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/// OpenGL Mathematics (glm.g-truc.net)
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/// @ref gtx_matrix_interpolation
/// @file glm/gtx/matrix_interpolation.hpp
/// @date 2011-03-05 / 2011-03-05
/// @author Christophe Riccio
///////////////////////////////////////////////////////////////////////////////////

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

                if((abs(mat[1][0] - mat[0][1]) < epsilon) && (abs(mat[2][0] - mat[0][2]) < epsilon) && (abs(mat[2][1] - mat[1][2]) < epsilon))
                {
                        if ((abs(mat[1][0] + mat[0][1]) < epsilon2) && (abs(mat[2][0] + mat[0][2]) < epsilon2) && (abs(mat[2][1] + mat[1][2]) < epsilon2) && (abs(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 = static_cast<T>(3.1415926535897932384626433832795);
                        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, precision P>
        GLM_FUNC_QUALIFIER tmat4x4<T, P> axisAngleMatrix
        (
                tvec3<T, P> const & axis,
                T const angle
        )
        {
                T c = cos(angle);
                T s = sin(angle);
                T t = static_cast<T>(1) - c;
                tvec3<T, P> n = normalize(axis);

                return tmat4x4<T, P>(
                        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, precision P>
        GLM_FUNC_QUALIFIER tmat4x4<T, P> extractMatrixRotation
        (
                tmat4x4<T, P> const & mat
        )
        {
                return tmat4x4<T, P>(
                        mat[0][0], mat[0][1], mat[0][2], 0.0,
                        mat[1][0], mat[1][1], mat[1][2], 0.0,
                        mat[2][0], mat[2][1], mat[2][2], 0.0,
                        0.0,       0.0,       0.0,       1.0
                );
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tmat4x4<T, P> interpolate
        (
                tmat4x4<T, P> const & m1,
                tmat4x4<T, P> const & m2,
                T const delta
        )
        {
                tmat4x4<T, P> m1rot = extractMatrixRotation(m1);
                tmat4x4<T, P> dltRotation = m2 * transpose(m1rot);
                tvec3<T, P> dltAxis;
                T dltAngle;
                axisAngle(dltRotation, dltAxis, dltAngle);
                tmat4x4<T, P> out = axisAngleMatrix(dltAxis, dltAngle * delta) * m1rot;
                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 glm