///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net)
/// Permission is hereby granted, free of charge, to any person obtaining a copy
/// of this software and associated documentation files (the "Software"), to deal
/// in the Software without restriction, including without limitation the rights
/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
/// copies of the Software, and to permit persons to whom the Software is
/// furnished to do so, subject to the following conditions:
/// 
/// The above copyright notice and this permission notice shall be included in
/// all copies or substantial portions of the Software.
/// 
/// Restrictions:
///		By making use of the Software for military purposes, you choose to make
///		a Bunny unhappy.
/// 
/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
/// THE SOFTWARE.
///
/// @ref gtc_quaternion
/// @file glm/gtc/quaternion.hpp
/// @date 2009-05-21 / 2012-12-20
/// @author Christophe Riccio
///
/// @see core (dependence)
/// @see gtc_half_float (dependence)
/// @see gtc_constants (dependence)
///
/// @defgroup gtc_quaternion GLM_GTC_quaternion
/// @ingroup gtc
/// 
/// @brief Defines a templated quaternion type and several quaternion operations.
/// 
/// <glm/gtc/quaternion.hpp> need to be included to use these functionalities.
///////////////////////////////////////////////////////////////////////////////////

#pragma once

// Dependency:
#include "../mat3x3.hpp"
#include "../mat4x4.hpp"
#include "../vec3.hpp"
#include "../vec4.hpp"
#include "../gtc/constants.hpp"

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

namespace glm
{
	/// @addtogroup gtc_quaternion
	/// @{

	template <typename T, precision P = defaultp>
	struct tquat
	{
		// -- Implementation detail --

		typedef tquat<T, P> type;
		typedef T value_type;

#		ifdef GLM_META_PROG_HELPERS
			static GLM_RELAXED_CONSTEXPR length_t components = 4;
			static GLM_RELAXED_CONSTEXPR precision prec = P;
#		endif//GLM_META_PROG_HELPERS

		// -- Data --

		T x, y, z, w;

		// -- Component accesses --

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

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

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

		// -- Implicit basic constructors --

		GLM_FUNC_DECL tquat() GLM_DEFAULT_CTOR;
		GLM_FUNC_DECL tquat(tquat<T, P> const & q) GLM_DEFAULT;
		template <precision Q>
		GLM_FUNC_DECL tquat(tquat<T, Q> const & q);

		// -- Explicit basic constructors --

		GLM_FUNC_DECL explicit tquat(ctor);
		GLM_FUNC_DECL explicit tquat(T const & s, tvec3<T, P> const & v);
		GLM_FUNC_DECL tquat(T const & w, T const & x, T const & y, T const & z);

		// -- Conversion constructors --

		template <typename U, precision Q>
		GLM_FUNC_DECL GLM_EXPLICIT tquat(tquat<U, Q> const & q);

		/// Explicit conversion operators
#		if GLM_HAS_EXPLICIT_CONVERSION_OPERATORS
			GLM_FUNC_DECL explicit operator tmat3x3<T, P>();
			GLM_FUNC_DECL explicit operator tmat4x4<T, P>();
#		endif

		/// Create a quaternion from two normalized axis
		///
		/// @param u A first normalized axis
		/// @param v A second normalized axis
		/// @see gtc_quaternion
		/// @see http://lolengine.net/blog/2013/09/18/beautiful-maths-quaternion-from-vectors
		GLM_FUNC_DECL explicit tquat(tvec3<T, P> const & u,	tvec3<T, P> const & v);

		/// Build a quaternion from euler angles (pitch, yaw, roll), in radians.
		GLM_FUNC_DECL explicit tquat(tvec3<T, P> const & eulerAngles);
		GLM_FUNC_DECL explicit tquat(tmat3x3<T, P> const & m);
		GLM_FUNC_DECL explicit tquat(tmat4x4<T, P> const & m);

		// -- Unary arithmetic operators --

		GLM_FUNC_DECL tquat<T, P> & operator=(tquat<T, P> const & m) GLM_DEFAULT;

		template <typename U>
		GLM_FUNC_DECL tquat<T, P> & operator=(tquat<U, P> const & m);
		template <typename U>
		GLM_FUNC_DECL tquat<T, P> & operator+=(tquat<U, P> const & q);
		template <typename U>
		GLM_FUNC_DECL tquat<T, P> & operator*=(tquat<U, P> const & q);
		template <typename U>
		GLM_FUNC_DECL tquat<T, P> & operator*=(U s);
		template <typename U>
		GLM_FUNC_DECL tquat<T, P> & operator/=(U s);
	};

	// -- Unary bit operators --

	template <typename T, precision P>
	GLM_FUNC_DECL tquat<T, P> operator-(tquat<T, P> const & q);

	// -- Binary operators --

	template <typename T, precision P>
	GLM_FUNC_DECL tquat<T, P> operator+(tquat<T, P> const & q, tquat<T, P> const & p);

	template <typename T, precision P>
	GLM_FUNC_DECL tquat<T, P> operator*(tquat<T, P> const & q, tquat<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 tquat<T, P> operator*(tquat<T, P> const & q, T const & s);

	template <typename T, precision P>
	GLM_FUNC_DECL tquat<T, P> operator*(T const & s, tquat<T, P> const & q);

	template <typename T, precision P>
	GLM_FUNC_DECL tquat<T, P> operator/(tquat<T, P> const & q, T const & s);

	/// Returns the length of the quaternion.
	/// 
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL T length(tquat<T, P> const & q);

	/// Returns the normalized quaternion.
	/// 
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tquat<T, P> normalize(tquat<T, P> const & q);
		
