41 lines
1.4 KiB
C
41 lines
1.4 KiB
C
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// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla Public License
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// v. 2.0. If a copy of the MPL was not distributed with this file, You can
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// obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef IGL_SVD3X3_H
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#define IGL_SVD3X3_H
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#include "igl_inline.h"
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#include <Eigen/Dense>
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namespace igl
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{
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// Super fast 3x3 SVD according to http://pages.cs.wisc.edu/~sifakis/project_pages/svd.html
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// The resulting decomposition is A = U * diag(S[0], S[1], S[2]) * V'
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// BEWARE: this SVD algorithm guarantees that det(U) = det(V) = 1, but this
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// comes at the cost that 'sigma3' can be negative
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// for computing polar decomposition it's great because all we need to do is U*V'
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// and the result will automatically have positive determinant
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//
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// Inputs:
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// A 3x3 matrix
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// Outputs:
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// U 3x3 left singular vectors
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// S 3x1 singular values
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// V 3x3 right singular vectors
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//
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// Known bugs: this will not work correctly for double precision.
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template<typename T>
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IGL_INLINE void svd3x3(
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const Eigen::Matrix<T, 3, 3>& A,
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Eigen::Matrix<T, 3, 3> &U,
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Eigen::Matrix<T, 3, 1> &S,
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Eigen::Matrix<T, 3, 3>&V);
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}
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#ifndef IGL_STATIC_LIBRARY
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# include "svd3x3.cpp"
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#endif
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#endif
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