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 unApplyQuadricToNeighborAll() {
50 for(Vertex p : vertices)
51 p.unApplyQuadricToNeighbor();
53 public void recomputeAllFundamentalQuadrics() {
54 for(Vertex p : vertices)
55 p.recomputeFundamentalQuadric();
57 public void applyQuadricToNeighborAll() {
58 for(Vertex p : vertices)
59 p.applyQuadricToNeighbor();
62 public void transform(Matrix m) {
63 ArrayList<Vertex> set = new ArrayList<Vertex>();
64 for(Vertex v : vertices) set.add(v);
65 for(Vertex v : set) v.transform(m);
68 public void rebuild() { /*vertices.rebuild();*/ }
69 public Vec diagonal() { return vertices.diagonal(); }
70 public Point centroid() { return vertices.centroid(); }
71 public Vertex nearest(Point p) { return vertices.nearest(p); }
73 /** compute the volume of the mesh */
74 public float volume() {
77 double area = t.area();
78 Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
79 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
80 double height = Math.abs(t.norm().dot(origin_to_centroid));
81 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
87 // Vertexices //////////////////////////////////////////////////////////////////////////////
89 /** a vertex in the mesh */
90 public final class Vertex extends HasPoint implements Visitor<T> {
91 public String toString() { return p.toString(); }
93 E e; // some edge *leaving* this point
95 /** the nearest vertex in the "score_against" mesh */
96 Vertex nearest_in_other_mesh;
97 /** the number of vertices in the other mesh for which this is the nearest_in_other_mesh */
99 /** the total error quadric (contributions from all vertices in other mesh for which this is nearest) */
100 Matrix quadric = Matrix.ZERO;
102 Matrix binding = Matrix.ONE;
103 Vertex bound_to = this;
105 boolean quadricStale = false;
107 public Matrix errorQuadric() { return quadric; }
108 public Point getPoint() { return p; }
109 public float score() { return oldscore; }
111 private Matrix fundamentalQuadric = null;
112 public Matrix fundamentalQuadric() {
113 if (fundamentalQuadric == null) recomputeFundamentalQuadric();
114 return fundamentalQuadric;
117 private Vertex(Point p) {
119 if (vertices.get(p) != null) throw new Error();
123 private void glNormal(GL gl) {
125 gl.glNormal3f(norm.x, norm.y, norm.z);
128 public void recomputeFundamentalQuadric() {
129 if (!quadricStale && fundamentalQuadric != null) return;
130 quadricStale = false;
131 unApplyQuadricToNeighbor();
132 Matrix m = Matrix.ZERO;
134 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
136 m = m.plus(t.norm().fundamentalQuadric(t.centroid()));
139 fundamentalQuadric = m.times(1/(float)count);
140 applyQuadricToNeighbor();
143 public void unApplyQuadricToNeighbor() {
144 if (nearest_in_other_mesh == null) return;
145 if (fundamentalQuadric == null) return;
146 nearest_in_other_mesh.unComputeError();
147 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.minus(fundamentalQuadric);
148 nearest_in_other_mesh.quadric_count--;
149 if (nearest_in_other_mesh.quadric_count==0)
150 nearest_in_other_mesh.quadric = Matrix.ZERO;
151 nearest_in_other_mesh.computeError();
152 nearest_in_other_mesh = null;
155 public void applyQuadricToNeighbor() {
156 if (score_against == null) return;
158 Vertex new_nearest = score_against.nearest(p);
159 if (nearest_in_other_mesh != null && new_nearest == nearest_in_other_mesh) return;
161 if (nearest_in_other_mesh != null) unApplyQuadricToNeighbor();
162 if (nearest_in_other_mesh != null) throw new Error();
164 nearest_in_other_mesh = new_nearest;
166 // don't attract to vertices that face the other way
167 if (nearest_in_other_mesh.e == null || nearest_in_other_mesh.norm().dot(norm()) < 0) {
168 nearest_in_other_mesh = null;
170 nearest_in_other_mesh.unComputeError();
171 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.plus(fundamentalQuadric());
172 nearest_in_other_mesh.quadric_count++;
173 nearest_in_other_mesh.computeError();
178 public void reComputeErrorAround() {
180 if (nearest_in_other_mesh != null) nearest_in_other_mesh.reComputeError();
181 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
182 e.p2.reComputeError();
184 public void reComputeError() {
188 public void unComputeError() {
192 public void computeError() {
195 ? (quadric.preAndPostMultiply(p) * 100) / quadric_count
198 : nearest_in_other_mesh != null
199 ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p) * 100 * 10
200 : score_against != null
201 ? score_against.nearest(p).fundamentalQuadric().preAndPostMultiply(p) * 100 * 10
