/**
* This returns an enumeration of all Darts in Graph G in a canonical order starting with
* firstDart. The order is canonical in the sense that it only depends on the oriented isomorphism
* class of G (and firstDart). That is, if there is an oriented iso G <-> G' sending firstDart <->
* firstDart', then that bijection will send getDarts <-> getDarts'.
*
* <p>This enumeration is useful in finding explicit bijections of isomorphic graphs.
*/
public static Dart[] getDarts(Dart firstDart, Graph G) {
/**
* Description of algorithm: Return all the couples around V0=firstDart.V, then all couples
* around V1, .... The order for couples around firstDart.V is counterclockwise starting with
* firstDart.F. clockwise around V1,... So we need to order the vertices V0,V1,... and pick the
* first face to use at each vertex and the rest is determined. Order on V0,... = first
* encountered. Order on faces at vertex = first encountered.
*/
distinctFIFO vQueue = new distinctFIFO();
util.ConditionGetter fQueue = new util.ConditionGetter();
fQueue.add(firstDart.getF());
vQueue.put(firstDart.getV());
Collection coups = new ArrayList();
int coupsIndex = 0;
Vertex V;
while ((V = (Vertex) vQueue.remove()) != null) {
Face F = (Face) fQueue.get(new incidence(V));
for (int i = 0; i < V.size(); i++) {
Face Fx = V.next(F, i);
coups.add(new Dart(V, Fx));
vQueue.put(Fx.next(V, 1));
fQueue.add(Fx);
}
}
return (Dart[]) coups.toArray(new Dart[coups.size()]);
}
public void testDart() {
String S = Formatter.testString; // see formatterString.gif
Graph G = Graph.getInstance(new Formatter(S));
Vertex V = null;
int coupleCount = 0;
for (Enumeration E = G.vertexEnumeration(); E.hasMoreElements(); /*--*/ ) {
Vertex W = (Vertex) E.nextElement();
coupleCount += W.size();
if (W.size() == 3) V = W;
}
jassert(V.size() == 3);
Face F = V.getAny();
while (F.size() != 5) F = V.next(F, 1);
jassert(F.size() == 5);
Dart C = new Dart(V, F);
Dart[] list = Dart.getDarts(C, G);
// compute the expected number of return values;
jassert(list.length == coupleCount);
jassert(list[0].getV() == C.getV());
jassert(list[0].getF() == C.getF());
// check integrity of each couple.
for (int i = 0; i < list.length; i++) {
V = list[i].getV();
F = list[i].getF();
jassert(V.next(F, 0) == F);
jassert(F.next(V, 0) == V);
}
// check that all couples are distinct.
Hashtable table = new Hashtable(); // { V-> set of F }
for (Enumeration E = G.vertexEnumeration(); E.hasMoreElements(); /*--*/ ) {
V = (Vertex) E.nextElement();
table.put(V, new HashSet());
}
for (int i = 0; i < list.length; i++) {
V = list[i].getV();
F = list[i].getF();
HashSet H = (HashSet) table.get(V);
jassert(!H.contains(F));
H.add(F);
}
}
public boolean check(Object A) {
Face F = (Face) A;
return (V.next(F, 0) == F); // note: V.next(F,0)==F iff V lies on F.
}