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140 lines
3.9 KiB
C++
140 lines
3.9 KiB
C++
// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2014 Stefan Brugger <stefanbrugger@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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#include "procrustes.h"
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#include "polar_svd.h"
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#include "polar_dec.h"
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template <
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typename DerivedX,
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typename DerivedY,
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typename Scalar,
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typename DerivedR,
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typename DerivedT>
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IGL_INLINE void igl::procrustes(
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const Eigen::PlainObjectBase<DerivedX>& X,
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const Eigen::PlainObjectBase<DerivedY>& Y,
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bool includeScaling,
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bool includeReflections,
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Scalar& scale,
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Eigen::PlainObjectBase<DerivedR>& R,
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Eigen::PlainObjectBase<DerivedT>& t)
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{
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using namespace Eigen;
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assert (X.rows() == Y.rows() && "Same number of points");
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assert(X.cols() == Y.cols() && "Points have same dimensions");
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// Center data
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const VectorXd Xmean = X.colwise().mean();
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const VectorXd Ymean = Y.colwise().mean();
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MatrixXd XC = X.rowwise() - Xmean.transpose();
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MatrixXd YC = Y.rowwise() - Ymean.transpose();
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// Scale
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scale = 1.;
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if (includeScaling)
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{
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double scaleX = XC.norm() / XC.rows();
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double scaleY = YC.norm() / YC.rows();
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scale = scaleY/scaleX;
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XC *= scale;
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assert (std::abs(XC.norm() / XC.rows() - scaleY) < 1e-8);
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}
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// Rotation
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MatrixXd S = XC.transpose() * YC;
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MatrixXd T;
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if (includeReflections)
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{
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polar_dec(S,R,T);
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}else
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{
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polar_svd(S,R,T);
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}
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// R.transposeInPlace();
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// Translation
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t = Ymean - scale*R.transpose()*Xmean;
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}
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template <
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typename DerivedX,
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typename DerivedY,
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typename Scalar,
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int DIM,
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int TType>
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IGL_INLINE void igl::procrustes(
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const Eigen::PlainObjectBase<DerivedX>& X,
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const Eigen::PlainObjectBase<DerivedY>& Y,
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bool includeScaling,
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bool includeReflections,
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Eigen::Transform<Scalar,DIM,TType>& T)
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{
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using namespace Eigen;
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double scale;
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MatrixXd R;
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VectorXd t;
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procrustes(X,Y,includeScaling,includeReflections,scale,R,t);
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// Combine
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T = Translation<Scalar,DIM>(t) * R * Scaling(scale);
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}
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template <
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typename DerivedX,
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typename DerivedY,
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typename DerivedR,
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typename DerivedT>
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IGL_INLINE void igl::procrustes(
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const Eigen::PlainObjectBase<DerivedX>& X,
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const Eigen::PlainObjectBase<DerivedY>& Y,
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bool includeScaling,
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bool includeReflections,
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Eigen::PlainObjectBase<DerivedR>& S,
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Eigen::PlainObjectBase<DerivedT>& t)
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{
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double scale;
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procrustes(X,Y,includeScaling,includeReflections,scale,S,t);
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S *= scale;
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}
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template <
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typename DerivedX,
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typename DerivedY,
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typename DerivedR,
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typename DerivedT>
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IGL_INLINE void igl::procrustes(
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const Eigen::PlainObjectBase<DerivedX>& X,
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const Eigen::PlainObjectBase<DerivedY>& Y,
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Eigen::PlainObjectBase<DerivedR>& R,
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Eigen::PlainObjectBase<DerivedT>& t)
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{
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procrustes(X,Y,false,false,R,t);
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}
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template <
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typename DerivedX,
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typename DerivedY,
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typename Scalar,
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typename DerivedT>
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IGL_INLINE void igl::procrustes(
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const Eigen::PlainObjectBase<DerivedX>& X,
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const Eigen::PlainObjectBase<DerivedY>& Y,
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Eigen::Rotation2D<Scalar>& R,
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Eigen::PlainObjectBase<DerivedT>& t)
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{
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using namespace Eigen;
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assert (X.cols() == 2 && Y.cols() == 2 && "Points must have dimension 2");
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Matrix2d Rmat;
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procrustes(X,Y,false,false,Rmat,t);
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R.fromRotationMatrix(Rmat);
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}
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#ifdef IGL_STATIC_LIBRARY
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template void igl::procrustes<Eigen::Matrix<double, 3, 2, 0, 3, 2>, Eigen::Matrix<double, 3, 2, 0, 3, 2>, double, Eigen::Matrix<double, 2, 2, 0, 2, 2>, Eigen::Matrix<double, 2, 1, 0, 2, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, 3, 2, 0, 3, 2> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, 3, 2, 0, 3, 2> > const&, bool, bool, double&, Eigen::PlainObjectBase<Eigen::Matrix<double, 2, 2, 0, 2, 2> >&, Eigen::PlainObjectBase<Eigen::Matrix<double, 2, 1, 0, 2, 1> >&);
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#endif
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