Example #1
  Relaxes the vertex v to a new position
  We will store v's new relaxed position as the oddVertexData
  We only relax non-boundary vertices
  PRE: v has an even generation
       v is not a boundary edge
void TriangleMesh::relaxVertex(Vertex& v) {
  if (v.isBoundary())

  Vertex::iterator vitr = v.current();

  //The (elementwise) sum of the vertices around v.
  VertexData vertexSum;

  int vertexCounter = 0;

  for(; !vitr.isDone(); ++vitr) {  
    vertexSum = vertexSum + vitr->next->vertex->getData();

  //the combination value alpha, as determined by the sqrt(3) algorithm.
  float alpha = (4 - 2*cos(2*Globals::PI/vertexCounter) )/9.0f;

  //Save the new, relaxed value in the "odd" Vertex Data 
  v.addOddData(v.getData()*(1-alpha) + vertexSum*(alpha/vertexCounter));