1 package edu.berkeley.qfat;
4 import java.awt.event.*;
6 import javax.media.opengl.*;
7 import javax.media.opengl.glu.*;
8 import edu.berkeley.qfat.geom.*;
9 import edu.berkeley.qfat.geom.HasBindingGroup;
10 import edu.wlu.cs.levy.CG.KDTree;
11 import edu.berkeley.qfat.geom.Point;
12 import com.infomatiq.jsi.IntProcedure;
14 public class Mesh implements Iterable<Mesh.T> {
16 public static final float EPSILON = (float)0.0001;
17 public static final Random random = new Random();
19 private RTree<T> triangles = new RTree<T>();
20 private PointSet<Vertex> vertices = new PointSet<Vertex>();
22 public boolean immutableVertices;
23 public Mesh error_against = null;
24 public double error = 0;
26 public Mesh(boolean immutableVertices) { this.immutableVertices = immutableVertices; }
28 public void makeVerticesImmutable() { this.immutableVertices = true; }
29 public float error() { return (float)error; }
31 public int size() { return vertices.size(); }
32 public Iterable<Vertex> vertices() { return vertices; }
33 public Iterator<T> iterator() { return triangles.iterator(); }
35 public void rebindPoints() {
37 for(Mesh.T t : this) {
42 // ask edges to re-implement their bindings
43 for(Mesh.T t : this) {
48 System.out.println("rebound!");
51 public void transform(Matrix m) {
52 ArrayList<Vertex> set = new ArrayList<Vertex>();
53 for(Vertex v : vertices) set.add(v);
54 for(Vertex v : set) v.transform(m.times(v.p), true);
57 public void rebuild() { /*vertices.rebuild();*/ }
58 public Vec diagonal() { return vertices.diagonal(); }
59 public Point centroid() { return vertices.centroid(); }
60 public Vertex nearest(Point p) { return vertices.nearest(p); }
62 /** compute the volume of the mesh */
63 public float volume() {
66 double area = t.area();
67 Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
68 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
69 double height = Math.abs(t.norm().dot(origin_to_centroid));
70 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
76 // Vertexices //////////////////////////////////////////////////////////////////////////////
78 /** a vertex in the mesh */
79 public final class Vertex extends HasQuadric implements Visitor {
80 public Point p, oldp, goodp;
81 E e; // some edge *leaving* this point
83 private boolean illegal = false;
85 public Point getPoint() { return p; }
86 public float error() { return olderror; }
88 private Vertex(Point p) {
91 if (vertices.get(p) != null) throw new Error();
95 public void reinsert() {
96 vertices.remove(this);
98 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.t.reinsert();
101 public float olderror = 0;
102 public void setError(float nerror) {
108 public float averageTriangleArea() {
111 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
117 public float averageEdgeLength() {
120 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
127 public Matrix _recomputeFundamentalQuadric() {
128 Matrix m = Matrix.ZERO;
130 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
131 m = m.plus(e.t.norm().fundamentalQuadric(e.t.centroid()));
134 return m.times(1/(float)count);
137 public HasQuadric nearest() { return error_against==null ? null : error_against.vertices.nearest(p, this); }
138 public void computeError() {
139 if (error_against==null) return;
141 nearest_in_other_mesh != null
142 ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p)
143 : nearest().fundamentalQuadric().preAndPostMultiply(p);
144 if (quadric_count != 0)
145 nerror = (nerror + quadric.preAndPostMultiply(p))/(quadric_count+1);
147 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
148 double ang = Math.abs(e.dihedralAngle());
149 if (ang > Math.PI) throw new Error();
150 float minangle = (float)(Math.PI * 0.8);
151 if (ang > minangle) nerror += (ang - minangle);
153 if (e.t.aspect() < 0.2) {
154 nerror += (0.2-e.t.aspect()) * 10;
162 public boolean move(Matrix m, boolean ignoreProblems) {
166 // t2' = t2.getMatrix(t1) * t1'
167 // t2' = t2.getMatrix(t1) * M * t1
168 // t1 = t1.getMatrix(t2) * t2
169 // M * t1 = M * t1.getMatrix(t2) * t2
170 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
171 good &= v.transform(v.getBindingMatrix(this).times(m).times(this.p),
174 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
175 if (good || ignoreProblems) v.reComputeErrorAround();
