private void Triangulate()
{
// From O'Rourke (1994) Computational Geometry in C, section 2.1
// Monotone Partitioning
// To identify the chains: The vertices in each chain of a monotone
// polygon are sorted with respect to the line of monotonicity [y-axis].
// Then the vertices can be sorted by the y-axis in linear time: Find a
// Highest vertex, find a lowest, and partition the boundary between the two
// chains. The vertices in each chain are sorted with respect to y.
// Two sorted lists of vertices can be merged in linear time into one list
// sorted by y.
Debug.Assert(face.EdgeCount > 3);
var vertices = face.Vertices.Cast <TVertex>();
IComparer <Point2D> pointComparer = new HighYLowXComparer();
// TODO: Replace with Transform extension method. Consider removing transform comparer
IComparer <TVertex> vertexComparer = new TransformComparer <TVertex, Point2D>(pointComparer, v => v.Position);
Pair <TVertex, TVertex> minMax = vertices.MinMax(vertexComparer);
meshUtilities = new MonotoneMeshUtilities <TVertex>(pointComparer);
LeftToRightEdgeComparer xEdgeComparer = new LeftToRightEdgeComparer();
sweeplineUtilities = new SweeplineUtilities(xEdgeComparer);
// Assign each vertex to the left or right chain
IEnumerable <ChainVertex> leftChainReversed = TraceLeftAndUp(minMax.First);
IEnumerable <ChainVertex> leftChain = leftChainReversed.Reverse();
IEnumerable <ChainVertex> rightChain = TraceRightAndDown(minMax.Second);
// From Berg et al (2000) Computational Geometry Algorithms and Applications
// 1. Merge the vertices on the right chain with those on the left
// chain into one sequence sorted on decreasing y-coordinate. If
// two vertices have the same y-coordinate the left one comes first.
// Let u1 to un denote the sorted sequence.
IComparer <ChainVertex> chainVertexComparer = vertexComparer.Transform <ChainVertex, TVertex>(p => p.Vertex).Invert();
IEnumerable <ChainVertex> mergedVertices = rightChain.MergeSorted(leftChain, chainVertexComparer);
List <ChainVertex> u = new List <ChainVertex>(mergedVertices);
// 2. Initialize an empty stack and push u1 and u2 onto it
// This stack contains all the vertices of the polygon that have
// already been encountered, but which may require additional diagonals
Stack <ChainVertex> stack = new Stack <ChainVertex>();
stack.Push(u[0]);
stack.Push(u[1]);
for (int j = 2; j < u.Count - 1; ++j)
{
// If u[j] and the vertext on top of the stack are of different chains
if (u[j].Chain != stack.Peek().Chain)
{
// Insert a diagonal from u[j] to each popped vertex...
// We progessively subdivide the new faces created by the splitting
// so we must keep track of which face to split
FaceBase faceToSplit = face;
while (stack.Count > 1)
{
TEdge edge = splitFace(mesh, faceToSplit, u[j], stack.Pop());
faceToSplit = edge.Faces.First; // First is always the new face
}
// ... except the last one
if (stack.Count > 0)
{
stack.Pop();
}
// Push u j-1 and uj onto the stack
stack.Push(u[j - 1]);
stack.Push(u[j]);
}
else
{
// Pop one vertex from the stack; this vertex is already connected
ChainVertex previous = stack.Pop();
// We progressively split triangles from the original face
TFace faceToSplit = face;
while (stack.Count > 0 && CanInsertDiagonal(u[j], stack.Peek(), previous))
{
previous = stack.Pop();
splitFace(mesh, faceToSplit, u[j], previous);
}
// Push the last vertex popped back onto the stack
stack.Push(previous);
// Push uj onto the stack
stack.Push(u[j]);
}
}
// Add diagonals from un to all vertices except the first and last one
stack.Pop();
// Which chain is the stack of vertices on - affects which face we split
Chain stackChain = stack.Peek().Chain;
FaceBase finalFaceToSplit = face;
while (stack.Count > 1)
{
TEdge edge = splitFace(mesh, finalFaceToSplit, u[u.Count - 1], stack.Pop());
finalFaceToSplit = stackChain == Chain.Left ? edge.Faces.First : edge.Faces.Second;
}
Debug.Assert(stack.Count == 1);
triangulated = true;
}