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129 lines
5.3 KiB
129 lines
5.3 KiB
// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2020 Oded Stein <oded.stein@columbia.edu>
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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_CURVED_HESSIAN_ENERGY_H
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#define IGL_CURVED_HESSIAN_ENERGY_H
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#include "igl_inline.h"
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#include <Eigen/Core>
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#include <Eigen/Sparse>
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namespace igl
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{
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/// Computes the curved Hessian energy using the Crouzeix-Raviart
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/// discretization.
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/// See Oded Stein, Alec Jacobson, Max Wardetzky, Eitan Grinspun, 2020.
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/// "A Smoothness Energy without Boundary Distortion for Curved Surfaces"
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///
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/// @param[in] V #V by 3 list of mesh vertex positions
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/// @param[in] F #F by 3 list of mesh faces (must be triangles)
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/// @param[out] Q #V by #V Hessian energy matrix
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template <typename DerivedV, typename DerivedF, typename ScalarQ>
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IGL_INLINE void
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curved_hessian_energy(
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const Eigen::MatrixBase<DerivedV>& V,
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const Eigen::MatrixBase<DerivedF>& F,
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Eigen::SparseMatrix<ScalarQ>& Q);
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/// Computes the curved Hessian energy using the Crouzeix-Raviart
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/// discretization.
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/// See Oded Stein, Alec Jacobson, Max Wardetzky, Eitan Grinspun, 2020.
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/// "A Smoothness Energy without Boundary Distortion for Curved Surfaces"
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///
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/// @param[in] V #V by 3 list of mesh vertex positions
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/// @param[in] F #F by 3 list of mesh faces (must be triangles)
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/// @param[in] E #F by 3 a mapping from each halfedge to each edge
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/// @param[in] oE #F by 3 the orientation (e.g., -1 or 1) of each halfedge
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/// @param[out] Q #V by #V Hessian energy matrix
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template <typename DerivedV, typename DerivedF, typename DerivedE,
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typename DerivedOE, typename ScalarQ>
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IGL_INLINE void
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curved_hessian_energy(
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const Eigen::MatrixBase<DerivedV>& V,
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const Eigen::MatrixBase<DerivedF>& F,
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const Eigen::MatrixBase<DerivedE>& E,
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const Eigen::MatrixBase<DerivedOE>& oE,
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Eigen::SparseMatrix<ScalarQ>& Q);
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/// Computes the curved Hessian energy using the Crouzeix-Raviart
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/// discretization.
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/// See Oded Stein, Alec Jacobson, Max Wardetzky, Eitan Grinspun, 2020.
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/// "A Smoothness Energy without Boundary Distortion for Curved Surfaces"
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///
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/// @param[in] V #V by 3 list of mesh vertex positions
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/// @param[in] F #F by 3 list of mesh faces (must be triangles)
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/// @param[out] E #F by 3 a mapping from each halfedge to each edge
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/// @param[out] oE #F by 3 the orientation (e.g., -1 or 1) of each halfedge
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/// @param[out] Q #V by #V Hessian energy matrix
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template <typename DerivedV, typename DerivedF, typename DerivedE,
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typename DerivedOE, typename ScalarQ>
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IGL_INLINE void
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curved_hessian_energy(
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const Eigen::MatrixBase<DerivedV>& V,
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const Eigen::MatrixBase<DerivedF>& F,
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Eigen::PlainObjectBase<DerivedE>& E,
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Eigen::PlainObjectBase<DerivedOE>& oE,
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Eigen::SparseMatrix<ScalarQ>& Q);
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/// Computes the curved Hessian energy using the Crouzeix-Raviart
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/// discretization.
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/// See Oded Stein, Alec Jacobson, Max Wardetzky, Eitan Grinspun, 2020.
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/// "A Smoothness Energy without Boundary Distortion for Curved Surfaces"
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///
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/// @param[in] F #F by 3 list of mesh face indices into rows of V
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/// @param[in] l_sq #F by 3 list of squared edge lengths of each halfedge
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/// @param[in] E #F by 3 a mapping from each halfedge to each edge
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/// @param[in] oE #F by 3 the orientation (e.g., -1 or 1) of each halfedge
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/// compared to the orientation of the actual edge, as computed with
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/// orient_halfedges. will be computed if not provided.
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/// @param[out] Q #V by #V Hessian energy matrix
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template <typename DerivedF, typename DerivedL_sq, typename DerivedE,
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typename DerivedOE, typename ScalarQ>
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IGL_INLINE void
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curved_hessian_energy_intrinsic(
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const Eigen::MatrixBase<DerivedF>& F,
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const Eigen::MatrixBase<DerivedL_sq>& l_sq,
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const Eigen::MatrixBase<DerivedE>& E,
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const Eigen::MatrixBase<DerivedOE>& oE,
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Eigen::SparseMatrix<ScalarQ>& Q);
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/// Computes the curved Hessian energy using the Crouzeix-Raviart
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/// discretization.
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/// See Oded Stein, Alec Jacobson, Max Wardetzky, Eitan Grinspun, 2020.
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/// "A Smoothness Energy without Boundary Distortion for Curved Surfaces"
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///
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/// @param[in] F #F by 3 list of mesh face indices into rows of V
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/// @param[in] l_sq #F by 3 list of squared edge lengths of each halfedge
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/// @param[in] dA #F list of double areas
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/// @param[in] E #F by 3 a mapping from each halfedge to each edge
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/// @param[in] oE #F by 3 the orientation (e.g., -1 or 1) of each halfedge
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/// compared to the orientation of the actual edge, as computed with
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/// orient_halfedges. will be computed if not provided.
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/// @param[out] Q #V by #V Hessian energy matrix
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template <typename DerivedF, typename DerivedL_sq, typename DeriveddA,
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typename DerivedE, typename DerivedOE, typename ScalarQ>
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IGL_INLINE void
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curved_hessian_energy_intrinsic(
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const Eigen::MatrixBase<DerivedF>& F,
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const Eigen::MatrixBase<DerivedL_sq>& l_sq,
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const Eigen::MatrixBase<DeriveddA>& dA,
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const Eigen::MatrixBase<DerivedE>& E,
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const Eigen::MatrixBase<DerivedOE>& oE,
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Eigen::SparseMatrix<ScalarQ>& Q);
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}
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#ifndef IGL_STATIC_LIBRARY
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# include "curved_hessian_energy.cpp"
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#endif
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#endif
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