public static QuiverWithPotential <int> GetPointedFlowerQP(int numPeriods, int firstVertex = DefaultFirstVertex)
{
if (!PointedFlowerParameterIsValid(numPeriods))
{
throw new ArgumentOutOfRangeException(nameof(numPeriods));
}
int numLayers = UsefulQuivers.GetNumberOfLayersInPointedFlowerQuiver(numPeriods);
int numVerticesInFullInnerLayer = 2 * numPeriods;
int numVerticesInOuterLayer = 3 * numPeriods;
var potential = new Potential <int>();
if (numLayers == 2)
{
int centerVertex = GetLayerVertices(0).Single();
var nextLayer = GetLayerVertices(1);
for (int periodIndex = 0; periodIndex < numPeriods; periodIndex++)
{
int indexInNextLayer = 3 * periodIndex;
// Square
var positiveCycleVertices = new int[] { centerVertex, nextLayer[indexInNextLayer], nextLayer[indexInNextLayer + 1], nextLayer[indexInNextLayer + 2], centerVertex };
// Triangle
var negativeCycleVertices = new int[] { centerVertex, nextLayer[indexInNextLayer + 3], nextLayer[indexInNextLayer + 2], centerVertex };
potential = potential.AddCycle(new DetachedCycle <int>(positiveCycleVertices), +1);
potential = potential.AddCycle(new DetachedCycle <int>(negativeCycleVertices), -1);
}
return(new QuiverWithPotential <int>(potential));
}
// Polygons between first and second layer
{
int centerVertex = GetLayerVertices(0).Single();
var nextLayer = GetLayerVertices(1);
for (int periodIndex = 0; periodIndex < numPeriods; periodIndex++)
{
int indexInNextLayer = 2 * periodIndex;
// Triangles
var positiveCycleVertices = new int[] { centerVertex, nextLayer[indexInNextLayer], nextLayer[indexInNextLayer + 1], centerVertex };
var negativeCycleVertices = new int[] { centerVertex, nextLayer[indexInNextLayer + 2], nextLayer[indexInNextLayer + 1], centerVertex };
potential = potential.AddCycle(new DetachedCycle <int>(positiveCycleVertices), +1);
potential = potential.AddCycle(new DetachedCycle <int>(negativeCycleVertices), -1);
}
}
// Cobweb layers
for (int layerIndex = 1; layerIndex < numLayers - 2; layerIndex++) // 0-based layer index
{
var curLayer = GetLayerVertices(layerIndex);
var nextLayer = GetLayerVertices(layerIndex + 1);
for (int indexInLayer = 0; indexInLayer < numVerticesInFullInnerLayer; indexInLayer++)
{
int sign = (layerIndex + indexInLayer).Modulo(2) == 0 ? +1 : -1;
var squareVertices = sign == +1 ?
new int[] { curLayer[indexInLayer + 1], curLayer[indexInLayer], nextLayer[indexInLayer], nextLayer[indexInLayer + 1], curLayer[indexInLayer + 1] } :
new int[] { curLayer[indexInLayer], curLayer[indexInLayer + 1], nextLayer[indexInLayer + 1], nextLayer[indexInLayer], curLayer[indexInLayer] };
potential = potential.AddCycle(new DetachedCycle <int>(squareVertices), sign);
}
}
// Outermost layer of polygons
{
int layerIndex = numLayers - 2;
var curLayer = GetLayerVertices(layerIndex);
var nextLayer = GetLayerVertices(layerIndex + 1);
for (int indexInPeriod = 0; indexInPeriod < numPeriods; indexInPeriod++)
{
// Add pentagon
int indexInPenultimateLayer = 2 * indexInPeriod;
int indexInUltimateLayer = 3 * indexInPeriod;
int pentagonSign = layerIndex.Modulo(2) == 0 ? +1 : -1; // Remember that layerIndex is the index of the *penultimate* layer
var pentagonVertices = pentagonSign == +1 ?
new int[] { curLayer[indexInPenultimateLayer + 1], curLayer[indexInPenultimateLayer], nextLayer[indexInUltimateLayer], nextLayer[indexInUltimateLayer + 1], nextLayer[indexInUltimateLayer + 2], curLayer[indexInPenultimateLayer + 1] } :
new int[] { curLayer[indexInPenultimateLayer], curLayer[indexInPenultimateLayer + 1], nextLayer[indexInUltimateLayer + 2], nextLayer[indexInUltimateLayer + 1], nextLayer[indexInUltimateLayer], curLayer[indexInPenultimateLayer] };
potential = potential.AddCycle(new DetachedCycle <int>(pentagonVertices), pentagonSign);
// Add square
int squareSign = -pentagonSign;
indexInPenultimateLayer += 1;
indexInUltimateLayer += 2;
var squareVertices = squareSign == +1 ?
new int[] { curLayer[indexInPenultimateLayer + 1], curLayer[indexInPenultimateLayer], nextLayer[indexInUltimateLayer], nextLayer[indexInUltimateLayer + 1], curLayer[indexInPenultimateLayer + 1] } :
new int[] { curLayer[indexInPenultimateLayer], curLayer[indexInPenultimateLayer + 1], nextLayer[indexInUltimateLayer + 1], nextLayer[indexInUltimateLayer], curLayer[indexInPenultimateLayer] };
potential = potential.AddCycle(new DetachedCycle <int>(squareVertices), squareSign);
}
}
var qp = new QuiverWithPotential <int>(potential);
return(qp);
CircularList <int> GetLayerVertices(int layerIndex)
=> new CircularList <int>(GetVerticesInPointedFlowerQPLayer(numPeriods, layerIndex, firstVertex));
}
public static int GetNumberOfLayersInPointedFlowerQP(int numPeriods) => UsefulQuivers.GetNumberOfLayersInPointedFlowerQuiver(numPeriods);
