187 lines
6.3 KiB
Text
187 lines
6.3 KiB
Text
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/// @ref gtx_matrix_decompose
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#include "../gtc/constants.hpp"
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#include "../gtc/epsilon.hpp"
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namespace glm{
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namespace detail
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{
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/// Make a linear combination of two vectors and return the result.
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// result = (a * ascl) + (b * bscl)
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER vec<3, T, Q> combine(
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vec<3, T, Q> const& a,
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vec<3, T, Q> const& b,
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T ascl, T bscl)
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{
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return (a * ascl) + (b * bscl);
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER vec<3, T, Q> scale(vec<3, T, Q> const& v, T desiredLength)
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{
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return v * desiredLength / length(v);
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}
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}//namespace detail
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// Matrix decompose
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// http://www.opensource.apple.com/source/WebCore/WebCore-514/platform/graphics/transforms/TransformationMatrix.cpp
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// Decomposes the mode matrix to translations,rotation scale components
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template<typename T, qualifier Q>
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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)
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{
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mat<4, 4, T, Q> LocalMatrix(ModelMatrix);
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// Normalize the matrix.
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if(epsilonEqual(LocalMatrix[3][3], static_cast<T>(0), epsilon<T>()))
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return false;
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for(length_t i = 0; i < 4; ++i)
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for(length_t j = 0; j < 4; ++j)
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LocalMatrix[i][j] /= LocalMatrix[3][3];
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// perspectiveMatrix is used to solve for perspective, but it also provides
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// an easy way to test for singularity of the upper 3x3 component.
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mat<4, 4, T, Q> PerspectiveMatrix(LocalMatrix);
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for(length_t i = 0; i < 3; i++)
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PerspectiveMatrix[i][3] = static_cast<T>(0);
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PerspectiveMatrix[3][3] = static_cast<T>(1);
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/// TODO: Fixme!
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if(epsilonEqual(determinant(PerspectiveMatrix), static_cast<T>(0), epsilon<T>()))
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return false;
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// First, isolate perspective. This is the messiest.
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if(
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epsilonNotEqual(LocalMatrix[0][3], static_cast<T>(0), epsilon<T>()) ||
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epsilonNotEqual(LocalMatrix[1][3], static_cast<T>(0), epsilon<T>()) ||
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epsilonNotEqual(LocalMatrix[2][3], static_cast<T>(0), epsilon<T>()))
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{
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// rightHandSide is the right hand side of the equation.
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vec<4, T, Q> RightHandSide;
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RightHandSide[0] = LocalMatrix[0][3];
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RightHandSide[1] = LocalMatrix[1][3];
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RightHandSide[2] = LocalMatrix[2][3];
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RightHandSide[3] = LocalMatrix[3][3];
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// Solve the equation by inverting PerspectiveMatrix and multiplying
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// rightHandSide by the inverse. (This is the easiest way, not
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// necessarily the best.)
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mat<4, 4, T, Q> InversePerspectiveMatrix = glm::inverse(PerspectiveMatrix);// inverse(PerspectiveMatrix, inversePerspectiveMatrix);
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mat<4, 4, T, Q> TransposedInversePerspectiveMatrix = glm::transpose(InversePerspectiveMatrix);// transposeMatrix4(inversePerspectiveMatrix, transposedInversePerspectiveMatrix);
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Perspective = TransposedInversePerspectiveMatrix * RightHandSide;
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// v4MulPointByMatrix(rightHandSide, transposedInversePerspectiveMatrix, perspectivePoint);
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// Clear the perspective partition
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LocalMatrix[0][3] = LocalMatrix[1][3] = LocalMatrix[2][3] = static_cast<T>(0);
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LocalMatrix[3][3] = static_cast<T>(1);
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}
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else
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{
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// No perspective.
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Perspective = vec<4, T, Q>(0, 0, 0, 1);
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}
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// Next take care of translation (easy).
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Translation = vec<3, T, Q>(LocalMatrix[3]);
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LocalMatrix[3] = vec<4, T, Q>(0, 0, 0, LocalMatrix[3].w);
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vec<3, T, Q> Row[3], Pdum3;
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// Now get scale and shear.
