Merge branch 'Rename_MeshTools_Files' into 'master'

Rename mesh tools files

See merge request !213

libs_required/MeshTools/Curvature.hh

+/*===========================================================================*\
+*                                                                            *
+*                              OpenFlipper                                   *
+ *           Copyright (c) 2001-2015, RWTH-Aachen University                 *
+ *           Department of Computer Graphics and Multimedia                  *
+ *                          All rights reserved.                             *
+ *                            www.openflipper.org                            *
+ *                                                                           *
+ *---------------------------------------------------------------------------*
+ * This file is part of OpenFlipper.                                         *
+ *---------------------------------------------------------------------------*
+ *                                                                           *
+ * Redistribution and use in source and binary forms, with or without        *
+ * modification, are permitted provided that the following conditions        *
+ * are met:                                                                  *
+ *                                                                           *
+ * 1. Redistributions of source code must retain the above copyright notice, *
+ *    this list of conditions and the following disclaimer.                  *
+ *                                                                           *
+ * 2. Redistributions in binary form must reproduce the above copyright      *
+ *    notice, this list of conditions and the following disclaimer in the    *
+ *    documentation and/or other materials provided with the distribution.   *
+ *                                                                           *
+ * 3. Neither the name of the copyright holder nor the names of its          *
+ *    contributors may be used to endorse or promote products derived from   *
+ *    this software without specific prior written permission.               *
+ *                                                                           *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS       *
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED *
+ * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A           *
+ * PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER *
+ * OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,  *
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,       *
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR        *
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF    *
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING      *
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS        *
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.              *
+*                                                                            *
+\*===========================================================================*/
+
+/*===========================================================================*\
+*                                                                            *
+*   $Revision$                                                       *
+*   $LastChangedBy$                                                *
+*   $Date$                     *
+*                                                                            *
+\*===========================================================================*/
+
+
+
+
+//=============================================================================
+//
+//
+//=============================================================================
+
+
+#ifndef CURVATURE_HH
+#define CURVATURE_HH
+
+
+/*! \file Curvature.hh
+    \brief Functions for calculating curvatures
+    
+*/
+
+//== INCLUDES =================================================================
+
+#include <vector>
+
+//== FORWARDDECLARATIONS ======================================================
+
+//== NAMESPACES ===============================================================
+
+namespace curvature {
+
+//== DEFINITIONS ==============================================================
+
+/*! compute consistent dirscrete gaussian curvature (vertex is a small sphere patch, edges are small cylinders)
+*/
+template< typename MeshT >
+double
+gauss_curvature(MeshT& _mesh, const typename MeshT::VertexHandle& _vh);
+   
+/**
+* Mean Curvature Normal Operator
+* warning: if mean curvature < 0 _n points to the inside
+* warning: if mean curvature = 0 -> no normal information
+@param _n       mean_curvature(vit)*n(vit)
+@param _area global vertex area
+*/
+template<class MeshT, class VectorT, class REALT>
+void discrete_mean_curv_op( const MeshT&                           _m,
+                                                const typename MeshT::VertexHandle& _vh, 
+                                                VectorT&                         _n,
+                                                REALT&                           _area );   
+
+   
+//=============================================================================
+} 
+//=============================================================================
+#if defined(INCLUDE_TEMPLATES) && !defined(CURVATURE_C)
+#define CURVATURE_TEMPLATES
+#include "CurvatureT.cc"
+#endif
+//=============================================================================
+#endif // CURVATURE_HH defined
+//=============================================================================
+

