//
// Triangulate a single face
//
// After the edges of a triangle have been split,
// we need to connect the new (odd) vertices so each
// face is split into four faces. The figure below shows
// one step of that process by adding an edge connecting
// vertices v1 and v3. Once this is complete we will
// update f->e = enew and lather, rinse, repeat.
// We're done when e = e->next->next->next; this
// condition also prevents us from triangulating a
// face that has already been triangulated.
//
// Interestingly enough, this routine will triangulate
// any polygon whether the edges have been split or not.
//
// * : even vertex (old vertices from before edge splitt
// o : odd vertex (created from edge split)
// f : original face
// e = f->e : edge emanating from even vertex
// enew, esym : newly added edge and its symmetric edge
// fnew : newly added face
//
// v2
// *
// / \ . avoiding
// / \ . backslash
// e2 /fnew \ e1 = e->next . as
// / esym \ . last
// v3 o.........o v1 = e1->v . character
// / enew \ . on
// e3 / \ e = f->e . line
// / f \ .
// / \ .
// v4 *---------o---------* v0 = e->v
// v5
public void triangulate(Face f) {
Edge e = E.get(f.e);
Edge e1 = E.get(e.next);
// check to make sure this face isn't already triangular
if (e.i != E.get(E.get(e.next).next).next) {
// done when e == e->next->next->next
do {
Edge e2 = E.get(e1.next);
Edge e3 = E.get(e2.next);
// Edge = {i, sym, v, f, prev, next}
Edge enew = new Edge();
enew.i = E.size();
Edge esym = new Edge();
esym.i = enew.i + 1;
// Face = {i, e}
Face fnew = new Face();
fnew.i = F.size();
fnew.e = e1.i;
// set up esym
esym.sym = enew.i;
esym.v = e3.v;
esym.f = fnew.i;
esym.prev = e2.i;
esym.next = e1.i;
// set up enew
enew.sym = esym.i;
enew.v = e1.v;
enew.f = f.i;
enew.prev = e1.prev;
enew.next = e2.next;
E.add(enew);
E.add(esym);
F.add(fnew);
// clean up loose ends
// e1.prev.next, e2.next.prev, e1.prev, e2.next, e1.f, e2.f
E.get(e1.prev).next = enew.i;
e3.prev = enew.i;
e1.prev = esym.i;
e2.next = esym.i;
e1.f = fnew.i;
e2.f = fnew.i;
f.e = enew.i;
// set e1 and e2 for next step
e1 = e3;
// e2 = E.get(e3.next);
} while (e.i != E.get(E.get(e.next).next).next);
}
}
protected void splitEdge(int e, Vec3 newPos) {
Edge edge = E.get(e);
Edge sym = E.get(edge.sym);
Edge e0 = new Edge();
Edge e1 = new Edge();
Vert v0 = new Vert();
// set indices of new edges + vert
e0.i = E.size();
e1.i = e0.i + 1;
// set up v0
v0.coord = newPos;
v0.i = V.size();
v0.e = e0.i;
V.add(v0);
// set up e0
e0.v = v0.i;
e0.f = edge.f;
e0.next = edge.next;
e0.prev = edge.i;
e0.sym = edge.sym;
// set up e1
e1.v = v0.i;
e1.f = sym.f;
e1.next = sym.next;
e1.prev = edge.sym;
e1.sym = edge.i;
E.add(e0);
E.add(e1);
// clean up connections with e and e.sym
E.get(edge.next).prev = e0.i;
E.get(sym.next).prev = e1.i;
edge.next = e0.i;
sym.next = e1.i;
sym.sym = e0.i;
edge.sym = e1.i;
}
public Mesh(Vec3 verts[], int faces[][]) {
V = new Vector<Vert>(verts.length);
for (int i = 0; i < verts.length; i++) V.addElement(null);
F = new Vector<Face>(faces.length);
for (int i = 0; i < faces.length; i++) F.addElement(null);
int numEdges = 0;
for (int f = 0; f < faces.length; f++) numEdges += faces[f].length;
E = new Vector<Edge>(numEdges);
for (int i = 0; i < numEdges; i++) E.addElement(null);
originalFaceVerts = new Vector<Integer>(faces.length);
originalFaceEdges = new Vector<Integer>(faces.length);
Hashtable<IntPair, Edge> edgeTable = new Hashtable<IntPair, Edge>();
int ei = 0; // base index for group of edges for next face
for (int f = 0; f < faces.length; f++) {
int[] face = faces[f]; // current face
final int N = face.length; // number of edges in face
for (int i = 0; i < N; i++) {
Edge edge = new Edge();
edge.i = ei + i;
final int v = face[i];
final int vnext = face[(i + 1) % N];
IntPair key = new IntPair(vnext, v);
Edge sym = edgeTable.get(key);
if (sym == null) {
key = new IntPair(v, vnext);
edgeTable.put(key, edge);
} else {
edge.sym = sym.i;
sym.sym = ei + i;
}
edge.v = v;
if (V.get(v) == null) {
Vert wvert = new Vert();
wvert.i = v;
wvert.e = edge.i;
wvert.coord = new Vec3(verts[v]);
V.set(v, wvert);
}
edge.f = f;
edge.next = ei + (i + 1) % N;
edge.prev = ei + (i + N - 1) % N;
E.set(edge.i, edge);
}
Face wface = new Face();
wface.i = f;
wface.e = ei;
F.set(f, wface);
ei += N;
}
// ensure mesh is triangular
triangulate();
// get number of original faces
originalFaceCount = F.size();
// get one of each original face's vertices
for (int i = 0; i < originalFaceCount; i++) originalFaceVerts.add(E.get(F.get(i).e).v);
for (int i = 0; i < originalFaceCount; i++) originalFaceEdges.add(F.get(i).e);
// set the normals for the mesh
setNormals();
}