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for(length_t i = 0; i < 3; ++i)
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for(length_t j = 0; j < 3; ++j)
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Row[i][j] = LocalMatrix[i][j];
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// Compute X scale factor and normalize first row.
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Scale.x = length(Row[0]);// v3Length(Row[0]);
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Row[0] = detail::scale(Row[0], static_cast<T>(1));
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// Compute XY shear factor and make 2nd row orthogonal to 1st.
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Skew.z = dot(Row[0], Row[1]);
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Row[1] = detail::combine(Row[1], Row[0], static_cast<T>(1), -Skew.z);
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// Now, compute Y scale and normalize 2nd row.
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Scale.y = length(Row[1]);
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Row[1] = detail::scale(Row[1], static_cast<T>(1));
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Skew.z /= Scale.y;
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// Compute XZ and YZ shears, orthogonalize 3rd row.
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Skew.y = glm::dot(Row[0], Row[2]);
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Row[2] = detail::combine(Row[2], Row[0], static_cast<T>(1), -Skew.y);
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Skew.x = glm::dot(Row[1], Row[2]);
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Row[2] = detail::combine(Row[2], Row[1], static_cast<T>(1), -Skew.x);
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// Next, get Z scale and normalize 3rd row.
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Scale.z = length(Row[2]);
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Row[2] = detail::scale(Row[2], static_cast<T>(1));
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Skew.y /= Scale.z;
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Skew.x /= Scale.z;
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// At this point, the matrix (in rows[]) is orthonormal.
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// Check for a coordinate system flip. If the determinant
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// is -1, then negate the matrix and the scaling factors.
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Pdum3 = cross(Row[1], Row[2]); // v3Cross(row[1], row[2], Pdum3);
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if(dot(Row[0], Pdum3) < 0)
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{
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for(length_t i = 0; i < 3; i++)
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{
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Scale[i] *= static_cast<T>(-1);
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Row[i] *= static_cast<T>(-1);
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}
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}
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// Now, get the rotations out, as described in the gem.
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// FIXME - Add the ability to return either quaternions (which are
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// easier to recompose with) or Euler angles (rx, ry, rz), which
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// are easier for authors to deal with. The latter will only be useful
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// when we fix https://bugs.webkit.org/show_bug.cgi?id=23799, so I
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// will leave the Euler angle code here for now.
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// ret.rotateY = asin(-Row[0][2]);
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// if (cos(ret.rotateY) != 0) {
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// ret.rotateX = atan2(Row[1][2], Row[2][2]);
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// ret.rotateZ = atan2(Row[0][1], Row[0][0]);
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// } else {
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// ret.rotateX = atan2(-Row[2][0], Row[1][1]);
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// ret.rotateZ = 0;
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// }
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int i, j, k = 0;
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float root, trace = Row[0].x + Row[1].y + Row[2].z;
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if(trace > static_cast<T>(0))
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{
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root = sqrt(trace + static_cast<T>(1.0));
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Orientation.w = static_cast<T>(0.5) * root;
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root = static_cast<T>(0.5) / root;
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Orientation.x = root * (Row[1].z - Row[2].y);
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Orientation.y = root * (Row[2].x - Row[0].z);
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Orientation.z = root * (Row[0].y - Row[1].x);
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} // End if > 0
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else
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{
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static int Next[3] = {1, 2, 0};
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i = 0;
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if(Row[1].y > Row[0].x) i = 1;
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if(Row[2].z > Row[i][i]) i = 2;
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j = Next[i];
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k = Next[j];
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root = sqrt(Row[i][i] - Row[j][j] - Row[k][k] + static_cast<T>(1.0));
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Orientation[i] = static_cast<T>(0.5) * root;
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root = static_cast<T>(0.5) / root;
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Orientation[j] = root * (Row[i][j] + Row[j][i]);
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Orientation[k] = root * (Row[i][k] + Row[k][i]);
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Orientation.w = root * (Row[j][k] - Row[k][j]);
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} // End if <= 0
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return true;
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}
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}//namespace glm
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