// This file is part of libigl, a simple c++ geometry processing library.
// 
// Copyright (C) 2015 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_NORMAL_DERIVATIVE_H
#define IGL_NORMAL_DERIVATIVE_H
#include "igl_inline.h"

#include <Eigen/Core>
#include <Eigen/Sparse>
namespace igl 
{
  // NORMAL_DERIVATIVE Computes the directional derivative **normal** to
  // **all** (half-)edges of a triangle mesh (not just boundary edges). These
  // are integrated along the edge: they're the per-face constant gradient dot
  // the rotated edge vector (unit rotated edge vector for direction then
  // magnitude for integration).
  //
  // Inputs:
  //   V  #V by dim list of mesh vertex positions
  //   F  #F by 3|4 list of triangle|tetrahedron indices into V
  // Outputs:
  //   DD  #F*3|4 by #V sparse matrix representing operator to compute
  //     directional derivative with respect to each facet of each element.
  //
  template <
    typename DerivedV, 
    typename DerivedEle, 
    typename Scalar>
  IGL_INLINE void normal_derivative(
    const Eigen::PlainObjectBase<DerivedV> & V,
    const Eigen::PlainObjectBase<DerivedEle> & Ele,
    Eigen::SparseMatrix<Scalar>& DD);
}

#ifndef IGL_STATIC_LIBRARY
#  include "normal_derivative.cpp"
#endif

#endif