176 else v.transform(v.oldp, true);
181 /** does NOT update bound pairs! */
182 private boolean transform(Point newp, boolean ignoreProblems) {
184 if (immutableVertices) throw new Error();
186 unApplyQuadricToNeighbor();
189 applyQuadricToNeighbor();
191 if (!ignoreProblems) {
195 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.p2.quadricStale = true;
199 public void checkLegality() {
201 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
202 if (Math.abs(e.dihedralAngle()) > (Math.PI * 0.9) ||
203 Math.abs(e.next.dihedralAngle()) > (Math.PI * 0.9)) illegal = true;
204 if (e.t.aspect() < 0.1) illegal = true;
207 if (!illegal) triangles.range(oldp, this.p, (Visitor<T>)this);
210 public void reComputeErrorAround() {
212 if (nearest_in_other_mesh != null)
213 nearest_in_other_mesh.reComputeError();
214 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
215 e.p2.reComputeError();
218 public boolean visit(Object o) {
219 if (o instanceof Vertex)
220 return ((Vertex)o).e != null && ((Vertex)o).norm().dot(Vertex.this.norm()) >= 0;
222 if (illegal) return false;
223 for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
224 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { illegal = true; }
226 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { illegal = true; }
227 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { illegal = true; }
228 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { illegal = true; }
234 public E getFreeIncident() {
235 E ret = getFreeIncident(e, e);
236 if (ret != null) return ret;
237 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
238 System.out.println(e + " " + e.t);
239 throw new Error("unable to find free incident to " + this);
242 public E getFreeIncident(E start, E before) {
243 for(E e = start; e!=null; e=e.pair.next==before?null:e.pair.next)
244 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null)
249 public E getE(Point p2) {
250 Vertex v = vertices.get(p2);
251 if (v==null) return null;
254 public E getE(Vertex p2) {
255 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
256 if (e.p1 == this && e.p2 == p2) return e;
260 private void glNormal(GL gl) {
262 gl.glNormal3f(norm.x, norm.y, norm.z);
265 Vec norm = new Vec(0, 0, 0);
266 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
268 norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
272 public void bindTo(Vertex p) { bindTo(Matrix.ONE, p); }
275 public class BindingGroup {
276 private HashSet<E> set = new HashSet<E>();
277 public BindingGroup bind_others;
278 public BindingGroup other() { return bind_others; }
279 public BindingGroup(BindingGroup bind_others) { this.bind_others = bind_others; }
280 public BindingGroup() { this.bind_others = new BindingGroup(this); }
281 public BindingGroup(E e) { this(); set.add(e); }
282 public void add(E e) {
283 if (set.contains(e)) return;
285 BindingGroup e_bind_peers = e.bind_peers;
286 BindingGroup e_bind_to = e.bind_to;
288 e.bind_to = bind_others;
289 for (E epeer : e_bind_peers.set) add(epeer);
290 for (E eother : e_bind_to.set) bind_others.add(eother);
292 for(E eother : bind_others.set) {
293 if (e.next.bind_to.set.contains(eother.prev)) {
294 e.next.next.bindEdge(eother.prev.prev);
296 if (e.prev.bind_to.set.contains(eother.next)) {
297 e.prev.prev.bindEdge(eother.next.next);
302 public void dobind(E e) {
303 for(E ebound : set) {
304 e.p1.bindTo(Matrix.ONE, ebound.p2);
305 e.p2.bindTo(Matrix.ONE, ebound.p1);
310 /** [UNIQUE] an edge */
311 public final class E extends HasBindingGroup implements Comparable<E> {
313 public final Vertex p1, p2;
314 T t; // triangle to our "left"
315 E prev; // previous half-edge
316 E next; // next half-edge
317 E pair; // partner half-edge
318 public BindingGroup bind_peers = new BindingGroup(this);
319 public BindingGroup bind_to = bind_peers.other();
320 boolean shattered = false;
322 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
324 public void bindingGroupChanged(edu.berkeley.qfat.geom.BindingGroup newBindingGroup_) {
326 edu.berkeley.qfat.geom.BindingGroup<E> newBindingGroup =
327 (edu.berkeley.qfat.geom.BindingGroup<E>)newBindingGroup_;
328 if (newBindingGroup==null) return;
329 if (this==newBindingGroup.getMaster()) return;
330 for(E eother : (Iterable<E>)newBindingGroup) {
331 if (next==null || prev==null) continue;
