///////////////////////////////////////////////////////////////////////////////////////////////////
// OpenGL Mathematics Copyright (c) 2005 - 2011 G-Truc Creation (www.g-truc.net)
///////////////////////////////////////////////////////////////////////////////////////////////////
// Created : 2011-03-05
// Updated : 2011-03-05
// Licence : This source is under MIT License
// File    : glm/gtx/matrix_interpolation.inl
///////////////////////////////////////////////////////////////////////////////////////////////////

namespace glm{
namespace gtx{
namespace matrix_interpolation
{
    template <typename T>
    GLM_FUNC_QUALIFIER void axisAngle(
        detail::tmat4x4<T> const & mat,
        detail::tvec3<T> & axis,
        T & angle)
    {
        T epsilon = (T)0.01;
        T epsilon2 = (T)0.1;

        if ((fabs(mat[1][0] - mat[0][1]) < epsilon) && (fabs(mat[2][0] - mat[0][2]) < epsilon) && (fabs(mat[2][1] - mat[1][2]) < epsilon)) {
            if ((fabs(mat[1][0] + mat[0][1]) < epsilon2) && (fabs(mat[2][0] + mat[0][2]) < epsilon2) && (fabs(mat[2][1] + mat[1][2]) < epsilon2) && (fabs(mat[0][0] + mat[1][1] + mat[2][2] - (T)3.0) < epsilon2)) {
                angle = (T)0.0;
                axis.x = (T)1.0;
                axis.y = (T)0.0;
                axis.z = (T)0.0;
                return;
            }
            angle = M_1_PI;
            T xx = (mat[0][0] + (T)1.0) / (T)2.0;
            T yy = (mat[1][1] + (T)1.0) / (T)2.0;
            T zz = (mat[2][2] + (T)1.0) / (T)2.0;
            T xy = (mat[1][0] + mat[0][1]) / (T)4.0;
            T xz = (mat[2][0] + mat[0][2]) / (T)4.0;
            T yz = (mat[2][1] + mat[1][2]) / (T)4.0;
            if ((xx > yy) && (xx > zz)) {
                if (xx < epsilon) {
                    axis.x = (T)0.0;
                    axis.y = (T)0.7071;
                    axis.z = (T)0.7071;
                } else {
                    axis.x = sqrt(xx);
                    axis.y = xy / axis.x;
                    axis.z = xz / axis.x;
                }
            } else if (yy > zz) {
                if (yy < epsilon) {
                    axis.x = (T)0.7071;
                    axis.y = (T)0.0;
                    axis.z = (T)0.7071;
                } else {
                    axis.y = sqrt(yy);
                    axis.x = xy / axis.y;
                    axis.z = yz / axis.y;
                }
            } else {
                if (zz < epsilon) {
                    axis.x = (T)0.7071;
                    axis.y = (T)0.7071;
                    axis.z = (T)0.0;
                } else {
                    axis.z = sqrt(zz);
                    axis.x = xz / axis.z;
                    axis.y = yz / axis.z;
                }
            }
            return;
        }
        T s = sqrt((mat[2][1] - mat[1][2]) * (mat[2][1] - mat[1][2]) + (mat[2][0] - mat[0][2]) * (mat[2][0] - mat[0][2]) + (mat[1][0] - mat[0][1]) * (mat[1][0] - mat[0][1]));
        if (glm::abs(s) < T(0.001))
            s = (T)1.0;
        angle = acos((mat[0][0] + mat[1][1] + mat[2][2] - (T)1.0) / (T)2.0);
        axis.x = (mat[1][2] - mat[2][1]) / s;
        axis.y = (mat[2][0] - mat[0][2]) / s;
        axis.z = (mat[0][1] - mat[1][0]) / s;
    }

    template <typename T>
    GLM_FUNC_QUALIFIER detail::tmat4x4<T> axisAngleMatrix(
		detail::tvec3<T> const & axis,
		T const angle)
    {
        T c = cos(angle);
        T s = sin(angle);
        T t = T(1) - c;
        detail::tvec3<T> n = normalize(axis);

        return detail::tmat4x4<T>(
            t * n.x * n.x + c,          t * n.x * n.y + n.z * s,    t * n.x * n.z - n.y * s,    T(0),
            t * n.x * n.y - n.z * s,    t * n.y * n.y + c,          t * n.y * n.z + n.x * s,    T(0),
            t * n.x * n.z + n.y * s,    t * n.y * n.z - n.x * s,    t * n.z * n.z + c,          T(0),
            T(0),                        T(0),                        T(0),                     T(1)
        );
    }

    template <typename T>
    GLM_FUNC_QUALIFIER detail::tmat4x4<T> interpolate(
		detail::tmat4x4<T> const & m1,
		detail::tmat4x4<T> const & m2,
		T const delta)
    {
		detail::tmat4x4<T> dltRotation = m2 * transpose(m1);
		detail::tvec3<T> dltAxis;
		T dltAngle;
		axisAngle(dltRotation, dltAxis, dltAngle);
		detail::tmat4x4<T> out = axisAngleMatrix(dltAxis, dltAngle * delta) * rotationMatrix(m1);
		out[3][0] = m1[3][0] + delta * (m2[3][0] - m1[3][0]);
		out[3][1] = m1[3][1] + delta * (m2[3][1] - m1[3][1]);
		out[3][2] = m1[3][2] + delta * (m2[3][2] - m1[3][2]);
		return out;
    }

}//namespace transform
}//namespace gtx
}//namespace glm