///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net)
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/// The above copyright notice and this permission notice shall be included in
/// all copies or substantial portions of the Software.
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/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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///
/// @ref gtx_dual_quaternion
/// @file glm/gtx/dual_quaternion.hpp
/// @date 2013-02-10 / 2013-02-20
/// @author Maksim Vorobiev (msomeone@gmail.com)
///
/// @see core (dependence)
/// @see gtc_half_float (dependence)
/// @see gtc_constants (dependence)
/// @see gtc_quaternion (dependence)
///
/// @defgroup gtx_dual_quaternion GLM_GTX_dual_quaternion
/// @ingroup gtx
///
/// @brief Defines a templated dual-quaternion type and several dual-quaternion operations.
///
/// <glm/gtx/dual_quaternion.hpp> need to be included to use these functionalities.
///////////////////////////////////////////////////////////////////////////////////

#pragma once

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

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

namespace glm
{
	/// @addtogroup gtx_dual_quaternion
	/// @{

	template <typename T, precision P>
	struct tdualquat
	{
		typedef T value_type;
		typedef glm::tquat<T, P> part_type;
		
	public:
		glm::tquat<T, P> real, dual;
		
		//////////////////////////////////////
		// Component accesses

#		ifdef GLM_FORCE_SIZE_FUNC
			typedef size_t size_type;
			/// Return the count of components of a dual quaternion
			GLM_FUNC_DECL GLM_CONSTEXPR size_type size() const;

			GLM_FUNC_DECL part_type & operator[](size_type i);
			GLM_FUNC_DECL part_type const & operator[](size_type i) const;
#		else
			typedef length_t length_type;
			/// Return the count of components of a dual quaternion
			GLM_FUNC_DECL GLM_CONSTEXPR length_type length() const;

			GLM_FUNC_DECL part_type & operator[](length_type i);
			GLM_FUNC_DECL part_type const & operator[](length_type i) const;
#		endif//GLM_FORCE_SIZE_FUNC

		//////////////////////////////////////
		// Implicit basic constructors

		GLM_FUNC_DECL tdualquat();
		GLM_FUNC_DECL tdualquat(tdualquat<T, P> const & d);
		template <precision Q>
		GLM_FUNC_DECL tdualquat(tdualquat<T, Q> const & d);

		//////////////////////////////////////
		// Explicit basic constructors

		GLM_FUNC_DECL explicit tdualquat(ctor);
		GLM_FUNC_DECL explicit tdualquat(tquat<T, P> const & real);
		GLM_FUNC_DECL tdualquat(tquat<T, P> const & orientation, tvec3<T, P> const & translation);
		GLM_FUNC_DECL tdualquat(tquat<T, P> const & real, tquat<T, P> const & dual);

		//////////////////////////////////////////////////////////////
		// tdualquat conversions

#		ifdef GLM_FORCE_EXPLICIT_CTOR
			template <typename U, precision Q>
			GLM_FUNC_DECL explicit tdualquat(tdualquat<U, Q> const & q);
#		else
			template <typename U, precision Q>
			GLM_FUNC_DECL tdualquat(tdualquat<U, Q> const & q);
#		endif

		GLM_FUNC_DECL explicit tdualquat(tmat2x4<T, P> const & holder_mat);
		GLM_FUNC_DECL explicit tdualquat(tmat3x4<T, P> const & aug_mat);
		
		// Operators
		GLM_FUNC_DECL tdualquat<T, P> & operator=(tdualquat<T, P> const & m);

		template <typename U>
		GLM_FUNC_DECL tdualquat<T, P> & operator=(tdualquat<U, P> const & m);
		template <typename U>
		GLM_FUNC_DECL tdualquat<T, P> & operator*=(U s);
		template <typename U>
		GLM_FUNC_DECL tdualquat<T, P> & operator/=(U s);
	};
	
	template <typename T, precision P>
	GLM_FUNC_DECL tquat<T, P> operator- (
		tquat<T, P> const & q);
	
	template <typename T, precision P>
	GLM_FUNC_DECL tdualquat<T, P> operator+ (
		tdualquat<T, P> const & q,
		tdualquat<T, P> const & p);
	
	template <typename T, precision P>
	GLM_FUNC_DECL tdualquat<T, P> operator* (
		tdualquat<T, P> const & q,
		tdualquat<T, P> const & p);
	
	template <typename T, precision P>
	GLM_FUNC_DECL tvec3<T, P> operator* (
		tquat<T, P> const & q,
		tvec3<T, P> const & v);
	
	template <typename T, precision P>
	GLM_FUNC_DECL tvec3<T, P> operator* (
		tvec3<T, P> const & v,
		tquat<T, P> const & q);
	
	template <typename T, precision P>
	GLM_FUNC_DECL tvec4<T, P> operator* (
		tquat<T, P> const & q,
		tvec4<T, P> const & v);
	
	template <typename T, precision P>
	GLM_FUNC_DECL tvec4<T, P> operator* (
		tvec4<T, P> const & v,
		tquat<T, P> const & q);
	
	template <typename T, precision P>
	GLM_FUNC_DECL tdualquat<T, P> operator* (
		tdualquat<T, P> const & q,
		T const & s);
	
	template <typename T, precision P>
	GLM_FUNC_DECL tdualquat<T, P> operator* (
		T const & s,
		tdualquat<T, P> const & q);
	
	template <typename T, precision P>
	GLM_FUNC_DECL tdualquat<T, P> operator/ (
		tdualquat<T, P> const & q,
		T const & s);

	/// Returns the normalized quaternion.
	///
	/// @see gtx_dual_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tdualquat<T, P> normalize(
		tdualquat<T, P> const & q);

