private void processSiteEvent(final Event newSite) {
HalfEdge lBnd = coast.getHalfEdgeToTheLeftOf((newSite));
HalfEdge rBnd = coast.getHalfEdgeToTheRightOf(lBnd);
// if this half-edge has no edge,bot = bottom site (whatever that is)
Site bot = lBnd.getRightReg(bottomSite);
Edge e = edgeBisector.newEdgeThatBisects(bot, newSite);
HalfEdge bisector1 = new HalfEdge(e, Edge.LE);
// insert this new bisector edge between the left and right bounds
coast.insert(lBnd, bisector1);
// if the new bisector intersects with the left edge,
// remove the left edge's vertex, and put in the new one
Site p = lBnd.intersect(bisector1);
if (p != null) {
events.delete(lBnd);
events.insert(lBnd, p, p.distTo(newSite));
}
HalfEdge bisector2 = new HalfEdge(e, Edge.RE);
// insert the new HE to the right of the original bisector
coast.insert(bisector1, bisector2);
// if this new bisector intersects with the new HalfEdge
p = bisector2.intersect(rBnd);
if (p != null) {
// push the HE into the ordered linked list of vertices
events.insert(bisector2, p, p.distTo(newSite));
}
}
public void computeNormal(Vector3d normal, double minArea) {
computeNormal(normal);
if (area < minArea) {
System.out.println("area=" + area);
// make the normal more robust by removing
// components parallel to the longest edge
HalfEdge hedgeMax = null;
double lenSqrMax = 0;
HalfEdge hedge = he0;
do {
double lenSqr = hedge.lengthSquared();
if (lenSqr > lenSqrMax) {
hedgeMax = hedge;
lenSqrMax = lenSqr;
}
hedge = hedge.next;
} while (hedge != he0);
Point3d p2 = hedgeMax.head().pnt;
Point3d p1 = hedgeMax.tail().pnt;
double lenMax = Math.sqrt(lenSqrMax);
double ux = (p2.x - p1.x) / lenMax;
double uy = (p2.y - p1.y) / lenMax;
double uz = (p2.z - p1.z) / lenMax;
double dot = normal.x * ux + normal.y * uy + normal.z * uz;
normal.x -= dot * ux;
normal.y -= dot * uy;
normal.z -= dot * uz;
normal.normalize();
}
}
/** searches for all opposite HalfEdges */
public void computeOppositeHalfEdges() {
if (debug) {
System.out.println("Compute opposite half edges...");
}
for (HalfEdge halfEdge : halfEdges) {
halfEdge.setOpposite(computeOppositeHalfEdge(halfEdge));
}
}
public void getVertexIndices(int[] idxs) {
HalfEdge he = he0;
int i = 0;
do {
idxs[i++] = he.head().index;
he = he.next;
} while (he != he0);
}
public void computeCentroid(Point3d centroid) {
centroid.setZero();
HalfEdge he = he0;
do {
centroid.add(he.head().pnt);
he = he.next;
} while (he != he0);
centroid.scale(1 / (double) numVerts);
}
private void checkEdgeRing(EdgeGraph graph, Coordinate p, Coordinate[] dest) {
HalfEdge e = graph.findEdge(p, dest[0]);
HalfEdge onext = e;
int i = 0;
do {
assertTrue(onext.dest().equals2D(dest[i++]));
onext = onext.oNext();
} while (onext != e);
}
/**
* Finds the half-edge within this face which has tail <code>vt</code> and head <code>vh</code>.
*
* @param vt tail point
* @param vh head point
* @return the half-edge, or null if none is found.
*/
public HalfEdge findEdge(Vertex vt, Vertex vh) {
HalfEdge he = he0;
do {
if (he.head() == vh && he.tail() == vt) {
return he;
}
he = he.next;
} while (he != he0);
return null;
}
/**
* Determine neighbours vertices for the given vertex.
*
* @param vertex the vertex to get the neighbour for
* @return the determined neighbours.
