google3/third_party/libigl/include/igl/doublearea.h

// 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
{
  /// Computes twice the area for each input triangle or quad.
  ///
  /// @tparam  DerivedV  derived type of eigen matrix for V (e.g. derived from
  ///     MatrixXd)
  /// @tparam  DerivedF  derived type of eigen matrix for F (e.g. derived from
  ///     MatrixXi)
  /// @tparam  DeriveddblA  derived type of eigen matrix for dblA (e.g. derived from
  ///     MatrixXd)
  /// @param[in] V  #V by dim list of mesh vertex positions
  /// @param[in] F  #F by (3|4) list of mesh faces (must be triangles or quads)
  /// @param[out] dblA  #F list of triangle[quad] double areas (SIGNED only for 2D input)
  ///
  /// \bug For dim==3 complexity is O(#V + #F). Not just O(#F). This is a big deal
  /// if you have 1 million 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);
  /// Compute the twice the signed area of a each triangle.
  ///
  /// @param[in] A #F by dim list of triangle corner positions
  /// @param[in] B #F by dim list of triangle corner positions
  /// @param[in] C #F by dim list of triangle corner positions
  /// @param[out] D #F list of triangle double areas
  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);
  /// Compute the twice the signed area of a single triangle.
  ///
  /// @param[in] A triangle corner position
  /// @param[in] B triangle corner position
  /// @param[in] C triangle corner position
  /// @return 2*signed area of triangle
  ///
  /// \fileinfo
  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);
  /// Compute twice the area of each intrinsic triangle in a mesh.
  ///
  /// @param[in] l  #F by dim list of edge lengths using
  ///    for triangles, columns correspond to edges 23,31,12
  /// @param[in] 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.
  /// @param[out] 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);
  /// \overload
  ///
  /// \brief 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);
  /// Computes twice the area for each input quadrilateral.
  ///
  /// @param[in] V  #V by dim list of mesh vertex positions
  /// @param[in] F  #F by 4 list of mesh faces 
  /// @param[out] dblA  #F list of quadrilateral double areas
  ///
  /// \fileinfo
  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