/**
* splits the facet incident to h and g into two facets with a new diagonal between the two
* vertices denoted by h and g respectively. The second (new) facet is a copy of the first facet.
* Returns h->next() after the operation, i.e., the new diagonal. The new face is to the right of
* the new diagonal, the old face is to the left. The time is proportional to the distance from h
* to g around the facet.
*/
public Halfedge splitFacet(Halfedge h, Halfedge g) {
if (h == null || g == null) throw new Error("splitFacet: null pointer");
if (h.face != g.face) throw new Error("splitFacet: different incident facets");
if (h == g || h.next == g || g.next == h) {
throw new Error("loops and multiple edges are not allowed");
}
Halfedge<X> newDiagonal = new Halfedge<X>();
Halfedge<X> oppositeNewDiagonal = new Halfedge<X>();
Face<X> newFace = new Face<X>();
newFace.halfedge = g;
newDiagonal.opposite = oppositeNewDiagonal;
oppositeNewDiagonal.opposite = newDiagonal;
newDiagonal.face = h.face;
oppositeNewDiagonal.face = newFace;
// a completer
Halfedge p = h.next;
while (p != g) {
p.face = newFace;
p = p.next;
}
h.next = newDiagonal;
g.next = oppositeNewDiagonal;
return newDiagonal;
}
public int vertexDegree(Vertex v) {
int result = 0;
Halfedge e = v.getHalfedge();
Halfedge pEdge = e.getNext().getOpposite();
while (pEdge != e) {
pEdge = pEdge.getNext().getOpposite();
result++;
}
return result + 1;
}
public Halfedge<X> makeHole(Halfedge h) {
if (h == null || h.face == null) throw new Error("error making hole: h or h.face null");
this.facets.remove(h.getFace());
Halfedge p = h.next;
h.face = null;
int cont = 1;
while (p != h) {
p.face = null;
p = p.next;
}
return h;
}
public void createCenterVertex(Face<X> f) {
int degree = f.degree();
Point_[] neighbors = new Point_[degree];
Halfedge<X> e = f.getEdge();
neighbors[0] = e.getVertex().getPoint();
for (int i = 1; i < degree; i++) {
e = e.getNext();
neighbors[i] = e.getVertex().getPoint();
}
Point_ centerVertex;
if (neighbors[0].dimension() == 2) centerVertex = new Point_2();
else if (neighbors[0].dimension() == 3) centerVertex = new Point_3();
else throw new Error("error point dimension");
}
public Halfedge<X> fillHole(Halfedge h) {
if (h.face != null) throw new Error("error filling hole: h not boundary edge");
Face<X> newFace = new Face<X>();
this.facets.add(newFace);
newFace.setEdge(h);
Halfedge p = h.next;
h.face = newFace;
int cont = 1;
while (p != h) {
p.face = newFace;
p = p.next;
}
return h;
}
public String facesToString() {
String result = "List of faces\n";
Iterator it = this.facets.iterator();
int cont = 0;
while (it.hasNext()) {
Face<X> f = (Face<X>) it.next();
result = result + "f" + cont + " ";
Halfedge<X> e = f.getEdge();
while (e.getNext() != f.getEdge()) {
result = result + vertices.indexOf(e.getVertex()) + " ";
e = e.getNext();
}
result = result + vertices.indexOf(e.getVertex()) + "\n";
cont++;
}
return result;
}
/**
* a triangle with border edges is added to the polyhedral surface. Returns a non-border halfedge
* of the triangle.
