///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
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/// @ref gtx_matrix_decompose
/// @file glm/gtx/matrix_decompose.inl
/// @date 2014-08-29 / 2014-08-29
/// @author Christophe Riccio
///////////////////////////////////////////////////////////////////////////////////

namespace glm
{
        /// Make a linear combination of two vectors and return the result.
        // result = (a * ascl) + (b * bscl)
        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tvec3<T, P> combine(
                tvec3<T, P> const & a, 
                tvec3<T, P> const & b,
                T ascl, T bscl)
        {
                return (a * ascl) + (b * bscl);
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER void v3Scale(tvec3<T, P> & v, T desiredLength)
        {
                T len = glm::length(v);
                if(len != 0)
                {
                        T l = desiredLength / len;
                        v[0] *= l;
                        v[1] *= l;
                        v[2] *= l;
                }
        }

        /**
        * Matrix decompose
        * http://www.opensource.apple.com/source/WebCore/WebCore-514/platform/graphics/transforms/TransformationMatrix.cpp
        * Decomposes the mode matrix to translations,rotation scale components
        * 
        */

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER bool decompose(tmat4x4<T, P> const & ModelMatrix, tvec3<T, P> & Scale, tquat<T, P> & Orientation, tvec3<T, P> & Translation, tvec3<T, P> & Skew, tvec4<T, P> & Perspective)
        {
                tmat4x4<T, P> LocalMatrix(ModelMatrix);

                // Normalize the matrix.
                if(LocalMatrix[3][3] == static_cast<T>(0))
                        return false;

                for(length_t i = 0; i < 4; ++i)
                for(length_t j = 0; j < 4; ++j)
                        LocalMatrix[i][j] /= LocalMatrix[3][3];

                // perspectiveMatrix is used to solve for perspective, but it also provides
                // an easy way to test for singularity of the upper 3x3 component.
                tmat4x4<T, P> PerspectiveMatrix(LocalMatrix);

                for(length_t i = 0; i < 3; i++)
                        PerspectiveMatrix[i][3] = 0;
                PerspectiveMatrix[3][3] = 1;

                /// TODO: Fixme!
                if(determinant(PerspectiveMatrix) == static_cast<T>(0))
                        return false;

                // First, isolate perspective.  This is the messiest.
                if(LocalMatrix[0][3] != 0 || LocalMatrix[1][3] != 0 || LocalMatrix[2][3] != 0)
                {
                        // rightHandSide is the right hand side of the equation.
                        tvec4<T, P> RightHandSide;
                        RightHandSide[0] = LocalMatrix[0][3];
                        RightHandSide[1] = LocalMatrix[1][3];
                        RightHandSide[2] = LocalMatrix[2][3];
                        RightHandSide[3] = LocalMatrix[3][3];

                        // Solve the equation by inverting PerspectiveMatrix and multiplying
                        // rightHandSide by the inverse.  (This is the easiest way, not
                        // necessarily the best.)
                        tmat4x4<T, P> InversePerspectiveMatrix = glm::inverse(PerspectiveMatrix);//   inverse(PerspectiveMatrix, inversePerspectiveMatrix);
                        tmat4x4<T, P> TransposedInversePerspectiveMatrix = glm::transpose(InversePerspectiveMatrix);//   transposeMatrix4(inversePerspectiveMatrix, transposedInversePerspectiveMatrix);

                        Perspective = TransposedInversePerspectiveMatrix * RightHandSide;
                        //  v4MulPointByMatrix(rightHandSide, transposedInversePerspectiveMatrix, perspectivePoint);

                        // Clear the perspective partition
                        LocalMatrix[0][3] = LocalMatrix[1][3] = LocalMatrix[2][3] = 0;
                        LocalMatrix[3][3] = 1;
                }
                else
                {
                        // No perspective.
                        Perspective = tvec4<T, P>(0, 0, 0, 1);
                }

                // Next take care of translation (easy).
                Translation = tvec3<T, P>(LocalMatrix[3]);
                LocalMatrix[3] = tvec4<T, P>(0, 0, 0, LocalMatrix[3].w);

                tvec3<T, P> Row[3], Pdum3;

                // Now get scale and shear.
                for(length_t i = 0; i < 3; ++i)
                        Row[i] = LocalMatrix[i];

