// This file is part of libigl, a simple c++ geometry processing library.
// 
// Copyright (C) 2016 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_PER_VERTEX_POINT_TO_PLANE_QUADRICS_H
#define IGL_PER_VERTEX_POINT_TO_PLANE_QUADRICS_H
#include "igl_inline.h"
#include <Eigen/Core>
#include <vector>
#include <tuple>
namespace igl
{
  /// Compute quadrics per vertex of a "closed" triangle mesh (V,F). Rather than
  /// follow the qslim paper, this implements the lesser-known _follow up_
  /// "Simplifying Surfaces with Color and Texture using Quadric Error Metrics".
  /// This allows V to be n-dimensional (where the extra coordiantes store
  /// texture UVs, color RGBs, etc.
  ///
  /// @param[in] V  #V by n list of vertex positions. Assumes that vertices with
  ///     infinite coordinates are "points at infinity" being used to close up
  ///     boundary edges with faces. This allows special subspace quadrice for
  ///     boundary edges: There should never be more than one "point at
  ///     infinity" in a single triangle.
  /// @param[in] F  #F by 3 list of triangle indices into V
  /// @param[in] E  #E by 2 list of edge indices into V.
  /// @param[in] EMAP #F*3 list of indices into E, mapping each directed edge to unique
  ///     unique edge in E
  /// @param[in] EF  #E by 2 list of edge flaps, EF(e,0)=f means e=(i-->j) is the edge of
  ///     F(f,:) opposite the vth corner, where EI(e,0)=v. Similarly EF(e,1) "
  ///     e=(j->i)
  /// @param[in] EI  #E by 2 list of edge flap corners (see above).
  /// @param[out] quadrics  #V list of quadrics, where a quadric is a tuple {A,b,c} such
  ///     that the quadratic energy of moving this vertex to position x is
  ///     given by x'Ax - 2b + c
  ///
  IGL_INLINE void per_vertex_point_to_plane_quadrics(
    const Eigen::MatrixXd & V,
    const Eigen::MatrixXi & F,
    const Eigen::MatrixXi & EMAP,
    const Eigen::MatrixXi & EF,
    const Eigen::MatrixXi & EI,
    std::vector<
      std::tuple<
        Eigen::MatrixXd,
        Eigen::RowVectorXd,
        double> > & quadrics);
}
#ifndef IGL_STATIC_LIBRARY
#  include "per_vertex_point_to_plane_quadrics.cpp"
#endif
#endif