*/
public Halfedge<X> makeTriangle(X p1, X p2, X p3) {
Face<X> newFace = new Face<X>();
Vertex<X> newVertex1 = new Vertex<X>(p1);
Vertex<X> newVertex2 = new Vertex<X>(p2);
Vertex<X> newVertex3 = new Vertex<X>(p3);
Halfedge<X> e1 = new Halfedge<X>();
Halfedge<X> e2 = new Halfedge<X>();
Halfedge<X> e3 = new Halfedge<X>();
Halfedge<X> e1Opp = new Halfedge<X>();
Halfedge<X> e2Opp = new Halfedge<X>();
Halfedge<X> e3Opp = new Halfedge<X>();
// setting the new face
newFace.setEdge(e1);
// setting the new vertices (LCA: a' controler)
newVertex1.setEdge(e2);
newVertex2.setEdge(e3);
newVertex3.setEdge(e1);
// setting e1
e1.setFace(newFace);
e1.setVertex(newVertex1);
e1.setPrev(e3);
e1.setNext(e2);
e1.setOpposite(e1Opp);
// setting e2
e2.setFace(newFace);
e2.setVertex(newVertex2);
e2.setPrev(e1);
e2.setNext(e3);
e2.setOpposite(e2Opp);
// setting e3
e3.setFace(newFace);
e3.setVertex(newVertex3);
e3.setPrev(e2);
e3.setNext(e1);
e3.setOpposite(e3Opp);
// setting e1Opp (boundary halfedge opposite to e1)
e1Opp.setFace(null);
e1Opp.setVertex(newVertex3);
e1Opp.setPrev(e2Opp);
e1Opp.setNext(e3Opp);
e1Opp.setOpposite(e1);
// setting e2Opp (boundary halfedge opposite to e2)
e2Opp.setFace(null);
e2Opp.setVertex(newVertex1);
e2Opp.setPrev(e3Opp);
e2Opp.setNext(e1Opp);
e2Opp.setOpposite(e2);
// setting e3Opp (boundary halfedge opposite to e3)
e3Opp.setFace(null);
e3Opp.setVertex(newVertex2);
e3Opp.setPrev(e1Opp);
e3Opp.setNext(e2Opp);
e3Opp.setOpposite(e3);
this.facets.add(newFace);
this.vertices.add(newVertex1);
this.vertices.add(newVertex2);
this.vertices.add(newVertex3);
this.halfedges.add(e1);
this.halfedges.add(e1Opp);
this.halfedges.add(e2);
this.halfedges.add(e2Opp);
this.halfedges.add(e3);
this.halfedges.add(e3Opp);
return e1;
}
/**
* creates a new triangle facet within the hole incident to h by connecting the tip of h with two
* new halfedges and a new vertex. Returns the halfedge of the new edge that is incident to the
* new facet and the new vertex.
*/
public Halfedge<X> addTriangleToBorder(Halfedge h, X point) {
if (h.face != null) throw new Error("no border edge");
System.out.println("adding triangle to " + h);
Face<X> newFace = new Face<X>();
Vertex<X> newVertex = new Vertex<X>(point);
Halfedge<X> hPrev = new Halfedge<X>();
Halfedge<X> hNext = new Halfedge<X>();
Halfedge<X> hPrevOpp = new Halfedge<X>();
Halfedge<X> hNextOpp = new Halfedge<X>();
// setting the new face
newFace.setEdge(h);
// setting hPrev (halfedge preceding h in the new face)
hPrev.setFace(newFace);
hPrev.setVertex(h.getOpposite().getVertex());
hPrev.setPrev(hNext);
hPrev.setNext(h);
hPrev.setOpposite(hPrevOpp);
// setting hNext (halfedge following h in the new face)
hNext.setFace(newFace);
hNext.setVertex(newVertex);
hNext.setPrev(h);
hNext.setNext(hPrev);
hNext.setOpposite(hNextOpp);
// setting hPrevOpp (new boundary halfedge)
hPrevOpp.setFace(null);
hPrevOpp.setVertex(newVertex);
hPrevOpp.setPrev(h.getPrev());
hPrevOpp.setNext(hNextOpp);
hPrevOpp.setOpposite(hPrev);
// setting hNextOpp (the other new boundary halfedge)
hNextOpp.setFace(null);
hNextOpp.setVertex(h.getVertex());
hNextOpp.setPrev(hPrevOpp);
hNextOpp.setNext(h.getNext());
hNextOpp.setOpposite(hNext);
// updating old boundary halfedge informations
h.setFace(newFace);
h.setPrev(hPrev);
h.setNext(hNext);
// setting newVertex
newVertex.setEdge(hPrev); // LCA: a controler si c'est hPrev ou hNext
// adding new facet, vertex and the four halfedges
this.vertices.add(newVertex);
this.facets.add(newFace);
this.halfedges.add(hPrev);
this.halfedges.add(hNext);
this.halfedges.add(hPrevOpp);
this.halfedges.add(hNextOpp);
return hNext;
}
/**
* returns true if the polyhedral surface is combinatorially consistent. If borders==true
* normalization of the border edges is checked too. This method checks that each facet is at
* least a triangle and that the two incident facets of a non-border edge are distinct.
