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82 lines
2.9 KiB
82 lines
2.9 KiB
// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2014 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_COTMATRIX_H
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#define IGL_COTMATRIX_H
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#include "igl_inline.h"
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#include <Eigen/Dense>
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#include <Eigen/Sparse>
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// History:
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// Used const references rather than copying the entire mesh
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// Alec 9 October 2011
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// removed cotan (uniform weights) optional parameter it was building a buggy
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// half of the uniform laplacian, please see adjacency_matrix instead
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// Alec 9 October 2011
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namespace igl
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{
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// Constructs the cotangent stiffness matrix (discrete laplacian) for a given
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// mesh (V,F).
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//
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// Templates:
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// DerivedV derived type of eigen matrix for V (e.g. derived from
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// MatrixXd)
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// DerivedF derived type of eigen matrix for F (e.g. derived from
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// MatrixXi)
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// Scalar scalar type for eigen sparse matrix (e.g. double)
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// Inputs:
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// V #V by dim list of mesh vertex positions
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// F #F by simplex_size list of mesh elements (triangles or tetrahedra)
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// Outputs:
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// L #V by #V cotangent matrix, each row i corresponding to V(i,:)
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//
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// See also: adjacency_matrix
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//
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// Note: This Laplacian uses the convention that diagonal entries are
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// **minus** the sum of off-diagonal entries. The diagonal entries are
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// therefore in general negative and the matrix is **negative** semi-definite
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// (immediately, -L is **positive** semi-definite)
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//
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template <typename DerivedV, typename DerivedF, typename Scalar>
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IGL_INLINE void cotmatrix(
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const Eigen::MatrixBase<DerivedV> & V,
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const Eigen::MatrixBase<DerivedF> & F,
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Eigen::SparseMatrix<Scalar>& L);
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// Cotangent Laplacian (and mass matrix) for polygon meshes according to
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// "Polygon Laplacian Made Simple" [Bunge et al. 2020]
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//
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// Inputs:
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// V #V by 3 list of mesh vertex positions
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// I #I vectorized list of polygon corner indices into rows of some matrix V
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// C #polygons+1 list of cumulative polygon sizes so that C(i+1)-C(i) = size of
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// the ith polygon, and so I(C(i)) through I(C(i+1)-1) are the indices of
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// the ith polygon
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// Outputs:
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// L #V by #V polygon Laplacian made simple matrix
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// M #V by #V mass matrix
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// P #V+#polygons by #V prolongation operator
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template <
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typename DerivedV,
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typename DerivedI,
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typename DerivedC,
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typename Scalar>
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IGL_INLINE void cotmatrix(
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const Eigen::MatrixBase<DerivedV> & V,
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const Eigen::MatrixBase<DerivedI> & I,
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const Eigen::MatrixBase<DerivedC> & C,
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Eigen::SparseMatrix<Scalar>& L,
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Eigen::SparseMatrix<Scalar>& M,
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Eigen::SparseMatrix<Scalar>& P);
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}
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#ifndef IGL_STATIC_LIBRARY
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# include "cotmatrix.cpp"
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#endif
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#endif
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