cotmatrix_dense.h

// 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_DENSE_H
#define IGL_COTMATRIX_DENSE_H
#include <igl/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

  // 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>
  IGL_INLINE void cotmatrix_dense(
    const Eigen::MatrixBase<DerivedV> & V, 
    const Eigen::MatrixBase<DerivedF> & F, 
    Eigen::MatrixBase<Eigen::MatrixXd> & 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_dense(
    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_dense.cpp"
#endif

#endif