*/
private ArrayList<Vertex> getNeighboursVertices(Vertex vertex) {
ArrayList<Vertex> neighbours = new ArrayList<Vertex>();
HalfEdge first = vertex.getHalfEdge();
HalfEdge next = first;
do {
neighbours.add(next.getOpposite().getStartVertex());
next = next.getOpposite().getNext();
} while (next != first);
return neighbours;
}
public String getVertexString() {
String s = null;
HalfEdge he = he0;
do {
if (s == null) {
s = "" + he.head().index;
} else {
s += " " + he.head().index;
}
he = he.next;
} while (he != he0);
return s;
}
public int mergeAdjacentFace(HalfEdge hedgeAdj, Face[] discarded) {
Face oppFace = hedgeAdj.oppositeFace();
int numDiscarded = 0;
discarded[numDiscarded++] = oppFace;
oppFace.mark = DELETED;
HalfEdge hedgeOpp = hedgeAdj.getOpposite();
HalfEdge hedgeAdjPrev = hedgeAdj.prev;
HalfEdge hedgeAdjNext = hedgeAdj.next;
HalfEdge hedgeOppPrev = hedgeOpp.prev;
HalfEdge hedgeOppNext = hedgeOpp.next;
while (hedgeAdjPrev.oppositeFace() == oppFace) {
hedgeAdjPrev = hedgeAdjPrev.prev;
hedgeOppNext = hedgeOppNext.next;
}
while (hedgeAdjNext.oppositeFace() == oppFace) {
hedgeOppPrev = hedgeOppPrev.prev;
hedgeAdjNext = hedgeAdjNext.next;
}
HalfEdge hedge;
for (hedge = hedgeOppNext; hedge != hedgeOppPrev.next; hedge = hedge.next) {
hedge.face = this;
}
if (hedgeAdj == he0) {
he0 = hedgeAdjNext;
}
// handle the half edges at the head
Face discardedFace;
discardedFace = connectHalfEdges(hedgeOppPrev, hedgeAdjNext);
if (discardedFace != null) {
discarded[numDiscarded++] = discardedFace;
}
// handle the half edges at the tail
discardedFace = connectHalfEdges(hedgeAdjPrev, hedgeOppNext);
if (discardedFace != null) {
discarded[numDiscarded++] = discardedFace;
}
computeNormalAndCentroid();
checkConsistency();
return numDiscarded;
}
public static Face create(Vertex[] vtxArray, int[] indices) {
Face face = new Face();
HalfEdge hePrev = null;
for (int i = 0; i < indices.length; i++) {
HalfEdge he = new HalfEdge(vtxArray[indices[i]], face);
if (hePrev != null) {
he.setPrev(hePrev);
hePrev.setNext(he);
} else {
face.he0 = he;
}
hePrev = he;
}
face.he0.setPrev(hePrev);
hePrev.setNext(face.he0);
// compute the normal and offset
face.computeNormalAndCentroid();
return face;
}
/**
* Constructs a triangule Face from vertices v0, v1, and v2.
*
* @param v0 first vertex
* @param v1 second vertex
* @param v2 third vertex
*/
public static Face createTriangle(Vertex v0, Vertex v1, Vertex v2, double minArea) {
Face face = new Face();
HalfEdge he0 = new HalfEdge(v0, face);
HalfEdge he1 = new HalfEdge(v1, face);
HalfEdge he2 = new HalfEdge(v2, face);
he0.prev = he2;
he0.next = he1;
he1.prev = he0;
he1.next = he2;
he2.prev = he1;
he2.next = he0;
face.he0 = he0;
// compute the normal and offset
face.computeNormalAndCentroid(minArea);
return face;
}
private double areaSquared(HalfEdge hedge0, HalfEdge hedge1) {
// return the squared area of the triangle defined
// by the half edge hedge0 and the point at the
// head of hedge1.
Point3d p0 = hedge0.tail().pnt;
Point3d p1 = hedge0.head().pnt;
Point3d p2 = hedge1.head().pnt;
double dx1 = p1.x - p0.x;
double dy1 = p1.y - p0.y;
double dz1 = p1.z - p0.z;
double dx2 = p2.x - p0.x;
double dy2 = p2.y - p0.y;
double dz2 = p2.z - p0.z;
double x = dy1 * dz2 - dz1 * dy2;
double y = dz1 * dx2 - dx1 * dz2;
double z = dx1 * dy2 - dy1 * dx2;
return x * x + y * y + z * z;
}
public void computeNormal(Vector3d normal) {
HalfEdge he1 = he0.next;
HalfEdge he2 = he1.next;
Point3d p0 = he0.head().pnt;
Point3d p2 = he1.head().pnt;
double d2x = p2.x - p0.x;
double d2y = p2.y - p0.y;
double d2z = p2.z - p0.z;
normal.setZero();
numVerts = 2;
while (he2 != he0) {
double d1x = d2x;
double d1y = d2y;
double d1z = d2z;
p2 = he2.head().pnt;
d2x = p2.x - p0.x;
d2y = p2.y - p0.y;
d2z = p2.z - p0.z;
normal.x += d1y * d2z - d1z * d2y;
normal.y += d1z * d2x - d1x * d2z;
normal.z += d1x * d2y - d1y * d2x;
he1 = he2;
he2 = he2.next;
numVerts++;
}
area = normal.norm();
normal.scale(1 / area);
}
/**
* computes opposite halfEdge for the given half edge.
