public static QuiverWithPotential <int> GetEvenFlowerType1QP(int numVerticesInCenterPolygon, int firstVertex = DefaultFirstVertex)
{
if (!EvenFlowerType1ParameterIsValid(numVerticesInCenterPolygon))
{
throw new ArgumentOutOfRangeException(nameof(numVerticesInCenterPolygon));
}
int numLayers = UsefulQuivers.GetNumberOfLayersInEvenFlowerType1Quiver(numVerticesInCenterPolygon);
int numVerticesInFullInnerLayer = 2 * numVerticesInCenterPolygon;
int numVerticesInOuterLayer = 3 * numVerticesInCenterPolygon;
var potential = new Potential <int>();
// Center polygon
potential = potential.AddCycle(new DetachedCycle <int>(Enumerable.Range(firstVertex, numVerticesInCenterPolygon).AppendElement(firstVertex)), +1);
// Full inner layers
if (numLayers > 2)
{
// First layer (the squares and triangles between the first and second layers)
var curLayer = GetLayerVertices(0);
var nextLayer = GetLayerVertices(1);
for (int indexInLayer = 0; indexInLayer < numVerticesInCenterPolygon; indexInLayer++)
{
var triangleVertices = new int[] { curLayer[indexInLayer], nextLayer[2 * indexInLayer - 1], nextLayer[2 * indexInLayer], curLayer[indexInLayer] };
potential = potential.AddCycle(new DetachedCycle <int>(triangleVertices), +1);
var squareVertices = new int[] { curLayer[indexInLayer], curLayer[indexInLayer + 1], nextLayer[2 * indexInLayer + 1], nextLayer[2 * indexInLayer], curLayer[indexInLayer] };
potential = potential.AddCycle(new DetachedCycle <int>(squareVertices), -1);
}
// Remaining layers (only squares)
for (int layerIndex = 1; layerIndex < numLayers - 2; layerIndex++) // 0-based layer index
{
curLayer = GetLayerVertices(layerIndex);
nextLayer = GetLayerVertices(layerIndex + 1);
for (int indexInLayer = 0; indexInLayer < numVerticesInFullInnerLayer; indexInLayer++)
{
int sign = (layerIndex + indexInLayer).Modulo(2) == 1 ? +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);
}
}
}
// Outer layer
{
int layerIndex = numLayers - 2;
var curLayer = GetLayerVertices(layerIndex);
var nextLayer = GetLayerVertices(layerIndex + 1);
if (numLayers == 2)
{
// Add pentagons and triangle in this degenerate case
for (int indexInLayer = 0; indexInLayer < curLayer.Count; indexInLayer++)
{
var triangleVertices = new int[] { curLayer[indexInLayer], nextLayer[3 * indexInLayer - 1], nextLayer[3 * indexInLayer], curLayer[indexInLayer] };
potential = potential.AddCycle(new DetachedCycle <int>(triangleVertices), +1);
var pentagonVertices = new int[] { curLayer[indexInLayer], curLayer[indexInLayer + 1], nextLayer[3 * indexInLayer + 2], nextLayer[3 * indexInLayer + 1], nextLayer[3 * indexInLayer], curLayer[indexInLayer] };
potential = potential.AddCycle(new DetachedCycle <int>(pentagonVertices), -1);
}
}
else
{
// Add pentagons and squares in the non-degenerate case
for (int indexInCenterLayer = 0; indexInCenterLayer < numVerticesInCenterPolygon; indexInCenterLayer++)
{
// Add pentagon
int indexInPenultimateLayer = 2 * indexInCenterLayer;
int indexInUltimateLayer = 3 * indexInCenterLayer;
int pentagonSign = layerIndex.Modulo(2) == 1 ? +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>(GetVerticesInEvenFlowerType1QPLayer(numVerticesInCenterPolygon, layerIndex, firstVertex));
}
public static int GetNumberOfLayersInEvenFlowerType1QP(int numVerticesInCenterPolygon) => UsefulQuivers.GetNumberOfLayersInEvenFlowerType1Quiver(numVerticesInCenterPolygon);