libs_required/MeshTools/CurvatureT.cc

+/*===========================================================================*\
+*                                                                            *
+*                              OpenFlipper                                   *
+ *           Copyright (c) 2001-2015, RWTH-Aachen University                 *
+ *           Department of Computer Graphics and Multimedia                  *
+ *                          All rights reserved.                             *
+ *                            www.openflipper.org                            *
+ *                                                                           *
+ *---------------------------------------------------------------------------*
+ * This file is part of OpenFlipper.                                         *
+ *---------------------------------------------------------------------------*
+ *                                                                           *
+ * Redistribution and use in source and binary forms, with or without        *
+ * modification, are permitted provided that the following conditions        *
+ * are met:                                                                  *
+ *                                                                           *
+ * 1. Redistributions of source code must retain the above copyright notice, *
+ *    this list of conditions and the following disclaimer.                  *
+ *                                                                           *
+ * 2. Redistributions in binary form must reproduce the above copyright      *
+ *    notice, this list of conditions and the following disclaimer in the    *
+ *    documentation and/or other materials provided with the distribution.   *
+ *                                                                           *
+ * 3. Neither the name of the copyright holder nor the names of its          *
+ *    contributors may be used to endorse or promote products derived from   *
+ *    this software without specific prior written permission.               *
+ *                                                                           *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS       *
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED *
+ * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A           *
+ * PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER *
+ * OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,  *
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,       *
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR        *
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF    *
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING      *
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS        *
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.              *
+*                                                                            *
+\*===========================================================================*/
+
+/*===========================================================================*\
+*                                                                            *
+*   $Revision$                                                       *
+*   $LastChangedBy$                                                *
+*   $Date$                     *
+*                                                                            *
+\*===========================================================================*/
+
+
+
+
+//=============================================================================
+//
+//  IMPLEMENTATION
+//
+//=============================================================================
+
+#define CURVATURE_C
+
+//== INCLUDES =================================================================
+
+#include <ACG/Geometry/Algorithms.hh>
+#include "Math_Tools/Math_Tools.hh"
+
+#include <iostream>
+#include <OpenMesh/Core/Geometry/MathDefs.hh>
+
+#include <cmath>
+
+//== NAMESPACES ===============================================================
+
+namespace curvature {
+
+//== IMPLEMENTATION ==========================================================
+
+/*! compute consistent discrete gaussian curvature (vertex is a small sphere patch, edges are small cylinders)
+*/
+template< typename MeshT >
+double
+gauss_curvature(MeshT& _mesh, const typename MeshT::VertexHandle& _vh) {
