///////////////////////////////////////////////////////////////////////////////////
/// 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_matrix_transform
/// @file glm/gtc/matrix_transform.inl
/// @date 2009-04-29 / 2011-06-15
/// @author Christophe Riccio
///////////////////////////////////////////////////////////////////////////////////

#include "../geometric.hpp"
#include "../trigonometric.hpp"
#include "../matrix.hpp"

namespace glm
{
        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tmat4x4<T, P> translate
        (
                tmat4x4<T, P> const & m,
                tvec3<T, P> const & v
        )
        {
                tmat4x4<T, P> Result(m);
                Result[3] = m[0] * v[0] + m[1] * v[1] + m[2] * v[2] + m[3];
                return Result;
        }
        
        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tmat4x4<T, P> rotate
        (
                tmat4x4<T, P> const & m,
                T angle,
                tvec3<T, P> const & v
        )
        {
                T const a = angle;
                T const c = cos(a);
                T const s = sin(a);

                tvec3<T, P> axis(normalize(v));
                tvec3<T, P> temp((T(1) - c) * axis);

                tmat4x4<T, P> Rotate(uninitialize);
                Rotate[0][0] = c + temp[0] * axis[0];
                Rotate[0][1] = 0 + temp[0] * axis[1] + s * axis[2];
                Rotate[0][2] = 0 + temp[0] * axis[2] - s * axis[1];

                Rotate[1][0] = 0 + temp[1] * axis[0] - s * axis[2];
                Rotate[1][1] = c + temp[1] * axis[1];
                Rotate[1][2] = 0 + temp[1] * axis[2] + s * axis[0];

                Rotate[2][0] = 0 + temp[2] * axis[0] + s * axis[1];
                Rotate[2][1] = 0 + temp[2] * axis[1] - s * axis[0];
                Rotate[2][2] = c + temp[2] * axis[2];

                tmat4x4<T, P> Result(uninitialize);
                Result[0] = m[0] * Rotate[0][0] + m[1] * Rotate[0][1] + m[2] * Rotate[0][2];
                Result[1] = m[0] * Rotate[1][0] + m[1] * Rotate[1][1] + m[2] * Rotate[1][2];
                Result[2] = m[0] * Rotate[2][0] + m[1] * Rotate[2][1] + m[2] * Rotate[2][2];
                Result[3] = m[3];
                return Result;
        }
                
        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tmat4x4<T, P> rotate_slow
        (
                tmat4x4<T, P> const & m,
                T angle, 
                tvec3<T, P> const & v
        )
        {
                T const a = angle;
                T const c = cos(a);
                T const s = sin(a);
                tmat4x4<T, P> Result;

                tvec3<T, P> axis = normalize(v);

                Result[0][0] = c + (1 - c)      * axis.x     * axis.x;
                Result[0][1] = (1 - c) * axis.x * axis.y + s * axis.z;
                Result[0][2] = (1 - c) * axis.x * axis.z - s * axis.y;
                Result[0][3] = 0;

                Result[1][0] = (1 - c) * axis.y * axis.x - s * axis.z;
                Result[1][1] = c + (1 - c) * axis.y * axis.y;
                Result[1][2] = (1 - c) * axis.y * axis.z + s * axis.x;
                Result[1][3] = 0;

                Result[2][0] = (1 - c) * axis.z * axis.x + s * axis.y;
                Result[2][1] = (1 - c) * axis.z * axis.y - s * axis.x;
                Result[2][2] = c + (1 - c) * axis.z * axis.z;
                Result[2][3] = 0;

                Result[3] = tvec4<T, P>(0, 0, 0, 1);
                return m * Result;
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tmat4x4<T, P> scale
        (
                tmat4x4<T, P> const & m,
                tvec3<T, P> const & v
        )
        {
                tmat4x4<T, P> Result(uninitialize);
                Result[0] = m[0] * v[0];
                Result[1] = m[1] * v[1];
                Result[2] = m[2] * v[2];
                Result[3] = m[3];
                return Result;
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tmat4x4<T, P> scale_slow
        (
                tmat4x4<T, P> const & m,
                tvec3<T, P> const & v
        )
        {
                tmat4x4<T, P> Result(T(1));
                Result[0][0] = v.x;
                Result[1][1] = v.y;
                Result[2][2] = v.z;
                return m * Result;
        }