*
* @param halfEdge the halfEdge to compute the opposite for.
* @return the opposite HalfEdge to the given one.
*/
private HalfEdge computeOppositeHalfEdge(HalfEdge halfEdge) {
Vertex destination = halfEdge.getNext().getStartVertex();
for (HalfEdge opposite : halfEdges) {
if (!halfEdge.equals(opposite) && opposite.getStartVertex().equals(destination)) {
if (opposite.getNext().getStartVertex().equals(halfEdge.getStartVertex())) {
return opposite;
}
}
}
return null;
}
public void computeVertexNormals() {
for (HalfEdge first : halfEdges) {
HalfEdge cur = first;
Vector3 sum = cur.getFacet().getNormal();
do {
cur = cur.getOpposite().getNext();
sum.add(cur.getFacet().getNormal());
} while (cur != first);
first.getStartVertex().setNormal(sum.getNormalized());
}
}
public void triangulate(FaceList newFaces, double minArea) {
HalfEdge hedge;
if (numVertices() < 4) {
return;
}
Vertex v0 = he0.head();
Face prevFace = null;
hedge = he0.next;
HalfEdge oppPrev = hedge.opposite;
Face face0 = null;
for (hedge = hedge.next; hedge != he0.prev; hedge = hedge.next) {
Face face = createTriangle(v0, hedge.prev.head(), hedge.head(), minArea);
face.he0.next.setOpposite(oppPrev);
face.he0.prev.setOpposite(hedge.opposite);
oppPrev = face.he0;
newFaces.add(face);
if (face0 == null) {
face0 = face;
}
}
hedge = new HalfEdge(he0.prev.prev.head(), this);
hedge.setOpposite(oppPrev);
hedge.prev = he0;
hedge.prev.next = hedge;
hedge.next = he0.prev;
hedge.next.prev = hedge;
computeNormalAndCentroid(minArea);
checkConsistency();
for (Face face = face0; face != null; face = face.next) {
face.checkConsistency();
}
}
public void addHalfEdge(HalfEdge halfEdge) {
this.halfEdges.put(halfEdge.getId(), halfEdge);
}
void checkConsistency() {
// do a sanity check on the face
HalfEdge hedge = he0;
double maxd = 0;
int numv = 0;
if (numVerts < 3) {
throw new InternalErrorException("degenerate face: " + getVertexString());
}
do {
HalfEdge hedgeOpp = hedge.getOpposite();
if (hedgeOpp == null) {
throw new InternalErrorException(
"face "
+ getVertexString()
+ ": "
+ "unreflected half edge "
+ hedge.getVertexString());
} else if (hedgeOpp.getOpposite() != hedge) {
throw new InternalErrorException(
"face "
+ getVertexString()
+ ": "
+ "opposite half edge "
+ hedgeOpp.getVertexString()
+ " has opposite "
+ hedgeOpp.getOpposite().getVertexString());
}
if (hedgeOpp.head() != hedge.tail() || hedge.head() != hedgeOpp.tail()) {
throw new InternalErrorException(
"face "
+ getVertexString()
+ ": "
+ "half edge "
+ hedge.getVertexString()
+ " reflected by "
+ hedgeOpp.getVertexString());
}
Face oppFace = hedgeOpp.face;
if (oppFace == null) {
throw new InternalErrorException(
"face "
+ getVertexString()
+ ": "
+ "no face on half edge "
+ hedgeOpp.getVertexString());
} else if (oppFace.mark == DELETED) {
throw new InternalErrorException(
"face "
+ getVertexString()
+ ": "
+ "opposite face "
+ oppFace.getVertexString()
+ " not on hull");
}
double d = Math.abs(distanceToPlane(hedge.head().pnt));
if (d > maxd) {
maxd = d;
}
numv++;
hedge = hedge.next;
} while (hedge != he0);
if (numv != numVerts) {
throw new InternalErrorException(
"face " + getVertexString() + " numVerts=" + numVerts + " should be " + numv);
}
}
private void processCircleEvent() {
// pop the HalfEdge with the lowest vector off the ordered list
// of vectors
HalfEdge lBnd = events.extractMin();