332 if (eother.next==null || eother.prev==null) continue;
333 if (next.isBoundTo(eother.pair.prev.pair) && !prev.isBoundTo(eother.pair.next.pair))
334 prev.bindTo(next.getBindingMatrix(eother.pair.prev.pair), eother.pair.next.pair);
335 if (!next.isBoundTo(eother.pair.prev.pair) && prev.isBoundTo(eother.pair.next.pair))
336 next.bindTo(prev.getBindingMatrix(eother.pair.next.pair), eother.pair.prev.pair);
341 public float stretchRatio() {
342 Vertex nearest = error_against.nearest(midpoint());
343 float nearest_distance = midpoint().distance(nearest.p);
344 float other_distance =
345 (p1.p.distance(error_against.nearest(p1.p).p)+
346 p2.p.distance(error_against.nearest(p2.p).p))/2;
347 return nearest_distance/other_distance;
349 public float comparator() {
351 //return t==null?0:(1/t.aspect());
353 public int compareTo(E e) {
354 return e.comparator() > comparator() ? 1 : -1;
356 public void bindEdge(E e, Matrix m) {
358 pair._bindEdge(e.pair, m);
360 public void _bindEdge(E e, Matrix m) {
365 //assumes edges are identical length at binding time
366 Vec reflectionPlaneNormal = e.p2.p.minus(e.p1.p).norm();
367 float a = reflectionPlaneNormal.x;
368 float b = reflectionPlaneNormal.y;
369 float c = reflectionPlaneNormal.z;
370 Matrix reflectionMatrix =
371 new Matrix( 1-2*a*a, -2*a*b, -2*a*c, 0,
372 -2*a*b, 1-2*b*b, -2*b*c, 0,
373 -2*a*c, -2*b*c, 1-2*c*c, 0,
375 m = m.times(Matrix.translate(e.midpoint().minus(Point.ORIGIN))
376 .times(reflectionMatrix)
377 .times(Matrix.translate(Point.ORIGIN.minus(e.midpoint()))));
378 System.out.println(reflectionPlaneNormal);
379 System.out.println(" " + p1.p + " " + m.times(e.p1.p));
380 System.out.println(" " + p2.p + " " + m.times(e.p2.p));
382 if (m.times(e.p1.p).minus(p1.p).mag() > EPSILON) throw new Error();
383 if (m.times(e.p2.p).minus(p2.p).mag() > EPSILON) throw new Error();
387 public void dobind() {
388 //bind_to.dobind(this);
389 for(E e : (Iterable<E>)getBoundPeers()) {
390 if (e==this) continue;
391 p1.bindTo(getBindingMatrix(e), e.p1);
392 p2.bindTo(getBindingMatrix(e), e.p2);
396 public Point shatter() {
397 if (shattered || destroyed) return null;
403 for(E e : (Iterable<E>)getBoundPeers()) {
406 E pnext = e.pair.next;
407 E pprev = e.pair.prev;
408 Point mid = e.midpoint();
409 Vertex r = e.next.p2;
410 Vertex l = e.pair.next.p2;
413 newT(r.p, e.p1.p, mid, null, 0);
414 newT(r.p, mid, e.p2.p, null, 0);
415 newT(l.p, mid, e.p1.p, null, 0);
416 newT(l.p, e.p2.p, mid, null, 0);
420 for(E e : (Iterable<E>)getBoundPeers()) {
421 Point mid = e.midpoint();
423 first = e.p1.getE(mid);
426 firstq = e.p2.getE(mid).pair;
429 e.p1.getE(mid). bindTo(e.getBindingMatrix(firste), first);
430 e.p1.getE(mid).pair. bindTo(e.getBindingMatrix(firste), first.pair);
431 e.p2.getE(mid).pair. bindTo(e.getBindingMatrix(firste), firstq);
432 e.p2.getE(mid).pair.pair.bindTo(e.getBindingMatrix(firste), firstq.pair);
433 //e.p1.getE(mid).pair.prev.bindTo(e.pair.getBindingMatrix(firstx), first.pair.prev);
438 public boolean destroyed = false;
439 public void destroy() {
440 if (destroyed) return;
442 pair.destroyed = true;
444 if (t != null) t.destroy();
447 if (pair.t != null) pair.t.destroy();
450 if (next.t != null) next.t.destroy();
451 if (prev.t != null) prev.t.destroy();
455 if (pair.next.t != null) pair.next.t.destroy();
456 if (pair.prev.t != null) pair.next.t.destroy();
462 this.bind_peers = null;
463 pair.bind_peers = null;
464 pair.prev.next = next;
465 next.prev = pair.prev;
466 prev.next = pair.next;
468 if (p1.e == this) p1.e = prev.next;
469 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
472 private void sync() {
473 this.prev.next = this;
474 this.next.prev = this;
475 this.pair.pair = this;
476 bind_peers.add(this);
477 if (this.next.p1 != p2) throw new Error();
478 if (this.prev.p2 != p1) throw new Error();
479 if (this.p1.e == null) this.p1.e = this;
480 if (!added) added = true;
482 private boolean added = false;
484 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
486 public double dihedralAngle() {
487 Vec v1 = t.norm().times(-1);
488 Vec v2 = pair.t.norm().times(-1);
489 return Math.acos(v1.norm().dot(v2.norm()));
492 /** angle between this half-edge and the next */
493 public double angle() {
494 Vec v1 = next.p2.p.minus(p2.p);
495 Vec v2 = this.p1.p.minus(p2.p);
496 return Math.acos(v1.norm().dot(v2.norm()));
