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.wlu.cs.levy.CG.KDTree;
10 import edu.berkeley.qfat.geom.Point;
12 public class Mesh implements Iterable<Mesh.T> {
14 public static final float EPSILON = (float)0.0001;
15 public static final Random random = new Random();
17 private RTree<T> triangles = new RTree<T>();
18 private PointSet<Vertex> vertices = new PointSet<Vertex>();
20 public boolean immutableVertices;
21 public boolean ignorecollision = false;
22 public Mesh score_against = null;
23 public double score = 0;
25 public Mesh(boolean immutableVertices) { this.immutableVertices = immutableVertices; }
27 public void makeVerticesImmutable() { this.immutableVertices = true; }
28 public float score() { return (float)score; }
30 public int size() { return vertices.size(); }
31 public Iterable<Vertex> vertices() { return vertices; }
32 public Iterator<T> iterator() { return triangles.iterator(); }
34 public void rebindPoints() {
36 for(Mesh.T t : this) {
41 // ask edges to re-implement their bindings
42 for(Mesh.T t : this) {
49 public void transform(Matrix m) {
50 ArrayList<Vertex> set = new ArrayList<Vertex>();
51 for(Vertex v : vertices) set.add(v);
52 for(Vertex v : set) v.transform(m);
55 public void rebuild() { /*vertices.rebuild();*/ }
56 public Vec diagonal() { return vertices.diagonal(); }
57 public Point centroid() { return vertices.centroid(); }
58 public Vertex nearest(Point p) { return vertices.nearest(p); }
60 /** compute the volume of the mesh */
61 public float volume() {
64 double area = t.area();
65 Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
66 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
67 double height = Math.abs(t.norm().dot(origin_to_centroid));
68 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
74 // Vertexices //////////////////////////////////////////////////////////////////////////////
76 /** a vertex in the mesh */
77 public final class Vertex extends HasPoint implements Visitor<T> {
78 public String toString() { return p.toString(); }
80 E e; // some edge *leaving* this point
82 /** the nearest vertex in the "score_against" mesh */
83 Vertex nearest_in_other_mesh;
84 /** the number of vertices in the other mesh for which this is the nearest_in_other_mesh */
86 /** the total error quadric (contributions from all vertices in other mesh for which this is nearest) */
87 Matrix quadric = Matrix.ZERO;
89 Matrix binding = Matrix.ONE;
90 Vertex bound_to = this;
92 boolean quadricStale = false;
94 public Matrix errorQuadric() { return quadric; }
95 public Point getPoint() { return p; }
96 public float score() { return oldscore; }
98 private Matrix fundamentalQuadric = null;
99 public Matrix fundamentalQuadric() {
100 if (fundamentalQuadric == null) recomputeFundamentalQuadric();
101 return fundamentalQuadric;
104 private Vertex(Point p) {
106 if (vertices.get(p) != null) throw new Error();
110 private void glNormal(GL gl) {
112 gl.glNormal3f(norm.x, norm.y, norm.z);
115 public void recomputeFundamentalQuadric() {
116 unApplyQuadricToNeighbor();
117 if (quadricStale || fundamentalQuadric==null) {
118 Matrix m = Matrix.ZERO;
120 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
122 m = m.plus(t.norm().fundamentalQuadric(t.centroid()));
125 quadricStale = false;
126 fundamentalQuadric = m.times(1/(float)count);
128 applyQuadricToNeighbor();
131 public void unApplyQuadricToNeighbor() {
132 if (nearest_in_other_mesh == null) return;
133 if (fundamentalQuadric == null) return;
134 nearest_in_other_mesh.unComputeError();
135 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.minus(fundamentalQuadric);
136 nearest_in_other_mesh.quadric_count--;
137 if (nearest_in_other_mesh.quadric_count==0)
138 nearest_in_other_mesh.quadric = Matrix.ZERO;
139 nearest_in_other_mesh.computeError();
140 nearest_in_other_mesh = null;
143 public void applyQuadricToNeighbor() {
144 if (score_against == null) return;
146 Vertex new_nearest = score_against.nearest(p);
147 if (nearest_in_other_mesh != null && new_nearest == nearest_in_other_mesh) return;
149 if (nearest_in_other_mesh != null) unApplyQuadricToNeighbor();