*/
public boolean isValid(boolean borders) {
boolean valid = true;
System.out.print("Checking Polyhedron...");
int n = this.vertices.size();
int e = this.halfedges.size();
int f = this.facets.size();
for (int i = 0; i < this.halfedges.size(); i++) {
Halfedge<X> pedge = this.halfedges.get(i);
if (pedge.getOpposite() == null) {
System.out.print("error opposite: " + i);
valid = false;
// Face face=pedge.getFace();
// int[] ind=face.getVertexIndices(this);
// System.out.println(" "+ind[0]+" "+ind[1]+" "+ind[2]);
}
if (pedge.getNext() == null) {
System.out.println("error next_edge: " + i);
valid = false;
}
if (pedge.getPrev() == null) {
System.out.println("error prev_edge: " + i);
valid = false;
}
if (pedge.getVertex() == null) {
System.out.println("error vertex: " + i);
valid = false;
}
if (pedge.opposite != null && pedge.face == pedge.getOpposite().face) {
System.out.println("error edge: " + i);
valid = false;
}
}
for (int i = 0; i < this.facets.size(); i++) {
Face<X> pface = this.facets.get(i);
if (pface == null) {
System.out.println("error face pointer");
valid = false;
}
if (pface.halfedge == null) {
System.out.println("error face.halfedge");
valid = false;
}
if (pface.degree() < 3) {
System.out.println("error face degree");
return valid = false;
}
}
for (int i = 0; i < this.vertices.size(); i++) {
Vertex<X> pvertex = this.vertices.get(i);
// System.out.println(""+pvertex.toString());
if (pvertex == null) {
System.out.println("error vertex pointer:" + i);
valid = false;
}
if (pvertex.halfedge == null) {
System.out.println("error vertex.halfedge: " + i);
valid = false;
}
if (pvertex.getPoint() == null) {
System.out.println("error vertex.point: " + i);
valid = false;
}
}
if (valid == true) System.out.println("ok");
else System.out.println("not valid");
System.out.print("n: " + n + " e: " + e / 2 + " f: " + f + " - ");
int g = -(n - e / 2 + f - 2) / 2;
System.out.println("genus: " + g);
return valid;
}
private void fortunesAlgorithm() {
Site newSite, bottomSite, topSite, tempSite;
Vertex v, vertex;
Point newintstar = null;
LR leftRight;
Halfedge lbnd, rbnd, llbnd, rrbnd, bisector;
Edge edge;
Rectangle dataBounds = _sites.getSitesBounds();
int sqrt_nsites = (int) Math.sqrt(_sites.get_length() + 4);
HalfedgePriorityQueue heap =
new HalfedgePriorityQueue(dataBounds.y, dataBounds.height, sqrt_nsites);
EdgeList edgeList = new EdgeList(dataBounds.x, dataBounds.width, sqrt_nsites);
ArrayList<Halfedge> halfEdges = new ArrayList();
ArrayList<Vertex> vertices = new ArrayList();
Site bottomMostSite = _sites.next();
newSite = _sites.next();
for (; ; ) {
if (heap.empty() == false) {
newintstar = heap.min();
}
if (newSite != null && (heap.empty() || compareByYThenX(newSite, newintstar) < 0)) {
/* new site is smallest */
// trace("smallest: new site " + newSite);
// Step 8:
lbnd =
edgeList.edgeListLeftNeighbor(
newSite.get_coord()); // the Halfedge just to the left of newSite
// trace("lbnd: " + lbnd);
rbnd = lbnd.edgeListRightNeighbor; // the Halfedge just to the right
