermediate control point for squad interpolation.
	//! From GLM_GTX_quaternion extension.
	template <typename valType> 
	detail::tquat<valType> intermediate(
		detail::tquat<valType> const & prev, 
		detail::tquat<valType> const & curr, 
		detail::tquat<valType> const & next);

	//! Returns a exp of a quaternion. 
	//! From GLM_GTX_quaternion extension.
    template <typename valType> 
	detail::tquat<valType> exp(
		detail::tquat<valType> const & q, 
		valType const & exponent);

	//! Returns a log of a quaternion. 
	//! From GLM_GTX_quaternion extension.
    template <typename valType> 
	detail::tquat<valType> log(
		detail::tquat<valType> const & q);

	//! Returns x raised to the y power.
	//! From GLM_GTX_quaternion extension.
    template <typename valType> 
	detail::tquat<valType> pow(
		detail::tquat<valType> const & x, 
		valType const & y);

	//! Returns quarternion square root.
	//! From GLM_GTX_quaternion extension.
	//template <typename valType> 
	//detail::tquat<valType> sqrt(
	//	detail::tquat<valType> const & q);

	//! Rotates a 3 components vector by a quaternion. 
	//! From GLM_GTX_transform extension.
	template <typename valType> 
	detail::tvec3<valType> rotate(
		detail::tquat<valType> const & q, 
		detail::tvec3<valType> const & v);

    //! Rotates a 4 components vector by a quaternion.
	//! From GLM_GTX_transform extension.
	template <typename valType> 
	detail::tvec4<valType> rotate(
		detail::tquat<valType> const & q, 
		detail::tvec4<valType> const & v);
		
    //! Returns the quaternion rotation angle. 
	//! From GLM_GTX_quaternion extension.
	template <typename valType> 
	valType angle(
		detail::tquat<valType> const & x);

	//! Returns the q rotation axis. 
	//! From GLM_GTX_quaternion extension.
	template <typename valType> 
	detail::tvec3<valType> axis(
		detail::tquat<valType> const & x);

	//! Build a quaternion from an angle and a normalized axis. 
	//! From GLM_GTX_quaternion extension.
	template <typename valType> 
	detail::tquat<valType> angleAxis(
		valType const & angle, 
		valType const & x, 
		valType const & y, 
		valType const & z);

    //! Build a quaternion from an angle and a normalized axis.
	//! From GLM_GTX_quaternion extension.
	template <typename valType> 
	detail::tquat<valType> angleAxis(
		valType const & angle, 
		detail::tvec3<valType> const & axis);

	//! Extract the real component of a quaternion.
	//! From GLM_GTX_quaternion extension.
	template <typename valType> 
	valType extractRealComponent(
		detail::tquat<valType> const & q);

    //! Returns roll value of euler angles. 
	//! From GLM_GTX_quaternion extension.
	template <typename valType> 
	valType roll(
		detail::tquat<valType> const & x);

	//! Returns pitch value of euler angles. 
	//! From GLM_GTX_quaternion extension.
    template <typename valType> 
	valType pitch(
		detail::tquat<valType> const & x);

    //! Returns yaw value of euler angles. 
	//! From GLM_GTX_quaternion extension.
	template <typename valType> 
	valType yaw(
		detail::tquat<valType> const & x);
		
	//! Returns euler angles, yitch as x, yaw as y, roll as z. 
	//! From GLM_GTX_quaternion extension.
	template <typename valType> 
	detail::tvec3<valType> eularAngles(
		detail::tquat<valType> const & x);

	//! Converts a quaternion to a 3 * 3 matrix. 
	//! From GLM_GTX_quaternion extension.
    template <typename valType> 
	detail::tmat3x3<valType> toMat3(
		detail::tquat<valType> const & x){return gtc::quaternion::mat3_cast(x);}

	//! Converts a quaternion to a 4 * 4 matrix. 
	//! From GLM_GTX_quaternion extension.
	template <typename valType> 
	detail::tmat4x4<valType> toMat4(
		detail::tquat<valType> const & x){return gtc::quaternion::mat4_cast(x);}

	//! Converts a 3 * 3 matrix to a quaternion. 
	//! From GLM_GTX_quaternion extension.
	template <typename valType> 
	detail::tquat<valType> toQuat(
		detail::tmat3x3<valType> const & x){return gtc::quaternion::quat_cast(x);}

	//! Converts a 4 * 4 matrix to a quaternion. 
	//! From GLM_GTX_quaternion extension.
	template <typename valType> 
	detail::tquat<valType> toQuat(
		detail::tmat4x4<valType> const & x){return gtc::quaternion::quat_cast(x);}

	//! Quaternion interpolation using the rotation short path. 
	//! From GLM_GTX_quaternion extension.
	template <typename T>
	detail::tquat<T> shortMix(
		detail::tquat<T> const & x, 
		detail::tquat<T> const & y, 
		T const & a);

	//! Quaternion normalized linear interpolation. 
	//! From GLM_GTX_quaternion extension.
	template <typename T>
	detail::tquat<T> fastMix(
		detail::tquat<T> const & x, 
		detail::tquat<T> const & y, 
		T const & a);

	/// @}
}//namespace quaternion
}//namespace gtx
} //namespace glm

#include "quaternion.inl"

namespace glm{using namespace gtx::quaternion;}

#endif//glm_gtx_quaternion