// 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_PRINCIPAL_CURVATURE_H
#define IGL_PRINCIPAL_CURVATURE_H


#include <Eigen/Geometry>
#include <Eigen/Dense>
#include <vector>
#include <stdio.h>
#include <map>

#include <igl/igl_inline.h>
#include <igl/cotmatrix.h>
#include <igl/writeOFF.h>



namespace igl
{

  // Compute the principal curvature directions and magnitude of the given triangle mesh
  //   DerivedV derived from vertex positions matrix type: i.e. MatrixXd
  //   DerivedF derived from face indices matrix type: i.e. MatrixXi
  // Inputs:
  //   V       eigen matrix #V by 3
  //   F       #F by 3 list of mesh faces (must be triangles)
  //   radius  controls the size of the neighbourhood used, 1 = average edge lenght
  //
  // Outputs:
  //   PD1 #V by 3 maximal curvature direction for each vertex.
  //   PD2 #V by 3 minimal curvature direction for each vertex.  
  //  Note that to maximal/minimal curvature value is the rowise norm of PD1/PD2
  //
  // See also: moveVF, moveFV
  //
  // This function has been developed by: Nikolas De Giorgis, Luigi Rocca and Enrico Puppo.
  // The algorithm is based on:
  // Efficient Multi-scale Curvature and Crease Estimation
  // Daniele Panozzo, Enrico Puppo, Luigi Rocca
  // GraVisMa, 2010

template <typename DerivedV, typename DerivedF>
IGL_INLINE void principal_curvature(
                                     const Eigen::PlainObjectBase<DerivedV>& V,
                                     const Eigen::PlainObjectBase<DerivedF>& F,
                                     Eigen::PlainObjectBase<DerivedV>& PD1,
                                     Eigen::PlainObjectBase<DerivedV>& PD2,
                                     unsigned radius = 5,
                                     bool useKring = true
                                     );
}


#ifdef IGL_HEADER_ONLY
#include "principal_curvature.cpp"
#endif

#endif