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Blender V4.3
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Blender V4.3
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Go to the source code of this file.
Classes | |
| class | btMatrix2x2 |
| class | GivensRotation |
Functions | |
| static btScalar | copySign (btScalar x, btScalar y) |
| void | zeroChase (btMatrix3x3 &H, btMatrix3x3 &U, btMatrix3x3 &V) |
| zero chasing the 3X3 matrix to bidiagonal form original form of H: x x 0 x x x 0 0 x after zero chase: x x 0 0 x x 0 0 x | |
| void | makeUpperBidiag (btMatrix3x3 &H, btMatrix3x3 &U, btMatrix3x3 &V) |
| make a 3X3 matrix to upper bidiagonal form original form of H: x x x x x x x x x after zero chase: x x 0 0 x x 0 0 x | |
| void | makeLambdaShape (btMatrix3x3 &H, btMatrix3x3 &U, btMatrix3x3 &V) |
| make a 3X3 matrix to lambda shape original form of H: x x x x x x x x x after : x 0 0 x x 0 x 0 x | |
| void | polarDecomposition (const btMatrix2x2 &A, GivensRotation &R, const btMatrix2x2 &S_Sym) |
| 2x2 polar decomposition. | |
| void | polarDecomposition (const btMatrix2x2 &A, const btMatrix2x2 &R, const btMatrix2x2 &S_Sym) |
| void | singularValueDecomposition (const btMatrix2x2 &A, GivensRotation &U, const btMatrix2x2 &Sigma, GivensRotation &V, const btScalar tol=64 *std::numeric_limits< btScalar >::epsilon()) |
| 2x2 SVD (singular value decomposition) A=USV' | |
| void | singularValueDecomposition (const btMatrix2x2 &A, const btMatrix2x2 &U, const btMatrix2x2 &Sigma, const btMatrix2x2 &V, const btScalar tol=64 *std::numeric_limits< btScalar >::epsilon()) |
| 2x2 SVD (singular value decomposition) A=USV' | |
| btScalar | wilkinsonShift (const btScalar a1, const btScalar b1, const btScalar a2) |
| compute wilkinsonShift of the block a1 b1 b1 a2 based on the wilkinsonShift formula mu = c + d - sign (d) \ sqrt (d*d + b*b), where d = (a-c)/2 | |
| template<int t> | |
| void | process (btMatrix3x3 &B, btMatrix3x3 &U, btVector3 &sigma, btMatrix3x3 &V) |
| Helper function of 3X3 SVD for processing 2X2 SVD. | |
| void | flipSign (int i, btMatrix3x3 &U, btVector3 &sigma) |
| Helper function of 3X3 SVD for flipping signs due to flipping signs of sigma. | |
| void | flipSign (int i, btMatrix3x3 &U) |
| void | swapCol (btMatrix3x3 &A, int i, int j) |
| void | sort (btMatrix3x3 &U, btVector3 &sigma, btMatrix3x3 &V, int t) |
| Helper function of 3X3 SVD for sorting singular values. | |
| int | singularValueDecomposition (const btMatrix3x3 &A, btMatrix3x3 &U, btVector3 &sigma, btMatrix3x3 &V, btScalar tol=128 *std::numeric_limits< btScalar >::epsilon()) |
| 3X3 SVD (singular value decomposition) A=USV' | |
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Definition at line 653 of file btImplicitQRSVD.h.
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Helper function of 3X3 SVD for flipping signs due to flipping signs of sigma.
Definition at line 645 of file btImplicitQRSVD.h.
Referenced by sort().
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make a 3X3 matrix to lambda shape original form of H: x x x x x x x x x after : x 0 0 x x 0 x 0 x
Reduce H to of form x x 0 x x x x x x
Reduce H to of form x x 0 x x 0 x x x
Reduce H to of form x x 0 x x 0 x 0 x
Reduce H to of form x 0 0 x x 0 x 0 x
Definition at line 372 of file btImplicitQRSVD.h.
References GivensRotation::columnRotation(), GivensRotation::computeUnconventional(), H, GivensRotation::rowRotation(), and V.
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make a 3X3 matrix to upper bidiagonal form original form of H: x x x x x x x x x after zero chase: x x 0 0 x x 0 0 x
Reduce H to of form x x x x x x 0 x x
Definition at line 342 of file btImplicitQRSVD.h.
References GivensRotation::columnRotation(), H, GivensRotation::rowRotation(), V, and zeroChase().
Referenced by singularValueDecomposition().
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Definition at line 453 of file btImplicitQRSVD.h.
References GivensRotation::fill(), polarDecomposition(), and R.
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2x2 polar decomposition.
| [in] | A | matrix. |
| [out] | R | Robustly a rotation matrix. |
| [out] | S_Sym | Symmetric. Whole matrix is stored |
Polar guarantees negative sign is on the small magnitude singular value. S is guaranteed to be the closest one to identity. R is guaranteed to be the closest rotation to A.
