/usr/include/glm/gtx/matrix_decompose.inl is in libglm-dev 0.9.8.3-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 | /// @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.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] + 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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