face_tri3.c

一个用来实现偏微分方程中网格的计算库

// $Id: face_tri3.C 2789 2008-04-13 02:24:40Z roystgnr $

// The libMesh Finite Element Library.
// Copyright (C) 2002-2007  Benjamin S. Kirk, John W. Peterson
  
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
  
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.
  
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

// C++ includes

// Local includes
#include "side.h"
#include "edge_edge2.h"
#include "face_tri3.h"



// ------------------------------------------------------------
// Tri3 class static member initializations
const unsigned int Tri3::side_nodes_map[3][2] =
{
  {0, 1}, // Side 0
  {1, 2}, // Side 1
  {2, 0}  // Side 2
};


#ifdef ENABLE_AMR

const float Tri3::_embedding_matrix[4][3][3] =
{
  // embedding matrix for child 0
  {
    // 0    1    2  
    {1.0, 0.0, 0.0}, // 0
    {0.5, 0.5, 0.0}, // 1
    {0.5, 0.0, 0.5}  // 2
  },

  // embedding matrix for child 1
  {
    // 0    1    2  
    {0.5, 0.5, 0.0}, // 0
    {0.0, 1.0, 0.0}, // 1
    {0.0, 0.5, 0.5}  // 2
  },

  // embedding matrix for child 2
  {
    // 0    1    2  
    {0.5, 0.0, 0.5}, // 0
    {0.0, 0.5, 0.5}, // 1
    {0.0, 0.0, 1.0}  // 2
  },

  // embedding matrix for child 3
  {
    // 0    1    2  
    {0.5, 0.5, 0.0}, // 0
    {0.0, 0.5, 0.5}, // 1
    {0.5, 0.0, 0.5}  // 2
  }
};

#endif



// ------------------------------------------------------------
// Tri3 class member functions

bool Tri3::is_vertex(const unsigned int) const
{
  return true;
}

bool Tri3::is_edge(const unsigned int) const
{
  return false;
}

bool Tri3::is_face(const unsigned int) const
{
  return false;
}

bool Tri3::is_node_on_side(const unsigned int n,
			   const unsigned int s) const
{
  libmesh_assert(s < n_sides());
  for (unsigned int i = 0; i != 2; ++i)
    if (side_nodes_map[s][i] == n)
      return true;
  return false;
}

AutoPtr<Elem> Tri3::build_side (const unsigned int i,
				bool proxy) const
{
  libmesh_assert (i < this->n_sides());

  if (proxy)
    {
      AutoPtr<Elem> ap(new Side<Edge2,Tri3>(this,i));
      return ap;
    }

  else
    {
      Edge2* edge = new Edge2;

      switch (i)
	{
	case 0:
	  {
	    edge->set_node(0) = this->get_node(0);
	    edge->set_node(1) = this->get_node(1);
	
	    AutoPtr<Elem> ap(edge);  return ap;
	  }
	case 1:
	  {
	    edge->set_node(0) = this->get_node(1);
	    edge->set_node(1) = this->get_node(2);
	
	    AutoPtr<Elem> ap(edge);  return ap;
	  }
	case 2:
	  {
	    edge->set_node(0) = this->get_node(2);
	    edge->set_node(1) = this->get_node(0);
	
	    AutoPtr<Elem> ap(edge);  return ap;
	  }
	default:
	  {
	    libmesh_error();
	  }
	}
    }
  
  // We will never get here...  Look at the code above.
  libmesh_error();
  AutoPtr<Elem> ap(NULL);  return ap;
}


void Tri3::connectivity(const unsigned int sf,
			const IOPackage iop,
			std::vector<unsigned int>& conn) const
{
  libmesh_assert (sf <this->n_sub_elem());
  libmesh_assert (iop != INVALID_IO_PACKAGE);
  
  switch (iop)
    {
    case TECPLOT:
      {
	conn.resize(4);
	conn[0] = this->node(0)+1;
	conn[1] = this->node(1)+1;
	conn[2] = this->node(2)+1;
	conn[3] = this->node(2)+1;
	return;
      }

    case VTK:
      {
	conn.resize(3);
	conn[0] = this->node(0);
	conn[1] = this->node(1);
	conn[2] = this->node(2);
	return;
      }

    default:
      libmesh_error();
    }

  libmesh_error();
}






Real Tri3::volume () const
{
  // 3-node triangles have the following formula for computing the area
  Point v10 ( *(this->get_node(1)) - *(this->get_node(0)) );

  Point v20 ( *(this->get_node(2)) - *(this->get_node(0)) );

  return 0.5 * (v10.cross(v20)).size() ;
}



std::pair<Real, Real> Tri3::min_and_max_angle() const
{
  Point v10 ( this->point(1) - this->point(0) );
  Point v20 ( this->point(2) - this->point(0) );
  Point v21 ( this->point(2) - this->point(1) );

  const Real
    len_10=v10.size(),
    len_20=v20.size(),
    len_21=v21.size()
    ;

  const Real
    theta0=std::acos(( v10*v20)/len_10/len_20),
    theta1=std::acos((-v10*v21)/len_10/len_21),
    theta2=libMesh::pi - theta0 - theta1
    ;

  libmesh_assert(theta0 > 0.);
  libmesh_assert(theta1 > 0.);
  libmesh_assert(theta2 > 0.);
  
  return std::make_pair(std::min(theta0, std::min(theta1,theta2)),
			std::max(theta0, std::max(theta1,theta2)));
}