///////////////////////////////////////////////////////////////////////////////////
/// 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 gtx_rotate_vector
/// @file glm/gtx/rotate_vector.inl
/// @date 2006-11-02 / 2011-06-07
/// @author Christophe Riccio
///////////////////////////////////////////////////////////////////////////////////

namespace glm
{
        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tvec3<T, P> slerp
        (
                tvec3<T, P> const & x,
                tvec3<T, P> const & y,
                T const & a
        )
        {
                // get cosine of angle between vectors (-1 -> 1)
                T CosAlpha = dot(x, y);
                // get angle (0 -> pi)
                T Alpha = acos(CosAlpha);
                // get sine of angle between vectors (0 -> 1)
                T SinAlpha = sin(Alpha);
                // this breaks down when SinAlpha = 0, i.e. Alpha = 0 or pi
                T t1 = sin((static_cast<T>(1) - a) * Alpha) / SinAlpha;
                T t2 = sin(a * Alpha) / SinAlpha;

                // interpolate src vectors
                return x * t1 + y * t2;
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tvec2<T, P> rotate
        (
                tvec2<T, P> const & v,
                T const & angle
        )
        {
                tvec2<T, P> Result;
                T const Cos(cos(angle));
                T const Sin(sin(angle));

                Result.x = v.x * Cos - v.y * Sin;
                Result.y = v.x * Sin + v.y * Cos;
                return Result;
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tvec3<T, P> rotate
        (
                tvec3<T, P> const & v,
                T const & angle,
                tvec3<T, P> const & normal
        )
        {
                return tmat3x3<T, P>(glm::rotate(angle, normal)) * v;
        }
        /*
        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tvec3<T, P> rotateGTX(
                const tvec3<T, P>& x,
                T angle,
                const tvec3<T, P>& normal)
        {
                const T Cos = cos(radians(angle));
                const T Sin = sin(radians(angle));
                return x * Cos + ((x * normal) * (T(1) - Cos)) * normal + cross(x, normal) * Sin;
        }
        */
        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tvec4<T, P> rotate
        (
                tvec4<T, P> const & v,
                T const & angle,
                tvec3<T, P> const & normal
        )
        {
                return rotate(angle, normal) * v;
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tvec3<T, P> rotateX
        (
                tvec3<T, P> const & v,
                T const & angle
        )
        {
                tvec3<T, P> Result(v);
                T const Cos(cos(angle));
                T const Sin(sin(angle));

                Result.y = v.y * Cos - v.z * Sin;
                Result.z = v.y * Sin + v.z * Cos;
                return Result;
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tvec3<T, P> rotateY
        (
                tvec3<T, P> const & v,
                T const & angle
        )
        {
                tvec3<T, P> Result = v;
                T const Cos(cos(angle));
                T const Sin(sin(angle));

                Result.x =  v.x * Cos + v.z * Sin;
                Result.z = -v.x * Sin + v.z * Cos;
                return Result;
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tvec3<T, P> rotateZ
        (
                tvec3<T, P> const & v,
                T const & angle
        )
        {
                tvec3<T, P> Result = v;
                T const Cos(cos(angle));
                T const Sin(sin(angle));

                Result.x = v.x * Cos - v.y * Sin;
                Result.y = v.x * Sin + v.y * Cos;
                return Result;
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tvec4<T, P> rotateX
        (
                tvec4<T, P> const & v,
                T const & angle
        )
        {
                tvec4<T, P> Result = v;
                T const Cos(cos(angle));
                T const Sin(sin(angle));

                Result.y = v.y * Cos - v.z * Sin;
                Result.z = v.y * Sin + v.z * Cos;
                return Result;
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tvec4<T, P> rotateY
        (
                tvec4<T, P> const & v,
                T const & angle
        )
        {
                tvec4<T, P> Result = v;
                T const Cos(cos(angle));
                T const Sin(sin(angle));

                Result.x =  v.x * Cos + v.z * Sin;
                Result.z = -v.x * Sin + v.z * Cos;
                return Result;
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tvec4<T, P> rotateZ
        (
                tvec4<T, P> const & v,
                T const & angle
        )
        {
                tvec4<T, P> Result = v;
                T const Cos(cos(angle));
                T const Sin(sin(angle));

                Result.x = v.x * Cos - v.y * Sin;
                Result.y = v.x * Sin + v.y * Cos;
                return Result;
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tmat4x4<T, P> orientation
        (
                tvec3<T, P> const & Normal,
                tvec3<T, P> const & Up
        )
        {
                if(all(equal(Normal, Up)))
                        return tmat4x4<T, P>(T(1));

                tvec3<T, P> RotationAxis = cross(Up, Normal);
                T Angle = acos(dot(Normal, Up));

                return rotate(Angle, RotationAxis);
        }
}//namespace glm