/** Inserts point p in face c. Face c is split into 3 triangles. */
public TriangulationDSVertex_2<X> insertInTriangle(X p, TriangulationDSFace_2<X> t) {
if (t == null) throw new Error("Trying to star a null cell");
TriangulationDSFace_2<X> f1 = t.neighbor(1);
TriangulationDSFace_2<X> f2 = t.neighbor(2);
TriangulationDSFace_2<X> f0 = t.neighbor(0);
TriangulationDSVertex_2<X> v0 = t.vertex(0);
TriangulationDSVertex_2<X> v1 = t.vertex(1);
TriangulationDSVertex_2<X> v2 = t.vertex(2);
// create new vertex
TriangulationDSVertex_2<X> v = new TriangulationDSVertex_2<X>(p);
vertices.add(v);
// create and set two new faces
TriangulationDSFace_2<X> newFace2 = createFace(v0, v1, v, t, null, f2);
TriangulationDSFace_2<X> newFace1 = createFace(v0, v, v2, t, f1, newFace2);
newFace2.setNeighbor(1, newFace1);
// set new vertex and neighbors of old triangle
t.setVertex(0, v);
t.setNeighbor(1, newFace1);
t.setNeighbor(2, newFace2);
// set the faces incident to v and v0
v.setFace(t);
v0.setFace(newFace1);
// restore the marks of the initial triangle edges
for (int i = 0; i < 3; i++) t.unmark(i);
if (t.neighbor(0) != null) {
HalfedgeHandle<X> e = new HalfedgeHandle<X>(t, 0);
e.setMark(e.getOpposite().isMarked());
}
if (newFace1.neighbor(1) != null) {
HalfedgeHandle<X> e = new HalfedgeHandle<X>(newFace1, 1);
e.setMark(e.getOpposite().isMarked());
}
if (newFace2.neighbor(2) != null) {
HalfedgeHandle<X> e = new HalfedgeHandle<X>(newFace2, 2);
e.setMark(e.getOpposite().isMarked());
}
// return the new vertex
return v;
}
/**
* creates a new face in the triangulation, with the given incident vertices and adjacent
* triangles.
*/
public TriangulationDSFace_2<X> createFace(
TriangulationDSVertex_2<X> v1,
TriangulationDSVertex_2<X> v2,
TriangulationDSVertex_2<X> v3,
TriangulationDSFace_2<X> c1,
TriangulationDSFace_2<X> c2,
TriangulationDSFace_2<X> c3) {
TriangulationDSFace_2<X> newFace = new TriangulationDSFace_2<X>(v1, v2, v3, c1, c2, c3);
for (int i = 0; i < 3; i++) {
TriangulationDSFace_2<X> face = newFace.neighbors.get(i);
if (face != null) {
// update neighbor pointer in neighboring cell
face.setNeighbor(face.index(newFace), newFace);
}
}
this.faces.add(newFace);
return newFace;
}
/**
* Create a new triangulation from the face-vertex incidence relations It takes linear space and
* linear time.
*/
public TriangulationDS_2(X[] points, int[][] neighbors) {
if (points == null || neighbors == null || points[0] == null)
throw new Error("error: null vertices or null faces");
System.out.print("Creating triangulated 3D mesh... ");
this.faces = new ArrayList<TriangulationDSFace_2<X>>();
this.vertices = new ArrayList<TriangulationDSVertex_2<X>>();
for (int i = 0; i < points.length; i++) {
if (points[i] == null) throw new Error("null vertex error");
TriangulationDSVertex_2<X> v = new TriangulationDSVertex_2<X>(points[i]);
this.vertices.add(v);
}
// first pair (the key) represents the edges of the triangulation
// second pair (the associated value) represents the two neighboring faces (sharing an edge)
HashMap<Pair<Integer>, Pair<Integer>> edges = new HashMap<Pair<Integer>, Pair<Integer>>();
for (int i = 0; i < neighbors.length; i++) {
int i0 = neighbors[i][0], i1 = neighbors[i][1], i2 = neighbors[i][2];
createFace(this.vertices.get(i0), vertices.get(i1), vertices.get(i2), null, null, null);
for (int j = 0; j < 3; j++) {
int index1 = neighbors[i][(j + 1) % 3];
int index2 = neighbors[i][(j + 2) % 3];
Pair<Integer> edge;
if (index1 <= index2) edge = new Pair<Integer>(index1, index2);
else edge = new Pair<Integer>(index2, index1);
if (edges.containsKey(edge) == false) {
Pair<Integer> face;
