public static QuiverWithPotential <int> GetTriangleQP(int numRows, int firstVertex = DefaultFirstVertex)
{
if (!TriangleParameterIsValid(numRows))
{
throw new ArgumentOutOfRangeException(nameof(numRows));
}
if (numRows == 1)
{
var quiver = UsefulQuivers.GetTriangleQuiver(numRows, firstVertex);
return(new QuiverWithPotential <int>(quiver, new Potential <int>()));
}
var potential = new Potential <int>();
var curRowVertices = new List <int>()
{
firstVertex
};
int nextVertex = firstVertex + 1;
for (int rowIndex = 1; rowIndex <= numRows - 1; rowIndex++) // 1-based row index
{
var nextRowVertices = Enumerable.Range(nextVertex, rowIndex + 1).ToList();
nextVertex += rowIndex + 1;
// (2*rowIndex - 1) triangles to add. Draw a small triangle QP to realize that
// the cycles below are the ones to add.
for (int indexInRow = 0; indexInRow < rowIndex; indexInRow++)
{
var cycleVertices = new int[] { curRowVertices[indexInRow], nextRowVertices[indexInRow + 1], nextRowVertices[indexInRow], curRowVertices[indexInRow] };
potential = potential.AddCycle(new DetachedCycle <int>(cycleVertices), +1); // Positive for clockwise cycles.
}
for (int indexInRow = 0; indexInRow < rowIndex - 1; indexInRow++)
{
var cycleVertices = new int[] { curRowVertices[indexInRow + 1], curRowVertices[indexInRow], nextRowVertices[indexInRow + 1], curRowVertices[indexInRow + 1] };
potential = potential.AddCycle(new DetachedCycle <int>(cycleVertices), -1); // Negative for counterclockwise cycles.
}
curRowVertices = nextRowVertices;
}
var qp = new QuiverWithPotential <int>(potential);
return(qp);
}