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114 lines
3.6 KiB
114 lines
3.6 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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// Inputs:
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// V, F: input mesh
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//
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// Outputs:
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// Q: computed 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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// Version that exposes the edge orientation used.
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//
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// Inputs:
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// V, F: input mesh
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// E: a mapping from each halfedge to each edge, as computed with
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// orient_halfedges.
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// will be computed if not provided.
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// oE: the orientation of each halfedge compared to the orientation of the
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// actual edge, as computed with orient_halfedges.
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// will be computed if not provided.
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//
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// Outputs:
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// Q: computed Hessian energy matrix
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// E, oE: these are computed if they are not present, as described above
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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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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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// Version that uses intrinsic quantities as input
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//
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// Inputs:
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// F: input mesh connectivity
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// l_sq: squared edge lengths of each halfedge
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// dA: double area of each face
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// E: a mapping from each halfedge to each edge.
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// oE: the orientation of each halfedge compared to the orientation of the
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// actual edge.
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//
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// Outputs:
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// Q: computed 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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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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