if (index1 <= index2) face = new Pair<Integer>(i, -1);
else face = new Pair<Integer>(-1, i);
edges.put(edge, face);
} else {
Pair<Integer> face = edges.get(edge);
if (face.getFirst() == -1) face.setFirst(i);
else face.setSecond(i);
}
}
}
// System.out.println("setting neighboring faces");
for (int i = 0; i < neighbors.length; i++) {
TriangulationDSFace_2<X> currentFace = this.faces.get(i);
for (int j = 0; j < 3; j++) {
// setting vertex adjacent face
TriangulationDSVertex_2<X> v = this.vertices.get(neighbors[i][j]);
v.setFace(this.faces.get(i));
int index1 = neighbors[i][(j + 1) % 3];
int index2 = neighbors[i][(j + 2) % 3];
Pair<Integer> edge;
if (index1 <= index2) edge = new Pair<Integer>(index1, index2);
else edge = new Pair<Integer>(index2, index1);
if (edges.containsKey(edge) == false) throw new Error("error: edge not found");
else {
Pair<Integer> face = edges.get(edge);
if (face.getFirst() == -1 && face.getSecond() == -1)
throw new Error("error: wrong adjacent faces");
if (face.getFirst() == -1 || face.getSecond() == -1) ; // boundary edge
else {
int neighborFace;
if (index1 <= index2) neighborFace = face.getSecond();
else neighborFace = face.getFirst();
if (neighborFace < 0 || neighborFace >= this.faces.size())
throw new Error("error neighbor face index");
currentFace.setNeighbor(j, this.faces.get(neighborFace));
}
}
}
}
System.out.println("done");
}
/** flips an edge in the triangulation and returns the new edge */
public HalfedgeHandle<X> flipEdge(HalfedgeHandle<X> e) {
TriangulationDSFace_2<X> f1 = e.getFace();
TriangulationDSFace_2<X> f2 = e.getOpposite().getFace();
// retrieve vertices of quadrangle
ArrayList<TriangulationDSVertex_2<X>> vert = new ArrayList<TriangulationDSVertex_2<X>>();
vert.add(f1.vertex(e.index()));
vert.add(f1.vertex((e.index() + 1) % 3));
vert.add(f2.vertex(e.getOpposite().index()));
vert.add(f1.vertex((e.index() + 2) % 3));
// retrieve neighboring faces of quadrangle
ArrayList<TriangulationDSFace_2<X>> neighb = new ArrayList<TriangulationDSFace_2<X>>();
neighb.add(f1.neighbor((e.index() + 2) % 3));
neighb.add(f2.neighbor((e.getOpposite().index() + 1) % 3));
neighb.add(f2.neighbor((e.getOpposite().index() + 2) % 3));
neighb.add(f1.neighbor((e.index() + 1) % 3));
// reset the vertices of the 2 quadrangle faces
f1.setVertex(0, vert.get(0));
f1.setVertex(1, vert.get(1));
f1.setVertex(2, vert.get(2));
f2.setVertex(0, vert.get(0));
f2.setVertex(1, vert.get(2));
f2.setVertex(2, vert.get(3));
// reset the incident faces of the quandrangle vertices
vert.get(0).setFace(f1);
vert.get(1).setFace(f1);
vert.get(2).setFace(f2);
vert.get(3).setFace(f2);
// reset the neighbors of the 2 quadrangle faces
f1.setNeighbor(0, neighb.get(1));
f1.setNeighbor(1, f2);
f1.setNeighbor(2, neighb.get(0));
f2.setNeighbor(0, neighb.get(2));
f2.setNeighbor(1, neighb.get(3));
f2.setNeighbor(2, f1);
// reset the neighbors of the quadrangle neighbors (only modify what needs to be modified)
if (neighb.get(1) != null) neighb.get(1).setNeighbor(neighb.get(1).index(f2), f1);
if (neighb.get(3) != null) neighb.get(3).setNeighbor(neighb.get(3).index(f1), f2);
// reset the marks of the edges of the two faces
for (int i = 0; i < 3; i++) {
f1.unmark(i);
f2.unmark(i);
}
// restore the marks of the quadrangle edges (or rather their inner halfedges)
for (int i = 0; i < 3; i++) {
e = new HalfedgeHandle<X>(f1, i);
if (f1.neighbor(i) != null) e.setMark(e.getOpposite().isMarked());
e = new HalfedgeHandle<X>(f2, i);
if (f2.neighbor(i) != null) e.setMark(e.getOpposite().isMarked());
}
// return the new diagonal edge
return new HalfedgeHandle<X>(f1, 1);
}