triangle.cpp

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// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
// reserved. See file COPYRIGHT for details.
//
// This file is part of the MFEM library. For more information and source code
// availability see http://mfem.org.
//
// MFEM 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) version 2.1 dated February 1999.

#include "mesh_headers.hpp"

namespace mfem
{

Triangle::Triangle(const int *ind, int attr) : Element(Geometry::TRIANGLE)
{
   attribute = attr;
   for (int i = 0; i < 3; i++)
   {
      indices[i] = ind[i];
   }
   transform = 0;
}

Triangle::Triangle(int ind1, int ind2, int ind3, int attr)
   : Element(Geometry::TRIANGLE)
{
   attribute  = attr;
   indices[0] = ind1;
   indices[1] = ind2;
   indices[2] = ind3;
   transform = 0;
}

int Triangle::NeedRefinement(DSTable &v_to_v, int *middle) const
{
   int m;

   if ((m = v_to_v(indices[0], indices[1])) != -1 && middle[m] != -1) { return 1; }
   if ((m = v_to_v(indices[1], indices[2])) != -1 && middle[m] != -1) { return 1; }
   if ((m = v_to_v(indices[2], indices[0])) != -1 && middle[m] != -1) { return 1; }
   return 0;
}

void Triangle::SetVertices(const int *ind)
{
   for (int i = 0; i < 3; i++)
   {
      indices[i] = ind[i];
   }
}

void Triangle::MarkEdge(DenseMatrix &pmat)
{
   double d[3];
   int shift, v;

   d[0] = ( (pmat(0,1)-pmat(0,0))*(pmat(0,1)-pmat(0,0)) +
            (pmat(1,1)-pmat(1,0))*(pmat(1,1)-pmat(1,0)) );
   d[1] = ( (pmat(0,2)-pmat(0,1))*(pmat(0,2)-pmat(0,1)) +
            (pmat(1,2)-pmat(1,1))*(pmat(1,2)-pmat(1,1)) );
   d[2] = ( (pmat(0,2)-pmat(0,0))*(pmat(0,2)-pmat(0,0)) +
            (pmat(1,2)-pmat(1,0))*(pmat(1,2)-pmat(1,0)) );

   // if pmat has 3 rows, then use extra term in each sum
   if (pmat.Height()==3)
   {
      d[0] += (pmat(2,1)-pmat(2,0))*(pmat(2,1)-pmat(2,0));
      d[1] += (pmat(2,2)-pmat(2,1))*(pmat(2,2)-pmat(2,1));
      d[2] += (pmat(2,2)-pmat(2,0))*(pmat(2,2)-pmat(2,0));
   }

   if (d[0] >= d[1])
   {
      if (d[0] >= d[2]) { shift = 0; }
      else { shift = 2; }
   }
   else if (d[1] >= d[2]) { shift = 1; }
   else { shift = 2; }

   switch (shift)
   {
      case 0:
         break;
      case 1:
         v = indices[0];
         indices[0] = indices[1];
         indices[1] = indices[2];
         indices[2] = v;
         break;
      case 2:
         v = indices[0];
         indices[0] = indices[2];
         indices[2] = indices[1];
         indices[1] = v;
         break;
   }
}

void Triangle::MarkEdge(const DSTable &v_to_v, const int *length)
{
   int l, L, j, ind[3], i;

   L = length[ v_to_v(indices[0], indices[1]) ]; j = 0;
   if ( (l = length[ v_to_v(indices[1], indices[2]) ]) > L ) { L = l; j = 1; }
   if ( (l = length[ v_to_v(indices[2], indices[0]) ]) > L ) { L = l; j = 2; }

   for (i = 0; i < 3; i++)
   {
      ind[i] = indices[i];
   }

   switch (j)
   {
      case 1:
         indices[0] = ind[1]; indices[1] = ind[2]; indices[2] = ind[0];
         break;
      case 2:
         indices[0] = ind[2]; indices[1] = ind[0]; indices[2] = ind[1];
         break;
   }
}

// static method
void Triangle::GetPointMatrix(unsigned transform, DenseMatrix &pm)
{
   double *a = &pm(0,0), *b = &pm(0,1), *c = &pm(0,2);

   // initialize to identity
   a[0] = 0.0; a[1] = 0.0;
   b[0] = 1.0; b[1] = 0.0;
   c[0] = 0.0; c[1] = 1.0;

   int chain[12], n = 0;
   while (transform)
   {
      chain[n++] = (transform & 7) - 1;
      transform >>= 3;
   }

   /* The transformations and orientations here match
      Mesh::UniformRefinement and Mesh::Bisection for triangles:

          c                      c
           *                      *
           | \                    |\\
           |   \                  | \ \
           |  2  \  e             |  \  \
         f *-------*              |   \   \
           | \   3 | \            |    \    \
           |   \   |   \          |  4  \  5  \
           |  0  \ |  1  \        |      \      \
           *-------*-------*      *-------*-------*
          a        d        b    a        d        b
   */

   double d[2], e[2], f[2];
#define ASGN(a, b) (a[0] = b[0], a[1] = b[1])
#define AVG(a, b, c) (a[0] = (b[0] + c[0])*0.5, a[1] = (b[1] + c[1])*0.5)

   while (n)
   {
      switch (chain[--n])
      {
         case 0: AVG(b, a, b); AVG(c, a, c); break;
         case 1: AVG(a, a, b); AVG(c, b, c); break;
         case 2: AVG(a, a, c); AVG(b, b, c); break;

         case 3:
            AVG(d, a, b); AVG(e, b, c); AVG(f, c, a);
            ASGN(a, e); ASGN(b, f); ASGN(c, d); break;

         case 4:
            AVG(d, a, b); // N.B.: orientation
            ASGN(b, a); ASGN(a, c); ASGN(c, d); break;

         case 5:
            AVG(d, a, b); // N.B.: orientation
            ASGN(a, b); ASGN(b, c); ASGN(c, d); break;

         default:
            MFEM_ABORT("Invalid transform.");
      }
   }
}

void Triangle::GetVertices(Array<int> &v) const
{
   v.SetSize(3);
   for (int i = 0; i < 3; i++)
   {
      v[i] = indices[i];
   }
}

Linear2DFiniteElement TriangleFE;

} // namespace mfem