hessian.h 1.4 KB

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  1. // This file is part of libigl, a simple c++ geometry processing library.
  2. //
  3. // Copyright (C) 2017 Alec Jacobson <alecjacobson@gmail.com>
  4. // and Oded Stein <oded.stein@columbia.edu>
  5. //
  6. // This Source Code Form is subject to the terms of the Mozilla Public License
  7. // v. 2.0. If a copy of the MPL was not distributed with this file, You can
  8. // obtain one at http://mozilla.org/MPL/2.0/.
  9. #ifndef IGL_FEM_HESSIAN_H
  10. #define IGL_FEM_HESSIAN_H
  11. #include "igl_inline.h"
  12. #include <Eigen/Dense>
  13. #include <Eigen/Sparse>
  14. namespace igl
  15. {
  16. // Constructs the finite element Hessian matrix
  17. // as described in https://arxiv.org/abs/1707.04348,
  18. // Natural Boundary Conditions for Smoothing in Geometry Processing
  19. // (Oded Stein, Eitan Grinspun, Max Wardetzky, Alec Jacobson)
  20. // The interior vertices are NOT set to zero yet.
  21. //
  22. // Inputs:
  23. // V #V by dim list of mesh vertex positions
  24. // F #F by 3 list of mesh faces (must be triangles)
  25. // Outputs:
  26. // H #V by #V Hessian energy matrix, each column i
  27. // corresponding to V(i,:)
  28. //
  29. //
  30. //
  31. template <typename DerivedV, typename DerivedF, typename Scalar>
  32. IGL_INLINE void hessian(
  33. const Eigen::MatrixBase<DerivedV> & V,
  34. const Eigen::MatrixBase<DerivedF> & F,
  35. Eigen::SparseMatrix<Scalar>& H);
  36. }
  37. #ifndef IGL_STATIC_LIBRARY
  38. # include "hessian.cpp"
  39. #endif
  40. #endif