text: // This file is part of libigl, a simple c++ geometry processing library.
  //
  // Copyright (C) 2013 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_DOUBLEAREA_H
  #define IGL_DOUBLEAREA_H
  #include "igl_inline.h"
  #include <Eigen/Dense>
  namespace igl
  {
    // DOUBLEAREA computes twice the area for each input triangle[quad]
    //
    // 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)
    //   DeriveddblA  derived type of eigen matrix for dblA (e.g. derived from
    //     MatrixXd)
    // Inputs:
    //   V  #V by dim list of mesh vertex positions
    //   F  #F by simplex_size list of mesh faces (must be triangles or quads)
    // Outputs:
    //   dblA  #F list of triangle[quad] double areas (SIGNED only for 2D input)
    //
    // Known bug: For dim==3 complexity is O(#V + #F)!! Not just O(#F). This is a big deal
    // if you have 1million unreferenced vertices and 1 face
    template <typename DerivedV, typename DerivedF, typename DeriveddblA>
    IGL_INLINE void doublearea(
      const Eigen::MatrixBase<DerivedV> & V,
      const Eigen::MatrixBase<DerivedF> & F,
      Eigen::PlainObjectBase<DeriveddblA> & dblA);
    // Stream of triangles, computes signed area...
    template <
      typename DerivedA,
      typename DerivedB,
      typename DerivedC,
      typename DerivedD>
    IGL_INLINE void doublearea(
      const Eigen::MatrixBase<DerivedA> & A,
      const Eigen::MatrixBase<DerivedB> & B,
      const Eigen::MatrixBase<DerivedC> & C,
      Eigen::PlainObjectBase<DerivedD> & D);
    // Single triangle in 2D!
    //
    // This should handle streams of corners not just single corners
    template <
      typename DerivedA,
      typename DerivedB,
      typename DerivedC>
    IGL_INLINE typename DerivedA::Scalar doublearea_single(
      const Eigen::MatrixBase<DerivedA> & A,
      const Eigen::MatrixBase<DerivedB> & B,
      const Eigen::MatrixBase<DerivedC> & C);
    // Same as above but use instrinsic edge lengths rather than (V,F) mesh. This
    //
    // Inputs:
    //   l  #F by dim list of edge lengths using
    //     for triangles, columns correspond to edges 23,31,12
    //   nan_replacement  what value should be used for triangles whose given
    //     edge lengths do not obey the triangle inequality. These may be very
    //     wrong (e.g., [100 1 1]) or may be nearly degenerate triangles whose
    //     floating point side length computation leads to breach of the triangle
    //     inequality. One may wish to set this parameter to 0 if side lengths l
    //     are _known_ to come from a valid embedding (e.g., some mesh (V,F)). In
    //     that case, the only circumstance the triangle inequality is broken is
    //     when the triangle is nearly degenerate and floating point error
    //     dominates: hence replacing with zero is reasonable.
    // Outputs:
    //   dblA  #F list of triangle double areas
    template <typename Derivedl, typename DeriveddblA>
    IGL_INLINE void doublearea(
      const Eigen::MatrixBase<Derivedl> & l,
      const typename Derivedl::Scalar nan_replacement,
      Eigen::PlainObjectBase<DeriveddblA> & dblA);
    // default behavior is to assert on NaNs and leave them in place
    template <typename Derivedl, typename DeriveddblA>
    IGL_INLINE void doublearea(
      const Eigen::MatrixBase<Derivedl> & l,
      Eigen::PlainObjectBase<DeriveddblA> & dblA);
    // DOUBLEAREA_QUAD computes twice the area for each input quadrilateral
    //
    // Inputs:
    //   V  #V by dim list of mesh vertex positions
    //   F  #F by simplex_size list of mesh faces (must be quadrilaterals)
    // Outputs:
    //   dblA  #F list of quadrilateral double areas
    //
    template <typename DerivedV, typename DerivedF, typename DeriveddblA>
    IGL_INLINE void doublearea_quad(
    const Eigen::MatrixBase<DerivedV> & V,
    const Eigen::MatrixBase<DerivedF> & F,
    Eigen::PlainObjectBase<DeriveddblA> & dblA);
  
  }
  
  #ifndef IGL_STATIC_LIBRARY
  #  include "doublearea.cpp"
  #endif
  
  #endif
  