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// This file is part of libigl, a simple c++ geometry processing library.
//
// Copyright (C) 2014 Alec Jacobson <alecjacobson@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla Public License
// v. 2.0. If a copy of the MPL was not distributed with this file, You can
// obtain one at http://mozilla.org/MPL/2.0/.
#ifndef IGL_COTMATRIX_H
#define IGL_COTMATRIX_H
#include "igl_inline.h"
#include <Eigen/Dense>
#include <Eigen/Sparse>
// History:
// Used const references rather than copying the entire mesh
// Alec 9 October 2011
// removed cotan (uniform weights) optional parameter it was building a buggy
// half of the uniform laplacian, please see adjacency_matrix instead
// Alec 9 October 2011
namespace igl
{
// Constructs the cotangent stiffness matrix (discrete laplacian) for a given
// mesh (V,F).
//
// Templates:
// DerivedV derived type of eigen matrix for V (e.g. derived from
// MatrixXd)
// DerivedF derived type of eigen matrix for F (e.g. derived from
// MatrixXi)
// Scalar scalar type for eigen sparse matrix (e.g. double)
// Inputs:
// V #V by dim list of mesh vertex positions
// F #F by simplex_size list of mesh elements (triangles or tetrahedra)
// Outputs:
// L #V by #V cotangent matrix, each row i corresponding to V(i,:)
//
// See also: adjacency_matrix
//
// Note: This Laplacian uses the convention that diagonal entries are
// **minus** the sum of off-diagonal entries. The diagonal entries are
// therefore in general negative and the matrix is **negative** semi-definite
// (immediately, -L is **positive** semi-definite)
//
template <typename DerivedV, typename DerivedF, typename Scalar>
IGL_INLINE void cotmatrix(
const Eigen::MatrixBase<DerivedV> & V,
const Eigen::MatrixBase<DerivedF> & F,
Eigen::SparseMatrix<Scalar>& L);
// Cotangent Laplacian (and mass matrix) for polygon meshes according to
// "Polygon Laplacian Made Simple" [Bunge et al. 2020]
//
// Inputs:
// V #V by 3 list of mesh vertex positions
// I #I vectorized list of polygon corner indices into rows of some matrix V
// C #polygons+1 list of cumulative polygon sizes so that C(i+1)-C(i) = size of
// the ith polygon, and so I(C(i)) through I(C(i+1)-1) are the indices of
// the ith polygon
// Outputs:
// L #V by #V polygon Laplacian made simple matrix
// M #V by #V mass matrix
// P #V+#polygons by #V prolongation operator
template <
typename DerivedV,
typename DerivedI,
typename DerivedC,
typename Scalar>
IGL_INLINE void cotmatrix(
const Eigen::MatrixBase<DerivedV> & V,
const Eigen::MatrixBase<DerivedI> & I,
const Eigen::MatrixBase<DerivedC> & C,
Eigen::SparseMatrix<Scalar>& L,
Eigen::SparseMatrix<Scalar>& M,
Eigen::SparseMatrix<Scalar>& P);
}
#ifndef IGL_STATIC_LIBRARY
# include "cotmatrix.cpp"
#endif
#endif