	/// Returns dot product of q1 and q2, i.e., q1[0] * q2[0] + q1[1] * q2[1] + ...
	/// 
	/// @see gtc_quaternion
	template <typename T, precision P, template <typename, precision> class quatType>
	GLM_FUNC_DECL T dot(quatType<T, P> const & x, quatType<T, P> const & y);

	/// Spherical linear interpolation of two quaternions.
	/// The interpolation is oriented and the rotation is performed at constant speed.
	/// For short path spherical linear interpolation, use the slerp function.
	/// 
	/// @param x A quaternion
	/// @param y A quaternion
	/// @param a Interpolation factor. The interpolation is defined beyond the range [0, 1].
	/// @tparam T Value type used to build the quaternion. Supported: half, float or double.
	/// @see gtc_quaternion
	/// @see - slerp(tquat<T, P> const & x, tquat<T, P> const & y, T const & a)
	template <typename T, precision P>
	GLM_FUNC_DECL tquat<T, P> mix(tquat<T, P> const & x, tquat<T, P> const & y, T a);

	/// Linear interpolation of two quaternions.
	/// The interpolation is oriented.
	/// 
	/// @param x A quaternion
	/// @param y A quaternion
	/// @param a Interpolation factor. The interpolation is defined in the range [0, 1].
	/// @tparam T Value type used to build the quaternion. Supported: half, float or double.
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tquat<T, P> lerp(tquat<T, P> const & x, tquat<T, P> const & y, T a);

	/// Spherical linear interpolation of two quaternions.
	/// The interpolation always take the short path and the rotation is performed at constant speed.
	/// 
	/// @param x A quaternion
	/// @param y A quaternion
	/// @param a Interpolation factor. The interpolation is defined beyond the range [0, 1].
	/// @tparam T Value type used to build the quaternion. Supported: half, float or double.
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tquat<T, P> slerp(tquat<T, P> const & x, tquat<T, P> const & y, T a);

	/// Returns the q conjugate.
	/// 
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tquat<T, P> conjugate(tquat<T, P> const & q);

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

	/// Rotates a quaternion from a vector of 3 components axis and an angle.
	/// 
	/// @param q Source orientation
	/// @param angle Angle expressed in radians.
	/// @param axis Axis of the rotation
	/// 
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tquat<T, P> rotate(tquat<T, P> const & q, T const & angle, tvec3<T, P> const & axis);

	/// Returns euler angles, yitch as x, yaw as y, roll as z.
	/// The result is expressed in radians if GLM_FORCE_RADIANS is defined or degrees otherwise.
	/// 
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tvec3<T, P> eulerAngles(tquat<T, P> const & x);

	/// Returns roll value of euler angles expressed in radians.
	///
	/// @see gtx_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL T roll(tquat<T, P> const & x);

	/// Returns pitch value of euler angles expressed in radians.
	///
	/// @see gtx_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL T pitch(tquat<T, P> const & x);

	/// Returns yaw value of euler angles expressed in radians.
	///
	/// @see gtx_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL T yaw(tquat<T, P> const & x);

	/// Converts a quaternion to a 3 * 3 matrix.
	/// 
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tmat3x3<T, P> mat3_cast(tquat<T, P> const & x);

	/// Converts a quaternion to a 4 * 4 matrix.
	/// 
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tmat4x4<T, P> mat4_cast(tquat<T, P> const & x);

	/// Converts a 3 * 3 matrix to a quaternion.
	/// 
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tquat<T, P> quat_cast(tmat3x3<T, P> const & x);

	/// Converts a 4 * 4 matrix to a quaternion.
	/// 
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tquat<T, P> quat_cast(tmat4x4<T, P> const & x);

	/// Returns the quaternion rotation angle.
	///
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL T angle(tquat<T, P> const & x);

	/// Returns the q rotation axis.
	///
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tvec3<T, P> axis(tquat<T, P> const & x);

	/// Build a quaternion from an angle and a normalized axis.
	///
	/// @param angle Angle expressed in radians.
	/// @param axis Axis of the quaternion, must be normalized.
	///
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tquat<T, P> angleAxis(T const & angle, tvec3<T, P> const & axis);

	/// Returns the component-wise comparison result of x < y.
	/// 
	/// @tparam quatType Floating-point quaternion types.
	///
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tvec4<bool, P> lessThan(tquat<T, P> const & x, tquat<T, P> const & y);

	/// Returns the component-wise comparison of result x <= y.
	///
	/// @tparam quatType Floating-point quaternion types.
	///
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tvec4<bool, P> lessThanEqual(tquat<T, P> const & x, tquat<T, P> const & y);

	/// Returns the component-wise comparison of result x > y.
	///
	/// @tparam quatType Floating-point quaternion types.
	///
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tvec4<bool, P> greaterThan(tquat<T, P> const & x, tquat<T, P> const & y);

	/// Returns the component-wise comparison of result x >= y.
	///
	/// @tparam quatType Floating-point quaternion types.
	///
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tvec4<bool, P> greaterThanEqual(tquat<T, P> const & x, tquat<T, P> const & y);

	/// Returns the component-wise comparison of result x == y.
	///
	/// @tparam quatType Floating-point quaternion types.
	///
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tvec4<bool, P> equal(tquat<T, P> const & x, tquat<T, P> const & y);

	/// Returns the component-wise comparison of result x != y.
	/// 
	/// @tparam quatType Floating-point quaternion types.
	///
	/// @see gtc_quaternion
	template <typename T, precision P>
	GLM_FUNC_DECL tvec4<bool, P> notEqual(tquat<T, P> const & x, tquat<T, P> const & y);
	/// @}
} //namespace glm

#include "quaternion.inl"