+   if (_mesh.status(_vh).deleted())
+     return 0.0;
+  
+  double gauss_curv = 2.0 * M_PI;
+
+  /*
+
+  TODO: Check the boundary case.
+
+  If the vertex is a boundary vertex
+  if ( _mesh.is_boundary(_vh) )
+    gauss_curv = M_PI;
+
+  */
+
+  const typename MeshT::Point p0 = _mesh.point(_vh);
+
+  typename MeshT::CVOHIter voh_it( _mesh.cvoh_iter(_vh));
+  typename MeshT::CVOHIter n_voh_it = voh_it;
+
+  if ( ! voh_it->is_valid() )
+     return 0.0;
+   
+  // move to next
+  ++n_voh_it;
+
+  for(; voh_it.is_valid(); ++voh_it, ++n_voh_it)
+  {
+    typename MeshT::Point p1 = _mesh.point(_mesh.to_vertex_handle(   *voh_it));
+    typename MeshT::Point p2 = _mesh.point(_mesh.to_vertex_handle( *n_voh_it));
+
+    gauss_curv -= acos(OpenMesh::sane_aarg( ((p1-p0).normalize() | (p2-p0).normalize()) ));
+  }
+
+  return gauss_curv;
+}
+
+
+template<class MeshT, class VectorT, class REALT>
+void discrete_mean_curv_op( const MeshT&                        _m,
+                        	  const typename MeshT::VertexHandle& _vh,
+			                      VectorT&                            _n,
+			                      REALT&                              _area )
+{
+  _n = VectorT(0,0,0);
+  _area = 0.0;
+
+  typename MeshT::ConstVertexOHalfedgeIter voh_it = _m.cvoh_iter(_vh);
+  
+   if ( ! voh_it->is_valid() )
+     return;
+   
+  for(; voh_it.is_valid(); ++voh_it)
+  {
+    if ( _m.is_boundary( _m.edge_handle( *voh_it ) ) )
+      continue;
+    
+    const typename MeshT::Point p0 = _m.point( _vh );
+    const typename MeshT::Point p1 = _m.point( _m.to_vertex_handle( *voh_it));
+//     const typename MeshT::Point p2 = _m.point( _m.to_vertex_handle( _m.next_halfedge_handle( *voh_it)));
+    const typename MeshT::Point p2 = _m.point( _m.from_vertex_handle( _m.prev_halfedge_handle( *voh_it)));
+    const typename MeshT::Point p3 = _m.point( _m.to_vertex_handle( _m.next_halfedge_handle( _m.opposite_halfedge_handle(*voh_it))));
+
+    const REALT alpha = acos( OpenMesh::sane_aarg((p0-p2).normalize() | (p1-p2).normalize()) );
+    const REALT beta  = acos( OpenMesh::sane_aarg((p0-p3).normalize() | (p1-p3).normalize()) );
+      
+    REALT cotw = 0.0;
+    
+    if ( !OpenMesh::is_eq(alpha,M_PI/2.0) )
+      cotw += (REALT(1.0))/tan(alpha);
+    
+    if ( !OpenMesh::is_eq(beta,M_PI/2.0) )
+      cotw += (REALT(1.0))/tan(beta);
+
+#ifdef WIN32
+	if ( OpenMesh::is_zero(cotw) )
+		continue;
+#else
+    if ( OpenMesh::is_zero(cotw) || std::isinf(cotw) )
+		continue;
+#endif
+
+    // calculate area
+    const int obt = ACG::Geometry::isObtuse(p0,p1,p2);
+    if(obt == 0)
+    {
+      REALT gamma = acos( OpenMesh::sane_aarg((p0-p1).normalize() | (p2-p1).normalize()) );
+      
+      REALT tmp = 0.0;
+      if ( !OpenMesh::is_eq(alpha,M_PI/2.0) )
+        tmp += (p0-p1).sqrnorm()*1.0/tan(alpha);
+    
+      if ( !OpenMesh::is_eq(gamma,M_PI/2.0) )
+        tmp += (p0-p2).sqrnorm()*1.0/tan(gamma);
+      
+#ifdef WIN32
+	  if ( OpenMesh::is_zero(tmp) )
+		continue;
+#else
+      if ( OpenMesh::is_zero(tmp) || std::isinf(tmp) )
+		continue;
+#endif
+
+      _area += 0.125*( tmp );
+    }
+    else
+    {
+      if(obt == 1)
+      {
+	     _area += ((p1-p0) % (p2-p0)).norm() * 0.5 * 0.5;
+      }
+      else
+      {
+	     _area += ((p1-p0) % (p2-p0)).norm() * 0.5 * 0.25;
+      }
+    }
+    
+    _n += ((p0-p1)*cotw);
+
+    // error handling
+    //if(_area < 0) std::cerr << "error: triangle area < 0\n";
+//    if(isnan(_area))
+//    {
+//      REALT gamma = acos( ((p0-p1).normalize() | (p2-p1).normalize()) );
+
+/*
+      std::cerr << "***************************\n";
+      std::cerr << "error : trianlge area = nan\n";
+      std::cerr << "alpha : " << alpha << std::endl;
+      std::cerr << "beta  : " << beta  << std::endl;
+      std::cerr << "gamma : " << gamma << std::endl;
+      std::cerr << "cotw  : " << cotw  << std::endl;
+      std::cerr << "normal: " << _n << std::endl;
+      std::cerr << "p0    : " << p0 << std::endl;
+      std::cerr << "p1    : " << p1 << std::endl;
+      std::cerr << "p2    : " << p2 << std::endl;
+      std::cerr << "p3    : " << p3 << std::endl;
+      std::cerr << "***************************\n";
+*/
+//    }
+  }
+
+  _n /= 4.0*_area;
+}
+
+
+
+//=============================================================================
+} // curvature Namespace 
+//=============================================================================

