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43 lines
1.5 KiB
C++
43 lines
1.5 KiB
C++
// 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_POLAR_SVD3X3_H
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#define IGL_POLAR_SVD3X3_H
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#include <Eigen/Core>
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#include "igl_inline.h"
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namespace igl
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{
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// Computes the closest rotation to input matrix A using specialized 3x3 SVD
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// singular value decomposition (WunderSVD3x3)
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//
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// Inputs:
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// A 3 by 3 matrix to be decomposed
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// Outputs:
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// R 3 by 3 closest element in SO(3) (closeness in terms of Frobenius
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// metric)
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//
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// This means that det(R) = 1. Technically it's not polar decomposition
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// which guarantees positive semidefinite stretch factor (at the cost of
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// having det(R) = -1). "• The orthogonal factors U and V will be true
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// rotation matrices..." [McAdams, Selle, Tamstorf, Teran, Sefakis 2011]
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//
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template<typename Mat>
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IGL_INLINE void polar_svd3x3(const Mat& A, Mat& R);
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#ifdef __SSE__
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template<typename T>
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IGL_INLINE void polar_svd3x3_sse(const Eigen::Matrix<T, 3*4, 3>& A, Eigen::Matrix<T, 3*4, 3> &R);
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#endif
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#ifdef __AVX__
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template<typename T>
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IGL_INLINE void polar_svd3x3_avx(const Eigen::Matrix<T, 3*8, 3>& A, Eigen::Matrix<T, 3*8, 3> &R);
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#endif
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}
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#ifndef IGL_STATIC_LIBRARY
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# include "polar_svd3x3.cpp"
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#endif
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#endif
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