// 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/.
#include "grad.h"
#include <Eigen/Geometry>
#include <vector>

template <typename DerivedV, typename DerivedF>
IGL_INLINE void igl::grad(const Eigen::PlainObjectBase<DerivedV>&V,
                     const Eigen::PlainObjectBase<DerivedF>&F,
                    Eigen::SparseMatrix<typename DerivedV::Scalar> &G)
{
  Eigen::Matrix<typename DerivedV::Scalar,Eigen::Dynamic,3> 
    eperp21(F.rows(),3), eperp13(F.rows(),3);

  for (int i=0;i<F.rows();++i)
  {
    // renaming indices of vertices of triangles for convenience
    int i1 = F(i,0);
    int i2 = F(i,1);
    int i3 = F(i,2);

    // #F x 3 matrices of triangle edge vectors, named after opposite vertices
    Eigen::Matrix<typename DerivedV::Scalar, 1, 3> v32 = V.row(i3) - V.row(i2);
    Eigen::Matrix<typename DerivedV::Scalar, 1, 3> v13 = V.row(i1) - V.row(i3);
    Eigen::Matrix<typename DerivedV::Scalar, 1, 3> v21 = V.row(i2) - V.row(i1);

    // area of parallelogram is twice area of triangle
    // area of parallelogram is || v1 x v2 ||
    Eigen::Matrix<typename DerivedV::Scalar, 1, 3> n  = v32.cross(v13);

    // This does correct l2 norm of rows, so that it contains #F list of twice
    // triangle areas
    double dblA = std::sqrt(n.dot(n));

    // now normalize normals to get unit normals
    Eigen::Matrix<typename DerivedV::Scalar, 1, 3> u = n / dblA;

    // rotate each vector 90 degrees around normal
    double norm21 = std::sqrt(v21.dot(v21));
    double norm13 = std::sqrt(v13.dot(v13));
    eperp21.row(i) = u.cross(v21);
    eperp21.row(i) = eperp21.row(i) / std::sqrt(eperp21.row(i).dot(eperp21.row(i)));
    eperp21.row(i) *= norm21 / dblA;
    eperp13.row(i) = u.cross(v13);
    eperp13.row(i) = eperp13.row(i) / std::sqrt(eperp13.row(i).dot(eperp13.row(i)));
    eperp13.row(i) *= norm13 / dblA;
  }

  std::vector<int> rs;
  rs.reserve(F.rows()*4*3);
  std::vector<int> cs;
  cs.reserve(F.rows()*4*3);
  std::vector<double> vs;
  vs.reserve(F.rows()*4*3);

  // row indices
  for(int r=0;r<3;r++)
  {
    for(int j=0;j<4;j++)
    {
      for(int i=r*F.rows();i<(r+1)*F.rows();i++) rs.push_back(i);
    }
  }

  // column indices
  for(int r=0;r<3;r++)
  {
    for(int i=0;i<F.rows();i++) cs.push_back(F(i,1));
    for(int i=0;i<F.rows();i++) cs.push_back(F(i,0));
    for(int i=0;i<F.rows();i++) cs.push_back(F(i,2));
    for(int i=0;i<F.rows();i++) cs.push_back(F(i,0));
  }

  // values
  for(int i=0;i<F.rows();i++) vs.push_back(eperp13(i,0));
  for(int i=0;i<F.rows();i++) vs.push_back(-eperp13(i,0));
  for(int i=0;i<F.rows();i++) vs.push_back(eperp21(i,0));
  for(int i=0;i<F.rows();i++) vs.push_back(-eperp21(i,0));
  for(int i=0;i<F.rows();i++) vs.push_back(eperp13(i,1));
  for(int i=0;i<F.rows();i++) vs.push_back(-eperp13(i,1));
  for(int i=0;i<F.rows();i++) vs.push_back(eperp21(i,1));
  for(int i=0;i<F.rows();i++) vs.push_back(-eperp21(i,1));
  for(int i=0;i<F.rows();i++) vs.push_back(eperp13(i,2));
  for(int i=0;i<F.rows();i++) vs.push_back(-eperp13(i,2));
  for(int i=0;i<F.rows();i++) vs.push_back(eperp21(i,2));
  for(int i=0;i<F.rows();i++) vs.push_back(-eperp21(i,2));

  // create sparse gradient operator matrix
  G.resize(3*F.rows(),V.rows());
  std::vector<Eigen::Triplet<typename DerivedV::Scalar> > triplets;
  for (int i=0;i<(int)vs.size();++i)
  {
    triplets.push_back(Eigen::Triplet<typename DerivedV::Scalar>(rs[i],cs[i],vs[i]));
  }
  G.setFromTriplets(triplets.begin(), triplets.end());
}

#ifdef IGL_STATIC_LIBRARY
// Explicit template specialization
// template void igl::grad<double, int>(Eigen::Matrix<double, -1, -1, 0, -1,-1> const&, Eigen::Matrix<int, -1, -1, 0, -1, -1> const&,Eigen::SparseMatrix<double, 0, int>&);
template void igl::grad<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::SparseMatrix<Eigen::Matrix<double, -1, 3, 0, -1, 3>::Scalar, 0, int>&);
//template void igl::grad<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::SparseMatrix<Eigen::Matrix<double, -1, 3, 0, -1, 3>::Scalar, 0, int>&);
template void igl::grad<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::SparseMatrix<Eigen::Matrix<double, -1, -1, 0, -1, -1>::Scalar, 0, int>&);
#endif