        template <typename T>
        GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> ortho
        (
                T left,
                T right,
                T bottom,
                T top,
                T zNear,
                T zFar
        )
        {
                tmat4x4<T, defaultp> Result(1);
                Result[0][0] = static_cast<T>(2) / (right - left);
                Result[1][1] = static_cast<T>(2) / (top - bottom);
                Result[2][2] = - static_cast<T>(2) / (zFar - zNear);
                Result[3][0] = - (right + left) / (right - left);
                Result[3][1] = - (top + bottom) / (top - bottom);
                Result[3][2] = - (zFar + zNear) / (zFar - zNear);
                return Result;
        }

        template <typename T>
        GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> ortho
        (
                T left,
                T right,
                T bottom,
                T top
        )
        {
                tmat4x4<T, defaultp> Result(1);
                Result[0][0] = static_cast<T>(2) / (right - left);
                Result[1][1] = static_cast<T>(2) / (top - bottom);
                Result[2][2] = - static_cast<T>(1);
                Result[3][0] = - (right + left) / (right - left);
                Result[3][1] = - (top + bottom) / (top - bottom);
                return Result;
        }

        template <typename T>
        GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> frustum
        (
                T left,
                T right,
                T bottom,
                T top,
                T nearVal,
                T farVal
        )
        {
                tmat4x4<T, defaultp> Result(0);
                Result[0][0] = (static_cast<T>(2) * nearVal) / (right - left);
                Result[1][1] = (static_cast<T>(2) * nearVal) / (top - bottom);
                Result[2][0] = (right + left) / (right - left);
                Result[2][1] = (top + bottom) / (top - bottom);
                Result[2][2] = -(farVal + nearVal) / (farVal - nearVal);
                Result[2][3] = static_cast<T>(-1);
                Result[3][2] = -(static_cast<T>(2) * farVal * nearVal) / (farVal - nearVal);
                return Result;
        }

        template <typename T>
        GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspective
        (
                T fovy,
                T aspect,
                T zNear,
                T zFar
        )
        {
                assert(abs(aspect - std::numeric_limits<T>::epsilon()) > static_cast<T>(0));
                assert(zFar > zNear);

                T const tanHalfFovy = tan(fovy / static_cast<T>(2));

                tmat4x4<T, defaultp> Result(static_cast<T>(0));
                Result[0][0] = static_cast<T>(1) / (aspect * tanHalfFovy);
                Result[1][1] = static_cast<T>(1) / (tanHalfFovy);
                Result[2][2] = - (zFar + zNear) / (zFar - zNear);
                Result[2][3] = - static_cast<T>(1);
                Result[3][2] = - (static_cast<T>(2) * zFar * zNear) / (zFar - zNear);
                return Result;
        }
        
        template <typename T>
        GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspectiveFov
        (
                T fov,
                T width,
                T height,
                T zNear,
                T zFar
        )
        {
                assert(width > static_cast<T>(0));
                assert(height > static_cast<T>(0));
                assert(fov > static_cast<T>(0));
        
                T const rad = fov;
                T const h = glm::cos(static_cast<T>(0.5) * rad) / glm::sin(static_cast<T>(0.5) * rad);
                T const w = h * height / width; ///todo max(width , Height) / min(width , Height)?

                tmat4x4<T, defaultp> Result(static_cast<T>(0));
                Result[0][0] = w;
                Result[1][1] = h;
                Result[2][2] = - (zFar + zNear) / (zFar - zNear);
                Result[2][3] = - static_cast<T>(1);
                Result[3][2] = - (static_cast<T>(2) * zFar * zNear) / (zFar - zNear);
                return Result;
        }

        template <typename T>
        GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> infinitePerspective
        (
                T fovy,
                T aspect,
                T zNear
        )
        {
                T const range = tan(fovy / T(2)) * zNear;
                T const left = -range * aspect;
                T const right = range * aspect;
                T const bottom = -range;
                T const top = range;

                tmat4x4<T, defaultp> Result(T(0));
                Result[0][0] = (T(2) * zNear) / (right - left);
                Result[1][1] = (T(2) * zNear) / (top - bottom);
                Result[2][2] = - T(1);
                Result[2][3] = - T(1);
                Result[3][2] = - T(2) * zNear;
                return Result;
        }

