// v1 and v2 successive vertices must be along a boundary, with the Halfedge from v1 to v2 having no face (on the left).
// Then we create a new vertex 'outside' the boundary, create new edges and a face
// \ / /
// \/ old e / old edge
// v2 o <-----o v1
// \ new /
// new \ f / new edge
// edge \ / no face here...
// o v3
public Face CreateTriangle(Vertex v1,
Vertex v2,
TVertexTraits vt3 = default(TVertexTraits),
TFaceTraits ft = default(TFaceTraits))
{
Halfedge e12 = v1.HalfedgeTo(v2);
Halfedge e21 = e12.Opposite;
// Checks adjacency condition
if (e12 == null)
{
throw new InvalidOperationException("v1 and v2 must be neighbors - but no Halfedge found!");
}
if (e12.Face != null)
{
throw new InvalidOperationException("Halfedge from v1 to v2 must be a boundary - but a face was found for the Halfedge!");
}
var v3 = CreateVertex(vt3);
var e23 = CreateEdgeInvalid(v2, v3);
var e32 = e23.Opposite;
var e31 = CreateEdgeInvalid(v3, v1);
var e13 = e31.Opposite;
// New vertex won't have an Outgoing yet - e32 is good - it will be a boundary Halfedge
v3.Outgoing = e32;
// Fix v1 Outgoing to maintain Vertex boundary condition
v1.Outgoing = e13;
// This is the tricky part - updating the Halfedge adjacencies
e32.Next = e12.Next;
e13.Previous = e12.Previous;
e12.Previous.Next = e13;
e12.Next.Previous = e32;
e12.Next = e23;
e12.Previous = e31;
e32.Previous = e13;
e13.Next = e32;
e23.Previous = e12;
e23.Next = e31;
e31.Previous = e23;
e31.Next = e12;
// This will go around fixing up the faces along the ring of halfedges.
var f = CreateFace(e12, ft);
e12.AssertValid();
e21.AssertValid();
e23.AssertValid();
e32.AssertValid();
e31.AssertValid();
e13.AssertValid();
AssertValid();
return(f);
}