Subdivision::Subdivision(const Point2d& a, const Point2d& b, const Point2d& c)
// Initialize a subdivision to the triangle defined by the points a, b, c.
{
Point2d *da, *db, *dc;
da = new Point2d(a), db = new Point2d(b), dc = new Point2d(c);
Edge* ea = MakeEdge();
ea->EndPoints(da, db);
Edge* eb = MakeEdge();
Splice(ea->Sym(), eb);
eb->EndPoints(db, dc);
Edge* ec = MakeEdge();
Splice(eb->Sym(), ec);
ec->EndPoints(dc, da);
Splice(ec->Sym(), ea);
startingEdge = ea;
}
Edge *Subdivision::connect(Edge *a, Edge *b)
{
Edge *e = makeEdge();
splice(e, a->Lnext());
splice(e->Sym(), b);
e->EndPoints(a->Dest(), b->Org());
return e;
}
Edge* Connect(Edge* a, Edge* b)
// Add a new edge e connecting the destination of a to the
// origin of b, in such a way that all three have the same
// left face after the connection is complete.
// Additionally, the data pointers of the new edge are set.
{
Edge* e = MakeEdge();
Splice(e, a->Lnext());
Splice(e->Sym(), b);
e->EndPoints(a->Dest(), b->Org());
return e;
}
void Subdivision::initMesh(const Vec2& A,const Vec2& B,
const Vec2& C,const Vec2& D)
{
Vec2& a = A.clone();
Vec2& b = B.clone();
Vec2& c = C.clone();
Vec2& d = D.clone();
Edge *ea = makeEdge();
ea->EndPoints(a, b);
Edge *eb = makeEdge();
splice(ea->Sym(), eb);
eb->EndPoints(b, c);
Edge *ec = makeEdge();
splice(eb->Sym(), ec);
ec->EndPoints(c, d);
Edge *ed = makeEdge();
splice(ec->Sym(), ed);
ed->EndPoints(d, a);
splice(ed->Sym(), ea);
Edge *diag = makeEdge();
splice(ed->Sym(),diag);
splice(eb->Sym(),diag->Sym());
diag->EndPoints(a,c);
startingEdge = ea;
first_face = NULL;
makeFace(ea->Sym()).update(*this);
makeFace(ec->Sym()).update(*this);
}
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::makeEdge(Vec2& org, Vec2& dest)
{
Edge *e = new Edge();
e->EndPoints(org, dest);
return e;
}