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/// @ref gtx_matrix_decompose
/// @file glm/gtx/matrix_decompose.inl
namespace glm{
namespace detail
{
/// 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 tvec3<T, P> scale(tvec3<T, P> 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, 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] = static_cast<T>(0);
PerspectiveMatrix[3][3] = static_cast<T>(1);
/// TODO: Fixme!
if(determinant(PerspectiveMatrix) == static_cast<T>(0))
return false;
// First, isolate perspective. This is the messiest.
if(LocalMatrix[0][3] != static_cast<T>(0) || LocalMatrix[1][3] != static_cast<T>(0) || LocalMatrix[2][3] != static_cast<T>(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] = static_cast<T>(0);
LocalMatrix[3][3] = static_cast<T>(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)
for(int 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;
// }
T s, t, x, y, z, w;
t = Row[0][0] + Row[1][1] + Row[2][2] + static_cast<T>(1);
if(t > static_cast<T>(1e-4))
{
s = static_cast<T>(0.5) / sqrt(t);
w = static_cast<T>(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 (static_cast<T>(1) + Row[0][0] - Row[1][1] - Row[2][2]) * static_cast<T>(2); // S=4*qx
x = static_cast<T>(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 (static_cast<T>(1) + Row[1][1] - Row[0][0] - Row[2][2]) * static_cast<T>(2); // S=4*qy
x = (Row[0][1] + Row[1][0]) / s;
y = static_cast<T>(0.25) * s;
z = (Row[1][2] + Row[2][1]) / s;
w = (Row[0][2] - Row[2][0]) / s;
}
else
{
s = sqrt(static_cast<T>(1) + Row[2][2] - Row[0][0] - Row[1][1]) * static_cast<T>(2); // S=4*qz
x = (Row[0][2] + Row[2][0]) / s;
y = (Row[1][2] + Row[2][1]) / s;
z = static_cast<T>(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
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