150 if (nearest_in_other_mesh != null) throw new Error();
152 nearest_in_other_mesh = new_nearest;
154 // don't attract to vertices that face the other way
155 if (nearest_in_other_mesh.e == null || nearest_in_other_mesh.norm().dot(norm()) < 0) {
156 nearest_in_other_mesh = null;
158 nearest_in_other_mesh.unComputeError();
159 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.plus(fundamentalQuadric());
160 nearest_in_other_mesh.quadric_count++;
161 nearest_in_other_mesh.computeError();
166 public void reComputeErrorAround() {
168 if (nearest_in_other_mesh != null) nearest_in_other_mesh.reComputeError();
169 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
170 e.p2.reComputeError();
172 public void reComputeError() {
176 public void unComputeError() {
180 public void computeError() {
183 ? (quadric.preAndPostMultiply(p) * 100) / quadric_count
186 : nearest_in_other_mesh != null
187 ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p) * 100 * 10
188 : score_against != null
189 ? score_against.nearest(p).fundamentalQuadric().preAndPostMultiply(p) * 100 * 10
191 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
192 double ang = Math.abs(e.crossAngle());
193 if (ang > Math.PI) throw new Error();
194 float minangle = (float)(Math.PI * 0.8);
196 oldscore += (ang - minangle);
201 private void removeTrianglesFromRTree() {
202 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
203 if (e.t != null) e.t.removeFromRTree();
205 private void addTrianglesToRTree() {
206 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
207 if (e.t != null) e.t.addToRTree();
210 /** does NOT update bound pairs! */
211 public boolean transform(Matrix m) {
212 if (immutableVertices) throw new Error();
214 unApplyQuadricToNeighbor();
217 if (vertices.get(this.p)==null) throw new Error();
218 vertices.remove(this);
219 removeTrianglesFromRTree();
220 float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
221 float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
222 float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
223 this.p = new Point(newx, newy, newz);
224 addTrianglesToRTree();
227 applyQuadricToNeighbor();
231 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
232 if (Math.abs(e.crossAngle()) > (Math.PI * 0.9) || Math.abs(e.next.crossAngle()) > (Math.PI * 0.9)) good = false;
233 if (e.t.aspect() < 0.1) good = false;
234 e.p2.quadricStale = true;
237 if (!ignorecollision && good) triangles.range(oldp, this.p, (Visitor<T>)this);
239 reComputeErrorAround();
243 public void visit(T t) {
245 for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
246 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { good = false; }
248 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { good = false; }
249 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { good = false; }
250 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { good = false; }
254 private boolean good;
256 public boolean move(Vec v) {
257 Matrix m = Matrix.translate(v);
261 good &= p.transform(m);
267 public E getFreeIncident() {
268 E ret = getFreeIncident(e, e);
269 if (ret != null) return ret;
270 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
271 System.out.println(e + " " + e.t);
272 throw new Error("unable to find free incident to " + this);
275 public E getFreeIncident(E start, E before) {
276 for(E e = start; e!=null; e=e.pair.next==before?null:e.pair.next)
277 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null)
282 public E getE(Point p2) {
283 Vertex v = vertices.get(p2);
284 if (v==null) return null;
287 public E getE(Vertex p2) {
288 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
289 if (e.p1 == this && e.p2 == p2) return e;
294 Vec norm = new Vec(0, 0, 0);
295 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
297 norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
301 public boolean isBoundTo(Vertex p) {
302 for(Vertex px = p; px!=null; px=(px.bound_to==p?null:px.bound_to))
308 public void unbind() { bound_to = this; binding = Matrix.ONE; }
309 public void bind(Vertex p) { bind(p, Matrix.ONE); }