Definition at line 431 of file btImplicitQRSVD.h.
References A, b, btSqrt(), R, and SIMD_EPSILON.
Referenced by polarDecomposition(), and singularValueDecomposition().
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Helper function of 3X3 SVD for processing 2X2 SVD.
Definition at line 592 of file btImplicitQRSVD.h.
References B, GivensRotation::columnRotation(), btMatrix2x2::m_00, btMatrix2x2::m_01, btMatrix2x2::m_10, btMatrix2x2::m_11, GivensRotation::rowi, GivensRotation::rowk, singularValueDecomposition(), V, and v.
Referenced by add_cube(), addtovertices(), BKE_mball_polygonize(), build_bvh_spatial(), converge(), docube(), find_first_points(), freepolygonize(), init_meta(), make_face(), metaball(), polygonize(), setcenter(), setcorner(), setedge(), singularValueDecomposition(), and vertid().
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2x2 SVD (singular value decomposition) A=USV'
| [in] | A | Input matrix. |
| [out] | U | Robustly a rotation matrix. |
| [out] | Sigma | Vector of singular values sorted with decreasing magnitude. The second one can be negative. |
| [out] | V | Robustly a rotation matrix. |
Definition at line 549 of file btImplicitQRSVD.h.
References GivensRotation::fill(), singularValueDecomposition(), and V.
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2x2 SVD (singular value decomposition) A=USV'
| [in] | A | Input matrix. |
| [out] | U | Robustly a rotation matrix in Givens form |
| [out] | Sigma | matrix of singular values sorted with decreasing magnitude. The second one can be negative. |
| [out] | V | Robustly a rotation matrix in Givens form |
Definition at line 469 of file btImplicitQRSVD.h.
References btSqrt(), polarDecomposition(), btMatrix2x2::setIdentity(), SIMD_EPSILON, V, w(), x, y, and z().
Referenced by btDeformableLinearElasticityForce::addScaledElasticForce(), btDeformableNeoHookeanForce::addScaledElasticForce(), btSoftBody::getRigidTransform(), process(), and singularValueDecomposition().
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3X3 SVD (singular value decomposition) A=USV'
| [in] | A | Input matrix. |
| [out] | U | is a rotation matrix. |
| [out] | sigma | Diagonal matrix, sorted with decreasing magnitude. The third one can be negative. |
| [out] | V | is a rotation matrix. |
Do implicit shift QR until A^T A is block diagonal
Handle the cases of one of the alphas and betas being 0 Sorted by ease of handling and then frequency of occurrence
If B is of form x x 0 0 x 0 0 0 x
If B is of form x 0 0 0 x x 0 0 x
If B is of form x x 0 0 0 x 0 0 x
Reduce B to x x 0 0 0 0 0 0 x
If B is of form x x 0 0 x x 0 0 0
Reduce B to x x + 0 x 0 0 0 0
Reduce B to x x 0
If B is of form 0 x 0 0 x x 0 0 x
Reduce B to 0 0 + 0 x x 0 0 x
Reduce B to 0 0 0 0 x x 0 + x
Definition at line 750 of file btImplicitQRSVD.h.
References A, B, btFabs(), btMatrix3x3, btMax(), btSqrt(), GivensRotation::columnRotation(), GivensRotation::compute(), GivensRotation::computeUnconventional(), count, makeUpperBidiag(), process(), GivensRotation::rowRotation(), SIMD_EPSILON, sort(), V, wilkinsonShift(), and zeroChase().
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Helper function of 3X3 SVD for sorting singular values.
Definition at line 668 of file btImplicitQRSVD.h.
References btFabs(), flipSign(), swapCol(), and V.
Referenced by singularValueDecomposition().
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Definition at line 660 of file btImplicitQRSVD.h.
Referenced by sort().
compute wilkinsonShift of the block a1 b1 b1 a2 based on the wilkinsonShift formula mu = c + d - sign (d) \ sqrt (d*d + b*b), where d = (a-c)/2
Definition at line 572 of file btImplicitQRSVD.h.
References btFabs(), btSqrt(), copySign(), and SIMD_EPSILON.
Referenced by singularValueDecomposition().
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zero chasing the 3X3 matrix to bidiagonal form original form of H: x x 0 x x x 0 0 x after zero chase: x x 0 0 x x 0 0 x
Reduce H to of form x x + 0 x x 0 0 x
Reduce H to of form x x 0 0 x x 0 + x Can calculate r2 without multiplying by r1 since both entries are in first two rows thus no need to divide by sqrt(a^2+b^2)
Reduce H to of form x x 0 0 x x 0 0 x
Definition at line 286 of file btImplicitQRSVD.h.
References GivensRotation::columnRotation(), GivensRotation::compute(), H, GivensRotation::rowRotation(), and V.
Referenced by makeUpperBidiag(), and singularValueDecomposition().