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128 lines
3.9 KiB
128 lines
3.9 KiB
1 year ago
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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) 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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#ifndef IGL_PROCRUSTES_H
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#define IGL_PROCRUSTES_H
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#include "igl_inline.h"
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#include <Eigen/Dense>
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#include <Eigen/Geometry>
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namespace igl
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{
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/// Solve Procrustes problem in d dimensions. Given two point sets X,Y in R^d
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/// find best scale s, orthogonal R and translation t s.t. |s*X*R + t - Y|^2
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/// is minimized.
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///
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/// @tparam DerivedV point type
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/// @tparam Scalar scalar type
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/// @tparam DerivedR type of R
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/// @tparam DerivedT type of t
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/// @param[in] X #V by DIM first list of points
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/// @param[in] Y #V by DIM second list of points
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/// @param[in] includeScaling if scaling should be allowed
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/// @param[in] includeReflections if R is allowed to be a reflection
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/// @param[out] scale scaling
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/// @param[out] R orthogonal matrix
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/// @param[out] t translation
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///
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/// #### Example
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///
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/// \code{cpp}
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/// MatrixXd X, Y; (containing 3d points as rows)
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/// double scale;
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/// MatrixXd R;
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/// VectorXd t;
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/// igl::procrustes(X,Y,true,false,scale,R,t);
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/// R *= scale;
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/// MatrixXd Xprime = (X * R).rowwise() + t.transpose();
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/// \endcode
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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 DerivedR,
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typename DerivedT>
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IGL_INLINE void procrustes(
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const Eigen::MatrixBase<DerivedX>& X,
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const Eigen::MatrixBase<DerivedY>& Y,
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const bool includeScaling,
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const 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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/// \overload
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/// \brief Same as above but returns Eigen transformation object.
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///
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/// @param[out] T transformation that minimizes error
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///
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/// #### Example
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/// \code{cpp}
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/// MatrixXd X, Y; (containing 3d points as rows)
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/// AffineCompact3d T;
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/// igl::procrustes(X,Y,true,false,T);
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/// MatrixXd Xprime = (X * T.linear()).rowwise() + T.translation().transpose();
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/// \endcode
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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 procrustes(
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const Eigen::MatrixBase<DerivedX>& X,
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const Eigen::MatrixBase<DerivedY>& Y,
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const bool includeScaling,
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const bool includeReflections,
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Eigen::Transform<Scalar,DIM,TType>& T);
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/// \overload
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/// @param[out] S S=scale*R, instead of scale and R separately
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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 procrustes(
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const Eigen::MatrixBase<DerivedX>& X,
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const Eigen::MatrixBase<DerivedY>& Y,
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const bool includeScaling,
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const bool includeReflections,
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Eigen::PlainObjectBase<DerivedR>& S,
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Eigen::PlainObjectBase<DerivedT>& t);
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/// \overload
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/// \brief Convenient wrapper for rigid case (no scaling, no reflections)
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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 procrustes(
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const Eigen::MatrixBase<DerivedX>& X,
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const Eigen::MatrixBase<DerivedY>& Y,
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Eigen::PlainObjectBase<DerivedR>& R,
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Eigen::PlainObjectBase<DerivedT>& t);
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/// \overload
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/// \brief Convenient wrapper for 2D case.
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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 procrustes(
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const Eigen::MatrixBase<DerivedX>& X,
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const Eigen::MatrixBase<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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#ifndef IGL_STATIC_LIBRARY
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#include "procrustes.cpp"
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#endif
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#endif
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