310 public void bind(Vertex p, Matrix binding) {
311 if (isBoundTo(p)) return;
312 Vertex temp_bound_to = p.bound_to;
313 Matrix temp_binding = p.binding;
314 p.bound_to = this.bound_to;
315 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
316 this.bound_to = temp_bound_to;
317 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
321 public class BindingGroup {
322 private HashSet<E> set = new HashSet<E>();
323 public BindingGroup bind_others;
324 public BindingGroup other() { return bind_others; }
325 public BindingGroup(BindingGroup bind_others) { this.bind_others = bind_others; }
326 public BindingGroup() { this.bind_others = new BindingGroup(this); }
327 public BindingGroup(E e) { this(); set.add(e); }
328 public void add(E e) {
329 if (set.contains(e)) return;
331 BindingGroup e_bind_peers = e.bind_peers;
332 BindingGroup e_bind_to = e.bind_to;
334 e.bind_to = bind_others;
335 for (E epeer : e_bind_peers.set) add(epeer);
336 for (E eother : e_bind_to.set) bind_others.add(eother);
338 for(E eother : bind_others.set) {
339 if (e.next.bind_to.set.contains(eother.prev)) {
340 e.next.next.bindEdge(eother.prev.prev);
342 if (e.prev.bind_to.set.contains(eother.next)) {
343 e.prev.prev.bindEdge(eother.next.next);
348 public void dobind(E e) {
349 for(E ebound : set) {
350 e.p1.bind(ebound.p2);
351 e.p2.bind(ebound.p1);
354 public void shatter(BindingGroup bg1, BindingGroup bg2) {
356 e.shatter(e.midpoint(), bg1, bg2);
361 /** [UNIQUE] an edge */
362 public final class E implements Comparable<E> {
364 public final Vertex p1, p2;
365 T t; // triangle to our "left"
366 E prev; // previous half-edge
367 E next; // next half-edge
368 E pair; // partner half-edge
369 public BindingGroup bind_peers = new BindingGroup(this);
370 public BindingGroup bind_to = bind_peers.other();
371 boolean shattered = false;
373 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
374 public float comparator() {
375 Vertex nearest = score_against.nearest(midpoint());
376 return (float)Math.max(length(), midpoint().distance(nearest.p));
378 public int compareTo(E e) {
379 return e.comparator() > comparator() ? 1 : -1;
381 public void bindEdge(E e) { bind_to.add(e); }
382 public void dobind() { bind_to.dobind(this); }
384 public Point shatter() { return shatter(midpoint(), null, null); }
385 public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
386 if (shattered || destroyed) return mid;
393 int old_colorclass = t==null ? 0 : t.colorclass;
394 if (bg1==null) bg1 = new BindingGroup();
395 if (bg2==null) bg2 = new BindingGroup();
396 BindingGroup old_bind_to = bind_to;
397 bind_peers.shatter(bg1, bg2);
398 old_bind_to.shatter(bg2.other(), bg1.other());
402 newT(r.p, p1.p, mid, null, old_colorclass);
403 newT(r.p, mid, p2.p, null, old_colorclass);
404 bg1.add(p1.getE(mid));
405 bg2.add(p2.getE(mid).pair);
409 public boolean destroyed = false;
410 public void destroy() {
411 if (destroyed) return;
413 pair.destroyed = true;
415 if (t != null) t.destroy();
418 if (pair.t != null) pair.t.destroy();
421 if (next.t != null) next.t.destroy();
422 if (prev.t != null) prev.t.destroy();
426 if (pair.next.t != null) pair.next.t.destroy();
427 if (pair.prev.t != null) pair.next.t.destroy();
433 this.bind_peers = null;
434 pair.bind_peers = null;
435 pair.prev.next = next;
436 next.prev = pair.prev;
437 prev.next = pair.next;
439 if (p1.e == this) p1.e = prev.next;
440 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
443 private void sync() {
444 this.prev.next = this;
445 this.next.prev = this;
446 this.pair.pair = this;
447 bind_peers.add(this);
448 if (this.next.p1 != p2) throw new Error();
449 if (this.prev.p2 != p1) throw new Error();
450 if (this.p1.e == null) this.p1.e = this;
451 if (!added) added = true;
453 private boolean added = false;
455 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
457 public double crossAngle() {
458 Vec v1 = t.norm().times(-1);
459 Vec v2 = pair.t.norm().times(-1);
460 return Math.acos(v1.norm().dot(v2.norm()));
463 /** angle between this half-edge and the next */
464 public double angle() {
