186 lines
6.3 KiB
C++
186 lines
6.3 KiB
C++
/// @ref gtx_matrix_decompose
|
|
|
|
#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, 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);
|
|
|
|
/// 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
|