libs_required/MeshTools/MeshFunctions.hh

+/*===========================================================================*\
+*                                                                            *
+*                              OpenFlipper                                   *
+ *           Copyright (c) 2001-2015, RWTH-Aachen University                 *
+ *           Department of Computer Graphics and Multimedia                  *
+ *                          All rights reserved.                             *
+ *                            www.openflipper.org                            *
+ *                                                                           *
+ *---------------------------------------------------------------------------*
+ * This file is part of OpenFlipper.                                         *
+ *---------------------------------------------------------------------------*
+ *                                                                           *
+ * Redistribution and use in source and binary forms, with or without        *
+ * modification, are permitted provided that the following conditions        *
+ * are met:                                                                  *
+ *                                                                           *
+ * 1. Redistributions of source code must retain the above copyright notice, *
+ *    this list of conditions and the following disclaimer.                  *
+ *                                                                           *
+ * 2. Redistributions in binary form must reproduce the above copyright      *
+ *    notice, this list of conditions and the following disclaimer in the    *
+ *    documentation and/or other materials provided with the distribution.   *
+ *                                                                           *
+ * 3. Neither the name of the copyright holder nor the names of its          *
+ *    contributors may be used to endorse or promote products derived from   *
+ *    this software without specific prior written permission.               *
+ *                                                                           *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS       *
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED *
+ * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A           *
+ * PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER *
+ * OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,  *
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,       *
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR        *
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF    *
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING      *
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS        *
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.              *
+*                                                                            *
+\*===========================================================================*/
+
+/*===========================================================================*\
+*                                                                            *
+*   $Revision$                                                       *
+*   $LastChangedBy$                                                *
+*   $Date$                     *
+*                                                                            *
+\*===========================================================================*/
+
+
+
+
+//=============================================================================
+//
+//
+//=============================================================================
+
+
+#ifndef MESHFUNCTIONS_HH
+#define MESHFUNCTIONS_HH
+
+
+/*! \file MeshFunctions.hh
+    \brief Functions for modifying a Mesh
+    
+    General file with template functions doing modifications on a given Mesh 
+    (e.g smooth, reposition,... )
+*/
+
+//== INCLUDES =================================================================
+
+#include <vector>
+
+//== FORWARDDECLARATIONS ======================================================
+
+//== NAMESPACES ===============================================================
+
+/// Namespace providing different Mesh editing functions
+namespace MeshFunctions {
+
+//== DEFINITIONS ==============================================================
+
+/**
+    get one boundary at the vertex
+    @param _mesh Mesh
+    @param _vh   Vertex handle of one vertex of the boundary
+    @param _boundary Coords and vertex handles of the boundary
+  */
+template < typename MeshT , typename VectorT >
+bool get_boundary(MeshT& _mesh, 
+                               typename MeshT::VertexHandle _vh, 
+                               std::vector< std::pair< VectorT , typename MeshT::VertexHandle > >& _boundary);  
+
+/**
+    get boundary of a mesh (assumes that there is only one boundary!!
+    @param _mesh Mesh
+    @param _boundary Coords and vertex handles of the boundary
+    @return Found a boundary?
+  */
+template < typename MeshT , typename VectorT >
+bool get_boundary(MeshT& _mesh, 
+                               std::vector< std::pair< VectorT , 
+                               typename MeshT::VertexHandle > >& _boundary);  
+
+/**
+    function to smooth a boundary of a given mesh by moving each vertex to the 
+    mean Position of its adjazent verticies  
+    @param _mesh Mesh to work on
+    @param _vh Vertex handle on the boundary 
+*/ 
+template < typename MeshT , typename VectorT >
+void smooth_boundary(MeshT& _mesh , 
+                     typename MeshT::VertexHandle _vh);
+
+/**
+    Checks for two faces if they are adjazent
+    @param _mesh Mesh
+    @param _fh1  First Face 
+    @param _fh2  Second Face
+*/
+template < typename MeshT >
+bool neighbour(const MeshT& _mesh , 
+               const typename MeshT::FaceHandle& _fh1 ,
+               const typename MeshT::FaceHandle& _fh2 );
+
+/**
+   Checks if plane cuts the face
+   @param _porigin Planes origin
+   @param _pnormal Plane normal
+   @param _mesh    Mesh
+   @param _fh      Facehandle of face
+   @return triangle cut by plane?
+*/
+template < typename MeshT , typename VectorT >
+bool
+cut_face(const VectorT& _porigin, 
+               const VectorT& _pnormal, 
+               const MeshT& _mesh, 
+               const typename MeshT::FaceHandle& _fh);
+         
+/** Get the area of a mesh ( sum over all triangle areas)
+    @param _mesh Mesh to calculate area 
+    @return Area spanned by the mesh
+    */
+template < typename MeshT >
+double 
+calc_area( const MeshT& _mesh);
+
+/** Get the sum of the angles around a vertex
+    @param _mesh Mesh to work on
+    @param _vh Vertex
+    @return Sum of angles around the vertex
+    */
+template < typename MeshT >
+double 
+calc_angle_around( const MeshT& _mesh , const typename MeshT::VertexHandle& _vh);
+
+/**
+ * Transform geometry of the mesh using the specified
+ * transformation matrix.
+ * @param _matrix The transformation matrix
+ * @param _mesh The mesh that is to be transformed
+ */
+template< typename MeshT >
+void transformMesh(ACG::Matrix4x4d _matrix , MeshT& _mesh);
+
+/**
+ * Transform handle vertices only
+ * @param _matrix The transformation matrix
+ * @param _mesh The mesh that is to be transformed
+ */
+template< typename MeshT >
+void transformHandleVertices(ACG::Matrix4x4d _matrix , MeshT& _mesh);
+
+//=============================================================================
+} // MeshFunctions Namespace 
+//=============================================================================
+#if defined(INCLUDE_TEMPLATES) && !defined(MESHFUNCTIONS_C)
+#define MESHFUNCTIONS_TEMPLATES
+#include "MeshFunctionsT.cc"
+#endif
+//=============================================================================
+#endif // MESHFUNCTIONS_HH defined
+//=============================================================================
+