465 Vec v1 = next.p2.p.minus(p2.p);
466 Vec v2 = this.p1.p.minus(p2.p);
467 return Math.acos(v1.norm().dot(v2.norm()));
470 public void makeAdjacent(E e) {
471 if (this.next == e) return;
472 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
473 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
475 E freeIncident = p2.getFreeIncident(e, this);
477 e.prev.next = freeIncident.next;
478 freeIncident.next.prev = e.prev;
480 freeIncident.next = this.next;
481 this.next.prev = freeIncident;
490 /** creates an isolated edge out in the middle of space */
491 public E(Point p1, Point p2) {
492 if (vertices.get(p1) != null) throw new Error();
493 if (vertices.get(p2) != null) throw new Error();
494 this.p1 = new Vertex(p1);
495 this.p2 = new Vertex(p2);
496 this.prev = this.next = this.pair = new E(this, this, this);
498 this.p2.e = this.pair;
502 /** adds a new half-edge from prev.p2 to p2 */
503 public E(E prev, Point p) {
505 p2 = vertices.get(p);
506 if (p2 == null) p2 = new Vertex(p);
510 if (p2.getE(p1) != null) throw new Error();
512 this.next = this.pair = new E(this, this, prev.next);
514 E q = p2.getFreeIncident();
516 this.next.prev = this;
518 this.prev.next = this;
519 this.pair = new E(q, this, z);
521 if (p2.e==null) p2.e = this.pair;
525 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
526 public E(E prev, E pair, E next) {
534 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); }
535 public boolean has(Vertex v) { return v==p1 || v==p2; }
536 public float length() { return p1.p.minus(p2.p).mag(); }
537 public String toString() { return p1+"->"+p2; }
541 public E makeE(Point p1, Point p2) {
542 Vertex v1 = vertices.get(p1);
543 Vertex v2 = vertices.get(p2);
544 if (v1 != null && v2 != null) {
546 if (e != null) return e;
548 if (e != null) return e;
550 if (v1 != null) return new E(v1.getFreeIncident(), p2);
551 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
552 return new E(p1, p2);
554 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
556 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
557 float dot = norm.dot(norm2);
558 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
559 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
561 E e12 = makeE(p1, p2);
562 E e23 = makeE(p2, p3);
563 E e31 = makeE(p3, p1);
564 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
565 e12.makeAdjacent(e23);
566 e23.makeAdjacent(e31);
567 e31.makeAdjacent(e12);
569 T ret = e12.makeT(colorclass);
570 if (e12.t == null) throw new Error();
571 if (e23.t == null) throw new Error();
572 if (e31.t == null) throw new Error();
577 /** [UNIQUE] a triangle (face) */
578 public final class T extends Triangle {
580 public final int color;
581 public final int colorclass;
583 public void removeFromRTree() { triangles.remove(this); }
584 public void addToRTree() { triangles.insert(this); }
586 public void destroy() { triangles.remove(this); }
588 T(E e1, int colorclass) {
592 if (e1==e2 || e1==e3) throw new Error();
593 if (e3.next!=e1) throw new Error();
594 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
597 e1.next.next.t = this;
599 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
601 int color = Math.abs(random.nextInt());
604 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
605 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
606 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
610 this.colorclass = colorclass;
613 public E e1() { return e1; }
614 public E e2() { return e1.next; }
615 public E e3() { return e1.prev; }
616 public Vertex v1() { return e1.p1; }
617 public Vertex v2() { return e1.p2; }
618 public Vertex v3() { return e1.next.p2; }
619 public Point p1() { return e1.p1.p; }
620 public Point p2() { return e1.p2.p; }
621 public Point p3() { return e1.next.p2.p; }
622 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
623 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
625 public boolean shouldBeDrawn() {
626 if (e1().bind_to.set.size() == 0) return false;
627 if (e2().bind_to.set.size() == 0) return false;
628 if (e3().bind_to.set.size() == 0) return false;