        // Infinite projection matrix: http://www.terathon.com/gdc07_lengyel.pdf
        template <typename T>
        GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> tweakedInfinitePerspective
        (
                T fovy,
                T aspect,
                T zNear,
                T ep
        )
        {
                T const range = tan(fovy / T(2)) * zNear;       
                T const left = -range * aspect;
                T const right = range * aspect;
                T const bottom = -range;
                T const top = range;

                tmat4x4<T, defaultp> Result(T(0));
                Result[0][0] = (static_cast<T>(2) * zNear) / (right - left);
                Result[1][1] = (static_cast<T>(2) * zNear) / (top - bottom);
                Result[2][2] = ep - static_cast<T>(1);
                Result[2][3] = static_cast<T>(-1);
                Result[3][2] = (ep - static_cast<T>(2)) * zNear;
                return Result;
        }

        template <typename T>
        GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> tweakedInfinitePerspective
        (
                T fovy,
                T aspect,
                T zNear
        )
        {
                return tweakedInfinitePerspective(fovy, aspect, zNear, epsilon<T>());
        }

        template <typename T, typename U, precision P>
        GLM_FUNC_QUALIFIER tvec3<T, P> project
        (
                tvec3<T, P> const & obj,
                tmat4x4<T, P> const & model,
                tmat4x4<T, P> const & proj,
                tvec4<U, P> const & viewport
        )
        {
                tvec4<T, P> tmp = tvec4<T, P>(obj, T(1));
                tmp = model * tmp;
                tmp = proj * tmp;

                tmp /= tmp.w;
                tmp = tmp * T(0.5) + T(0.5);
                tmp[0] = tmp[0] * T(viewport[2]) + T(viewport[0]);
                tmp[1] = tmp[1] * T(viewport[3]) + T(viewport[1]);

                return tvec3<T, P>(tmp);
        }

        template <typename T, typename U, precision P>
        GLM_FUNC_QUALIFIER tvec3<T, P> unProject
        (
                tvec3<T, P> const & win,
                tmat4x4<T, P> const & model,
                tmat4x4<T, P> const & proj,
                tvec4<U, P> const & viewport
        )
        {
                tmat4x4<T, P> Inverse = inverse(proj * model);

                tvec4<T, P> tmp = tvec4<T, P>(win, T(1));
                tmp.x = (tmp.x - T(viewport[0])) / T(viewport[2]);
                tmp.y = (tmp.y - T(viewport[1])) / T(viewport[3]);
                tmp = tmp * T(2) - T(1);

                tvec4<T, P> obj = Inverse * tmp;
                obj /= obj.w;

                return tvec3<T, P>(obj);
        }

        template <typename T, precision P, typename U>
        GLM_FUNC_QUALIFIER tmat4x4<T, P> pickMatrix
        (
                tvec2<T, P> const & center,
                tvec2<T, P> const & delta,
                tvec4<U, P> const & viewport
        )
        {
                assert(delta.x > T(0) && delta.y > T(0));
                tmat4x4<T, P> Result(1.0f);

                if(!(delta.x > T(0) && delta.y > T(0)))
                        return Result; // Error

                tvec3<T, P> Temp(
                        (T(viewport[2]) - T(2) * (center.x - T(viewport[0]))) / delta.x,
                        (T(viewport[3]) - T(2) * (center.y - T(viewport[1]))) / delta.y,
                        T(0));

                // Translate and scale the picked region to the entire window
                Result = translate(Result, Temp);
                return scale(Result, tvec3<T, P>(T(viewport[2]) / delta.x, T(viewport[3]) / delta.y, T(1)));
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tmat4x4<T, P> lookAt
        (
                tvec3<T, P> const & eye,
                tvec3<T, P> const & center,
                tvec3<T, P> const & up
        )
        {
                tvec3<T, P> const f(normalize(center - eye));
                tvec3<T, P> const s(normalize(cross(f, up)));
                tvec3<T, P> const u(cross(s, f));

                tmat4x4<T, P> Result(1);
                Result[0][0] = s.x;
                Result[1][0] = s.y;
                Result[2][0] = s.z;
                Result[0][1] = u.x;
                Result[1][1] = u.y;
                Result[2][1] = u.z;
                Result[0][2] =-f.x;
                Result[1][2] =-f.y;
                Result[2][2] =-f.z;
                Result[3][0] =-dot(s, eye);
                Result[3][1] =-dot(u, eye);
                Result[3][2] = dot(f, eye);
                return Result;
        }
}//namespace glm