/// @ref gtx_matrix_decompose
/// @file glm/gtx/matrix_decompose.inl
#include "../gtc/constants.hpp"
#include "../gtc/epsilon.hpp"
namespace glm{
namespace detail
{
/// Make a linear combination of two vectors and return the result.
// 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, tquat<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);
/// TODO: Fixme!
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;
float 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
