matrix_decompose.inl

 
 
#include "../gtc/constants.hpp"
#include "../gtc/epsilon.hpp"
 
namespace glm{
namespace detail
{
    // result = (a * ascl) + (b * bscl)
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER vec<3, T, Q> combine(
        vec<3, T, Q> const& a,
        vec<3, T, Q> const& b,
        T ascl, T bscl)
    {
        return (a * ascl) + (b * bscl);
    }
 
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER vec<3, T, Q> scale(vec<3, T, Q> const& v, T desiredLength)
    {
        return v * desiredLength / length(v);
    }
}//namespace detail
 
    // 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, qualifier Q>
    GLM_FUNC_QUALIFIER bool decompose(mat<4, 4, T, Q> const& ModelMatrix, vec<3, T, Q> & Scale, qua<T, Q> & Orientation, vec<3, T, Q> & Translation, vec<3, T, Q> & Skew, vec<4, T, Q> & Perspective)
    {
        mat<4, 4, T, Q> LocalMatrix(ModelMatrix);
 
        // Normalize the matrix.
        if(epsilonEqual(LocalMatrix[3][3], static_cast<T>(0), epsilon<T>()))
            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.
        mat<4, 4, T, Q> PerspectiveMatrix(LocalMatrix);
 
        for(length_t i = 0; i < 3; i++)
            PerspectiveMatrix[i][3] = static_cast<T>(0);
        PerspectiveMatrix[3][3] = static_cast<T>(1);
 
        if(epsilonEqual(determinant(PerspectiveMatrix), static_cast<T>(0), epsilon<T>()))
            return false;
 
        // First, isolate perspective.  This is the messiest.
        if(
            epsilonNotEqual(LocalMatrix[0][3], static_cast<T>(0), epsilon<T>()) ||
            epsilonNotEqual(LocalMatrix[1][3], static_cast<T>(0), epsilon<T>()) ||
            epsilonNotEqual(LocalMatrix[2][3], static_cast<T>(0), epsilon<T>()))
        {
            // rightHandSide is the right hand side of the equation.
            vec<4, T, Q> 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.)
            mat<4, 4, T, Q> InversePerspectiveMatrix = glm::inverse(PerspectiveMatrix);//   inverse(PerspectiveMatrix, inversePerspectiveMatrix);
            mat<4, 4, T, Q> 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] = static_cast<T>(0);
            LocalMatrix[3][3] = static_cast<T>(1);
        }
        else
        {
            // No perspective.
            Perspective = vec<4, T, Q>(0, 0, 0, 1);
        }
 
        // Next take care of translation (easy).
        Translation = vec<3, T, Q>(LocalMatrix[3]);
        LocalMatrix[3] = vec<4, T, Q>(0, 0, 0, LocalMatrix[3].w);
 
        vec<3, T, Q> Row[3], Pdum3;
 
        // Now get scale and shear.
        for(length_t i = 0; i < 3; ++i)
        for(length_t j = 0; j < 3; ++j)
            Row[i][j] = LocalMatrix[i][j];
 
        // Compute X scale factor and normalize first row.
        Scale.x = length(Row[0]);// v3Length(Row[0]);
 
        Row[0] = detail::scale(Row[0], static_cast<T>(1));
 
        // Compute XY shear factor and make 2nd row orthogonal to 1st.
        Skew.z = dot(Row[0], Row[1]);
        Row[1] = detail::combine(Row[1], Row[0], static_cast<T>(1), -Skew.z);
 
        // Now, compute Y scale and normalize 2nd row.
        Scale.y = length(Row[1]);
        Row[1] = detail::scale(Row[1], static_cast<T>(1));
        Skew.z /= Scale.y;
 
        // Compute XZ and YZ shears, orthogonalize 3rd row.
        Skew.y = glm::dot(Row[0], Row[2]);
        Row[2] = detail::combine(Row[2], Row[0], static_cast<T>(1), -Skew.y);
        Skew.x = glm::dot(Row[1], Row[2]);
        Row[2] = detail::combine(Row[2], Row[1], static_cast<T>(1), -Skew.x);
 
        // Next, get Z scale and normalize 3rd row.
        Scale.z = length(Row[2]);
        Row[2] = detail::scale(Row[2], static_cast<T>(1));
        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[i] *= 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;
        // }
 
        int i, j, k = 0;
        T root, trace = Row[0].x + Row[1].y + Row[2].z;
        if(trace > static_cast<T>(0))
        {
            root = sqrt(trace + static_cast<T>(1.0));
            Orientation.w = static_cast<T>(0.5) * root;
            root = static_cast<T>(0.5) / root;
            Orientation.x = root * (Row[1].z - Row[2].y);
            Orientation.y = root * (Row[2].x - Row[0].z);
            Orientation.z = root * (Row[0].y - Row[1].x);
        } // End if > 0
        else
        {
            static int Next[3] = {1, 2, 0};
            i = 0;
            if(Row[1].y > Row[0].x) i = 1;
            if(Row[2].z > Row[i][i]) i = 2;
            j = Next[i];
            k = Next[j];
 
            root = sqrt(Row[i][i] - Row[j][j] - Row[k][k] + static_cast<T>(1.0));
 
            Orientation[i] = static_cast<T>(0.5) * root;
            root = static_cast<T>(0.5) / root;
            Orientation[j] = root * (Row[i][j] + Row[j][i]);
            Orientation[k] = root * (Row[i][k] + Row[k][i]);
            Orientation.w = root * (Row[j][k] - Row[k][j]);
        } // End if <= 0
 
        return true;
    }
}//namespace glm