                // Compute X scale factor and normalize first row.
                Scale.x = length(Row[0]);// v3Length(Row[0]);

                v3Scale(Row[0], 1.0);

                // Compute XY shear factor and make 2nd row orthogonal to 1st.
                Skew.z = dot(Row[0], Row[1]);
                Row[1] = combine(Row[1], Row[0], 1.0, -Skew.z);

                // Now, compute Y scale and normalize 2nd row.
                Scale.y = length(Row[1]);
                v3Scale(Row[1], 1.0);
                Skew.z /= Scale.y;

                // Compute XZ and YZ shears, orthogonalize 3rd row.
                Skew.y = glm::dot(Row[0], Row[2]);
                Row[2] = combine(Row[2], Row[0], 1.0, -Skew.y);
                Skew.x = glm::dot(Row[1], Row[2]);
                Row[2] = combine(Row[2], Row[1], 1.0, -Skew.x);

                // Next, get Z scale and normalize 3rd row.
                Scale.z = length(Row[2]);
                v3Scale(Row[2], 1.0);
                Skew.y /= Scale.z;
                Skew.x /= Scale.z;

                // At this point, the matrix (in rows[]) is orthonormal.
                // Check for a coordinate system flip.  If the determinant
                // is -1, then negate the matrix and the scaling factors.
                Pdum3 = cross(Row[1], Row[2]); // v3Cross(row[1], row[2], Pdum3);
                if(dot(Row[0], Pdum3) < 0)
                {
                        for(length_t i = 0; i < 3; i++)
                        {
                                Scale.x *= static_cast<T>(-1);
                                Row[i] *= static_cast<T>(-1);
                        }
                }

                // Now, get the rotations out, as described in the gem.

                // FIXME - Add the ability to return either quaternions (which are
                // easier to recompose with) or Euler angles (rx, ry, rz), which
                // are easier for authors to deal with. The latter will only be useful
                // when we fix https://bugs.webkit.org/show_bug.cgi?id=23799, so I
                // will leave the Euler angle code here for now.

                // ret.rotateY = asin(-Row[0][2]);
                // if (cos(ret.rotateY) != 0) {
                //     ret.rotateX = atan2(Row[1][2], Row[2][2]);
                //     ret.rotateZ = atan2(Row[0][1], Row[0][0]);
                // } else {
                //     ret.rotateX = atan2(-Row[2][0], Row[1][1]);
                //     ret.rotateZ = 0;
                // }

                T s, t, x, y, z, w;

                t = Row[0][0] + Row[1][1] + Row[2][2] + 1.0;

                if(t > 1e-4)
                {
                        s = 0.5 / sqrt(t);
                        w = 0.25 / s;
                        x = (Row[2][1] - Row[1][2]) * s;
                        y = (Row[0][2] - Row[2][0]) * s;
                        z = (Row[1][0] - Row[0][1]) * s;
                }
                else if(Row[0][0] > Row[1][1] && Row[0][0] > Row[2][2])
                { 
                        s = sqrt (1.0 + Row[0][0] - Row[1][1] - Row[2][2]) * 2.0; // S=4*qx 
                        x = 0.25 * s;
                        y = (Row[0][1] + Row[1][0]) / s; 
                        z = (Row[0][2] + Row[2][0]) / s; 
                        w = (Row[2][1] - Row[1][2]) / s;
                }
                else if(Row[1][1] > Row[2][2])
                { 
                        s = sqrt (1.0 + Row[1][1] - Row[0][0] - Row[2][2]) * 2.0; // S=4*qy
                        x = (Row[0][1] + Row[1][0]) / s; 
                        y = 0.25 * s;
                        z = (Row[1][2] + Row[2][1]) / s; 
                        w = (Row[0][2] - Row[2][0]) / s;
                }
                else
                { 
                        s = sqrt(1.0 + Row[2][2] - Row[0][0] - Row[1][1]) * 2.0; // S=4*qz
                        x = (Row[0][2] + Row[2][0]) / s;
                        y = (Row[1][2] + Row[2][1]) / s; 
                        z = 0.25 * s;
                        w = (Row[1][0] - Row[0][1]) / s;
                }

                Orientation.x = x;
                Orientation.y = y;
                Orientation.z = z;
                Orientation.w = w;

                return true;
        }
}//namespace glm