499 public void makeAdjacent(E e) {
500 if (this.next == e) return;
501 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
502 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
504 E freeIncident = p2.getFreeIncident(e, this);
506 e.prev.next = freeIncident.next;
507 freeIncident.next.prev = e.prev;
509 freeIncident.next = this.next;
510 this.next.prev = freeIncident;
519 /** creates an isolated edge out in the middle of space */
520 public E(Point p1, Point p2) {
521 if (vertices.get(p1) != null) throw new Error();
522 if (vertices.get(p2) != null) throw new Error();
523 this.p1 = new Vertex(p1);
524 this.p2 = new Vertex(p2);
525 this.prev = this.next = this.pair = new E(this, this, this);
527 this.p2.e = this.pair;
531 /** adds a new half-edge from prev.p2 to p2 */
532 public E(E prev, Point p) {
534 p2 = vertices.get(p);
535 if (p2 == null) p2 = new Vertex(p);
539 if (p2.getE(p1) != null) throw new Error();
541 this.next = this.pair = new E(this, this, prev.next);
543 E q = p2.getFreeIncident();
545 this.next.prev = this;
547 this.prev.next = this;
548 this.pair = new E(q, this, z);
550 if (p2.e==null) p2.e = this.pair;
554 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
555 public E(E prev, E pair, E next) {
563 public Point midpoint() { return new Point((p1.p.x+p2.p.x)/2, (p1.p.y+p2.p.y)/2, (p1.p.z+p2.p.z)/2); }
564 public boolean has(Vertex v) { return v==p1 || v==p2; }
565 public float length() { return p1.p.minus(p2.p).mag(); }
566 public String toString() { return p1+"->"+p2; }
570 public E makeE(Point p1, Point p2) {
571 Vertex v1 = vertices.get(p1);
572 Vertex v2 = vertices.get(p2);
573 if (v1 != null && v2 != null) {
575 if (e != null) return e;
577 if (e != null) return e;
579 if (v1 != null) return new E(v1.getFreeIncident(), p2);
580 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
581 return new E(p1, p2);
583 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
585 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
586 float dot = norm.dot(norm2);
587 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
588 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
590 E e12 = makeE(p1, p2);
591 E e23 = makeE(p2, p3);
592 E e31 = makeE(p3, p1);
593 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
594 e12.makeAdjacent(e23);
595 e23.makeAdjacent(e31);
596 e31.makeAdjacent(e12);
598 T ret = e12.makeT(colorclass);
599 if (e12.t == null) throw new Error();
600 if (e23.t == null) throw new Error();
601 if (e31.t == null) throw new Error();
605 /** [UNIQUE] a triangle (face) */
606 public final class T extends Triangle {
608 public final int color;
609 public final int colorclass;
611 T(E e1, int colorclass) {
615 if (e1==e2 || e1==e3) throw new Error();
616 if (e3.next!=e1) throw new Error();
617 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
620 e1.next.next.t = this;
622 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
624 int color = Math.abs(random.nextInt());
627 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
628 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
629 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
633 this.colorclass = colorclass;
636 public E e1() { return e1; }
637 public E e2() { return e1.next; }
638 public E e3() { return e1.prev; }
639 public Vertex v1() { return e1.p1; }
640 public Vertex v2() { return e1.p2; }
641 public Vertex v3() { return e1.next.p2; }
642 public Point p1() { return e1.p1.p; }
643 public Point p2() { return e1.p2.p; }
644 public Point p3() { return e1.next.p2.p; }
645 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
646 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
648 public void removeFromRTree() { triangles.remove(this); }
649 public void addToRTree() { triangles.insert(this); }
650 public void destroy() { triangles.remove(this); }
651 public void reinsert() { triangles.remove(this); triangles.add(this); }
653 public boolean shouldBeDrawn() {
655 if (e1().bindingGroupSize() <= 1) return false;
656 if (e2().bindingGroupSize() <= 1) return false;
657 if (e3().bindingGroupSize() <= 1) return false;
662 /** issue gl.glVertex() for each of the triangle's points */
663 public void glVertices(GL gl) {
664 if (!shouldBeDrawn()) return;
666 Point p1 = v1().goodp;
667 Point p2 = v2().goodp;
668 Point p3 = v3().goodp;