///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net)
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/// 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>
        struct tquat
        {
                typedef tquat<T, P> type;
                typedef T value_type;

        public:
                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();
                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);

                //////////////////////////////////////
                // Convertions

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

                //////////////////////////////////////
                // Operators
                GLM_FUNC_DECL tquat<T, P> & operator+=(tquat<T, P> const & q);
                GLM_FUNC_DECL tquat<T, P> & operator*=(tquat<T, P> const & q);
                GLM_FUNC_DECL tquat<T, P> & operator*=(T const & s);
                GLM_FUNC_DECL tquat<T, P> & operator/=(T const & 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 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"