// get the HalfEdge to the left of the above HE
HalfEdge llBnd = coast.getHalfEdgeToTheLeftOf(lBnd);
// get the HalfEdge to the right of the above HE
HalfEdge rBnd = coast.getHalfEdgeToTheRightOf(lBnd);
// get the HalfEdge to the right of the HE to the right of the
// lowest HE
HalfEdge rrBnd = coast.getHalfEdgeToTheRightOf(rBnd);
// get the Site to the left of the left HE which it bisects
Site bot = lBnd.getLeftReg(bottomSite);
// get the Site to the right of the right HE which it bisects
Site top = rBnd.getRightReg(bottomSite);
Site v = lBnd.vertex; // get the vertex that caused this event
// set the vertex number - couldn't do this
// earlier since we didn't know when it would be processed
v.sitenbr = nextVertexNbr++;
endpoint(lBnd.edge, lBnd.side, v);
// set the endpoint of
// the left HalfEdge to be this vector
endpoint(rBnd.edge, rBnd.side, v);
// set the endpoint of the right HalfEdge to be this vector
coast.delete(lBnd);
events.delete(rBnd);
// remove all vertex events to do with the right HE
coast.delete(rBnd); // mark the right HE for
// deletion - can't delete yet because there might be pointers
// to it in Hash Map
int pm = Edge.LE; // set the pm variable to zero
if (bot.y > top.y) {
// if the site to the left of the event is higher than the
// Site
// to the right of it, then swap them and set the 'pm'
// variable to 1
Site temp = bot;
bot = top;
top = temp;
pm = Edge.RE;
}
Edge e = edgeBisector.newEdgeThatBisects(bot, top); // create an Edge (or
// line)
// that is between the two Sites. This creates the formula of
// the line, and assigns a line number to it
HalfEdge bisector = new HalfEdge(e, pm); // create a HE from the Edge
// 'e',
// and make it point to that edge
// with its ELedge field
coast.insert(llBnd, bisector); // insert the new bisector to the
// right of the left HE
endpoint(e, Edge.RE - pm, v); // set one endpoint to the new edge
// to be the vector point 'v'.
// If the site to the left of this bisector is higher than the
// right Site, then this endpoint
// is put in position 0; otherwise in pos 1
// if left HE and the new bisector intersect, then delete
// the left HE, and reinsert it
Site p = llBnd.intersect(bisector);
if (p != null) {
events.delete(llBnd);
events.insert(llBnd, p, p.distTo(bot));
}
// if right HE and the new bisector intersect, then
// reinsert it
p = bisector.intersect(rrBnd);
if (p != null) {
events.insert(bisector, p, p.distTo(bot));
}
}
private Face connectHalfEdges(HalfEdge hedgePrev, HalfEdge hedge) {
Face discardedFace = null;
if (hedgePrev.oppositeFace()
== hedge.oppositeFace()) { // then there is a redundant edge that we can get rid off
Face oppFace = hedge.oppositeFace();
HalfEdge hedgeOpp;
if (hedgePrev == he0) {
he0 = hedge;
}
if (oppFace.numVertices() == 3) { // then we can get rid of the opposite face altogether
hedgeOpp = hedge.getOpposite().prev.getOpposite();
oppFace.mark = DELETED;
discardedFace = oppFace;
} else {
hedgeOpp = hedge.getOpposite().next;
if (oppFace.he0 == hedgeOpp.prev) {
oppFace.he0 = hedgeOpp;
}
hedgeOpp.prev = hedgeOpp.prev.prev;
hedgeOpp.prev.next = hedgeOpp;
}
hedge.prev = hedgePrev.prev;
hedge.prev.next = hedge;
hedge.opposite = hedgeOpp;
hedgeOpp.opposite = hedge;
// oppFace was modified, so need to recompute
oppFace.computeNormalAndCentroid();
} else {
hedgePrev.next = hedge;
hedge.prev = hedgePrev;
}
return discardedFace;
}