libigl/include/igl/cotmatrix.h

// This file is part of libigl, a simple c++ geometry processing library.
// 
// Copyright (C) 2014 Alec Jacobson <[email protected]>
// 
// 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).
  ///
  ///   @tparam DerivedV  derived type of eigen matrix for V (e.g. derived from
  ///     Eigen::MatrixXd)
  ///   @tparam DerivedF  derived type of eigen matrix for F (e.g. derived from
  ///     Eigen::MatrixXi)
  ///   @tparam Scalar  scalar type for eigen sparse matrix (e.g. double)
  ///   @param[in] V  #V by dim list of mesh vertex positions
  ///   @param[in] F  #F by simplex_size list of mesh elements (triangles or tetrahedra)
  ///   @param[out] L  #V by #V cotangent matrix, each row i corresponding to V(i,:)
  ///
  /// \see
  ///   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]
  ///
  /// @param[in] V  #V by 3 list of mesh vertex positions
  /// @param[in] I  #I vectorized list of polygon corner indices into rows of some matrix V
  /// @param[in] 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
  /// @param[out] L  #V by #V polygon Laplacian made simple matrix
  /// @param[out] M  #V by #V mass matrix
  /// @param[out] 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