void Subdivision::InsertSite(const Point2d& x)
// Inserts a new point into a subdivision representing a Delaunay
// triangulation, and fixes the affected edges so that the result
// is still a Delaunay triangulation. This is based on the
// pseudocode from Guibas and Stolfi (1985) p.120, with slight
// modifications and a bug fix.
{
Edge* e = Locate(x);
if ((x == e->Org2d()) || (x == e->Dest2d())) // point is already in
return;
else if (OnEdge(x, e)) {
e = e->Oprev();
DeleteEdge(e->Onext());
}
// Connect the new point to the vertices of the containing
// triangle (or quadrilateral, if the new point fell on an
// existing edge.)
Edge* base = MakeEdge();
base->EndPoints(e->Org(), new Point2d(x));
Splice(base, e);
startingEdge = base;
do {
base = Connect(e, base->Sym());
e = base->Oprev();
} while (e->Lnext() != startingEdge);
// Examine suspect edges to ensure that the Delaunay condition
// is satisfied.
do {
Edge* t = e->Oprev();
if (RightOf(t->Dest2d(), e) &&
InCircle(e->Org2d(), t->Dest2d(), e->Dest2d(), x)) {
Swap(e);
e = e->Oprev();
}
else if (e->Onext() == startingEdge) // no more suspect edges
return;
else // pop a suspect edge
e = e->Onext()->Lprev();
} while (TRUE);
}
Edge* Subdivision::Locate(const Point2d& x)
// Returns an edge e, s.t. either x is on e, or e is an edge of
// a triangle containing x. The search starts from startingEdge
// and proceeds in the general direction of x. Based on the
// pseudocode in Guibas and Stolfi (1985) p.121.
{
Edge* e = startingEdge;
while (TRUE) {
if (x == e->Org2d() || x == e->Dest2d())
return e;
else if (RightOf(x, e))
e = e->Sym();
else if (!RightOf(x, e->Onext()))
e = e->Onext();
else if (!RightOf(x, e->Dprev()))
e = e->Dprev();
else
return e;
}
}