libs_required/MeshTools/MeshFunctionsT.cc

+/*===========================================================================*\
+*                                                                            *
+*                              OpenFlipper                                   *
+ *           Copyright (c) 2001-2015, RWTH-Aachen University                 *
+ *           Department of Computer Graphics and Multimedia                  *
+ *                          All rights reserved.                             *
+ *                            www.openflipper.org                            *
+ *                                                                           *
+ *---------------------------------------------------------------------------*
+ * This file is part of OpenFlipper.                                         *
+ *---------------------------------------------------------------------------*
+ *                                                                           *
+ * Redistribution and use in source and binary forms, with or without        *
+ * modification, are permitted provided that the following conditions        *
+ * are met:                                                                  *
+ *                                                                           *
+ * 1. Redistributions of source code must retain the above copyright notice, *
+ *    this list of conditions and the following disclaimer.                  *
+ *                                                                           *
+ * 2. Redistributions in binary form must reproduce the above copyright      *
+ *    notice, this list of conditions and the following disclaimer in the    *
+ *    documentation and/or other materials provided with the distribution.   *
+ *                                                                           *
+ * 3. Neither the name of the copyright holder nor the names of its          *
+ *    contributors may be used to endorse or promote products derived from   *
+ *    this software without specific prior written permission.               *
+ *                                                                           *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS       *
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED *
+ * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A           *
+ * PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER *
+ * OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,  *
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,       *
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR        *
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF    *
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING      *
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS        *
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.              *
+*                                                                            *
+\*===========================================================================*/
+
+/*===========================================================================*\
+*                                                                            *
+*   $Revision$                                                       *
+*   $LastChangedBy$                                                *
+*   $Date$                     *
+*                                                                            *
+\*===========================================================================*/
+
+
+
+
+//=============================================================================
+//
+//  IMPLEMENTATION
+//
+//=============================================================================
+
+#define MESHFUNCTIONS_C
+
+//== INCLUDES =================================================================
+
+#include "MeshFunctions.hh"
+
+#include <ACG/Geometry/Algorithms.hh>
+#include "Math_Tools/Math_Tools.hh"
+
+#include <set>
+
+#include <iostream>
+
+#include <OpenMesh/Core/Geometry/MathDefs.hh>
+#include <ObjectTypes/TriangleMesh/TriangleMesh.hh>
+
+//== NAMESPACES ===============================================================
+
+namespace MeshFunctions {
+
+//== IMPLEMENTATION ==========================================================
+
+template < typename MeshT , typename VectorT >
+bool get_boundary(MeshT& _mesh, 
+                               typename MeshT::VertexHandle _vh, 
+                               std::vector< std::pair< VectorT , typename MeshT::VertexHandle > >& _boundary) 
+{
+   _boundary.clear();
+    typename MeshT::VertexHandle last  = _vh;