	/// Returns the linear interpolation of two dual quaternion.
	///
	/// @see gtc_dual_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tdualquat<T, P> lerp(
		tdualquat<T, P> const & x,
		tdualquat<T, P> const & y,
		T const & a);

	/// Returns the q inverse.
	///
	/// @see gtx_dual_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tdualquat<T, P> inverse(
		tdualquat<T, P> const & q);

	/// Converts a quaternion to a 2 * 4 matrix.
	///
	/// @see gtx_dual_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tmat2x4<T, P> mat2x4_cast(
		tdualquat<T, P> const & x);

	/// Converts a quaternion to a 3 * 4 matrix.
	///
	/// @see gtx_dual_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tmat3x4<T, P> mat3x4_cast(
		tdualquat<T, P> const & x);

	/// Converts a 2 * 4 matrix (matrix which holds real and dual parts) to a quaternion.
	///
	/// @see gtx_dual_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tdualquat<T, P> dualquat_cast(
		tmat2x4<T, P> const & x);

	/// Converts a 3 * 4 matrix (augmented matrix rotation + translation) to a quaternion.
	///
	/// @see gtx_dual_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tdualquat<T, P> dualquat_cast(
		tmat3x4<T, P> const & x);

	
	/// Dual-quaternion of low single-precision floating-point numbers.
	///
	/// @see gtx_dual_quaternion
	typedef tdualquat<float, lowp>		lowp_dualquat;
	
	/// Dual-quaternion of medium single-precision floating-point numbers.
	///
	/// @see gtx_dual_quaternion
	typedef tdualquat<float, mediump>	mediump_dualquat;
	
	/// Dual-quaternion of high single-precision floating-point numbers.
	///
	/// @see gtx_dual_quaternion
	typedef tdualquat<float, highp>		highp_dualquat;


	/// Dual-quaternion of low single-precision floating-point numbers.
	///
	/// @see gtx_dual_quaternion
	typedef tdualquat<float, lowp>		lowp_fdualquat;
	
	/// Dual-quaternion of medium single-precision floating-point numbers.
	///
	/// @see gtx_dual_quaternion
	typedef tdualquat<float, mediump>	mediump_fdualquat;
	
	/// Dual-quaternion of high single-precision floating-point numbers.
	///
	/// @see gtx_dual_quaternion
	typedef tdualquat<float, highp>		highp_fdualquat;
	
	
	/// Dual-quaternion of low double-precision floating-point numbers.
	///
	/// @see gtx_dual_quaternion
	typedef tdualquat<double, lowp>		lowp_ddualquat;
	
	/// Dual-quaternion of medium double-precision floating-point numbers.
	///
	/// @see gtx_dual_quaternion
	typedef tdualquat<double, mediump>	mediump_ddualquat;
	
	/// Dual-quaternion of high double-precision floating-point numbers.
	///
	/// @see gtx_dual_quaternion
	typedef tdualquat<double, highp>	highp_ddualquat;

	
#if(!defined(GLM_PRECISION_HIGHP_FLOAT) && !defined(GLM_PRECISION_MEDIUMP_FLOAT) && !defined(GLM_PRECISION_LOWP_FLOAT))
	/// Dual-quaternion of floating-point numbers.
	///
	/// @see gtx_dual_quaternion
	typedef highp_fdualquat			dualquat;
	
	/// Dual-quaternion of single-precision floating-point numbers.
	///
	/// @see gtx_dual_quaternion
	typedef highp_fdualquat			fdualquat;
#elif(defined(GLM_PRECISION_HIGHP_FLOAT) && !defined(GLM_PRECISION_MEDIUMP_FLOAT) && !defined(GLM_PRECISION_LOWP_FLOAT))
	typedef highp_fdualquat			dualquat;
	typedef highp_fdualquat			fdualquat;
#elif(!defined(GLM_PRECISION_HIGHP_FLOAT) && defined(GLM_PRECISION_MEDIUMP_FLOAT) && !defined(GLM_PRECISION_LOWP_FLOAT))
	typedef mediump_fdualquat		dualquat;
	typedef mediump_fdualquat		fdualquat;
#elif(!defined(GLM_PRECISION_HIGHP_FLOAT) && !defined(GLM_PRECISION_MEDIUMP_FLOAT) && defined(GLM_PRECISION_LOWP_FLOAT))
	typedef lowp_fdualquat			dualquat;
	typedef lowp_fdualquat			fdualquat;
#else
#	error "GLM error: multiple default precision requested for single-precision floating-point types"
#endif
	

#if(!defined(GLM_PRECISION_HIGHP_DOUBLE) && !defined(GLM_PRECISION_MEDIUMP_DOUBLE) && !defined(GLM_PRECISION_LOWP_DOUBLE))
	/// Dual-quaternion of default double-precision floating-point numbers.
	///
	/// @see gtx_dual_quaternion
	typedef highp_ddualquat			ddualquat;
#elif(defined(GLM_PRECISION_HIGHP_DOUBLE) && !defined(GLM_PRECISION_MEDIUMP_DOUBLE) && !defined(GLM_PRECISION_LOWP_DOUBLE))
	typedef highp_ddualquat			ddualquat;
#elif(!defined(GLM_PRECISION_HIGHP_DOUBLE) && defined(GLM_PRECISION_MEDIUMP_DOUBLE) && !defined(GLM_PRECISION_LOWP_DOUBLE))
	typedef mediump_ddualquat		ddualquat;
#elif(!defined(GLM_PRECISION_HIGHP_DOUBLE) && !defined(GLM_PRECISION_MEDIUMP_DOUBLE) && defined(GLM_PRECISION_LOWP_DOUBLE))
	typedef lowp_ddualquat			ddualquat;
#else
#	error "GLM error: Multiple default precision requested for double-precision floating-point types"
#endif

	/// @}
} //namespace glm

#include "dual_quaternion.inl"