// trace("rbnd: " + rbnd);
bottomSite = rightRegion(lbnd, bottomMostSite); // this is the same as leftRegion(rbnd)
// this Site determines the region containing the new site
// trace("new Site is in region of existing site: " + bottomSite);
// Step 9:
edge = Edge.createBisectingEdge(bottomSite, newSite);
// trace("new edge: " + edge);
_edges.add(edge);
bisector = Halfedge.create(edge, LR.LEFT);
halfEdges.add(bisector);
// inserting two Halfedges into edgeList constitutes Step 10:
// insert bisector to the right of lbnd:
edgeList.insert(lbnd, bisector);
// first half of Step 11:
if ((vertex = Vertex.intersect(lbnd, bisector)) != null) {
vertices.add(vertex);
heap.remove(lbnd);
lbnd.vertex = vertex;
lbnd.ystar = vertex.get_y() + newSite.dist(vertex);
heap.insert(lbnd);
}
lbnd = bisector;
bisector = Halfedge.create(edge, LR.RIGHT);
halfEdges.add(bisector);
// second Halfedge for Step 10:
// insert bisector to the right of lbnd:
edgeList.insert(lbnd, bisector);
// second half of Step 11:
if ((vertex = Vertex.intersect(bisector, rbnd)) != null) {
vertices.add(vertex);
bisector.vertex = vertex;
bisector.ystar = vertex.get_y() + newSite.dist(vertex);
heap.insert(bisector);
}
newSite = _sites.next();
} else if (heap.empty() == false) {
/* intersection is smallest */
lbnd = heap.extractMin();
llbnd = lbnd.edgeListLeftNeighbor;
rbnd = lbnd.edgeListRightNeighbor;
rrbnd = rbnd.edgeListRightNeighbor;
bottomSite = leftRegion(lbnd, bottomMostSite);
topSite = rightRegion(rbnd, bottomMostSite);
// these three sites define a Delaunay triangle
// (not actually using these for anything...)
// _triangles.push(new Triangle(bottomSite, topSite, rightRegion(lbnd)));
v = lbnd.vertex;
v.setIndex();
lbnd.edge.setVertex(lbnd.leftRight, v);
rbnd.edge.setVertex(rbnd.leftRight, v);
edgeList.remove(lbnd);
heap.remove(rbnd);
edgeList.remove(rbnd);
leftRight = LR.LEFT;
if (bottomSite.get_y() > topSite.get_y()) {
tempSite = bottomSite;
bottomSite = topSite;
topSite = tempSite;
leftRight = LR.RIGHT;
}
edge = Edge.createBisectingEdge(bottomSite, topSite);
_edges.add(edge);
bisector = Halfedge.create(edge, leftRight);
halfEdges.add(bisector);
edgeList.insert(llbnd, bisector);
edge.setVertex(LR.other(leftRight), v);
if ((vertex = Vertex.intersect(llbnd, bisector)) != null) {
vertices.add(vertex);
heap.remove(llbnd);
llbnd.vertex = vertex;
llbnd.ystar = vertex.get_y() + bottomSite.dist(vertex);
heap.insert(llbnd);
}
if ((vertex = Vertex.intersect(bisector, rrbnd)) != null) {
vertices.add(vertex);
bisector.vertex = vertex;
bisector.ystar = vertex.get_y() + bottomSite.dist(vertex);
heap.insert(bisector);
}
} else {
break;
}
}
// heap should be empty now
heap.dispose();
edgeList.dispose();
for (Halfedge halfEdge : halfEdges) {
halfEdge.reallyDispose();
}
halfEdges.clear();
// we need the vertices to clip the edges
for (Edge e : _edges) {
e.clipVertices(_plotBounds);
}
// but we don't actually ever use them again!
for (Vertex v0 : vertices) {
v0.dispose();
}
vertices.clear();
}