203 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
204 double ang = Math.abs(e.crossAngle());
205 if (ang > Math.PI) throw new Error();
206 float minangle = (float)(Math.PI * 0.8);
208 oldscore += (ang - minangle);
213 private void removeTrianglesFromRTree() {
214 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
215 if (e.t != null) e.t.removeFromRTree();
217 private void addTrianglesToRTree() {
218 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
219 if (e.t != null) e.t.addToRTree();
222 /** does NOT update bound pairs! */
223 public boolean transform(Matrix m) {
224 if (immutableVertices) throw new Error();
226 unApplyQuadricToNeighbor();
229 if (vertices.get(this.p)==null) throw new Error();
230 vertices.remove(this);
231 removeTrianglesFromRTree();
232 float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
233 float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
234 float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
235 this.p = new Point(newx, newy, newz);
236 addTrianglesToRTree();
239 applyQuadricToNeighbor();
243 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
244 if (Math.abs(e.crossAngle()) > (Math.PI * 0.9) || Math.abs(e.next.crossAngle()) > (Math.PI * 0.9)) good = false;
245 if (e.t.aspect() < 0.1) good = false;
246 e.p2.quadricStale = true;
249 if (!ignorecollision && good) triangles.range(oldp, this.p, (Visitor<T>)this);
251 reComputeErrorAround();
255 public void visit(T t) {
257 for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
258 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { good = false; }
260 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { good = false; }
261 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { good = false; }
262 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { good = false; }
266 private boolean good;
268 public boolean move(Vec v) {
269 Matrix m = Matrix.translate(v);
273 good &= p.transform(m);
279 public E getFreeIncident() {
280 E ret = getFreeIncident(e, e);
281 if (ret != null) return ret;
282 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
283 System.out.println(e + " " + e.t);
284 throw new Error("unable to find free incident to " + this);
287 public E getFreeIncident(E start, E before) {
288 for(E e = start; e!=null; e=e.pair.next==before?null:e.pair.next)
289 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null)
294 public E getE(Point p2) {
295 Vertex v = vertices.get(p2);
296 if (v==null) return null;
299 public E getE(Vertex p2) {
300 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
301 if (e.p1 == this && e.p2 == p2) return e;
306 Vec norm = new Vec(0, 0, 0);
307 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
309 norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
313 public boolean isBoundTo(Vertex p) {
314 for(Vertex px = p; px!=null; px=(px.bound_to==p?null:px.bound_to))
320 public void unbind() { bound_to = this; binding = Matrix.ONE; }
321 public void bind(Vertex p) { bind(p, Matrix.ONE); }
322 public void bind(Vertex p, Matrix binding) {
323 if (isBoundTo(p)) return;
324 Vertex temp_bound_to = p.bound_to;
325 Matrix temp_binding = p.binding;
326 p.bound_to = this.bound_to;
327 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
328 this.bound_to = temp_bound_to;
329 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
333 public class BindingGroup {
334 private HashSet<E> set = new HashSet<E>();
335 public BindingGroup bind_others;
336 public BindingGroup other() { return bind_others; }
337 public BindingGroup(BindingGroup bind_others) { this.bind_others = bind_others; }
338 public BindingGroup() { this.bind_others = new BindingGroup(this); }
339 public BindingGroup(E e) { this(); set.add(e); }
340 public void add(E e) {
341 if (set.contains(e)) return;
343 BindingGroup e_bind_peers = e.bind_peers;
344 BindingGroup e_bind_to = e.bind_to;
346 e.bind_to = bind_others;
347 for (E epeer : e_bind_peers.set) add(epeer);
348 for (E eother : e_bind_to.set) bind_others.add(eother);
350 for(E eother : bind_others.set) {
351 if (e.next.bind_to.set.contains(eother.prev)) {
352 e.next.next.bindEdge(eother.prev.prev);
354 if (e.prev.bind_to.set.contains(eother.next)) {
355 e.prev.prev.bindEdge(eother.next.next);
360 public void dobind(E e) {
361 for(E ebound : set) {
362 e.p1.bind(ebound.p2);
363 e.p2.bind(ebound.p1);
366 public void shatter(BindingGroup bg1, BindingGroup bg2) {
368 e.shatter(e.midpoint(), bg1, bg2);
373 /** [UNIQUE] an edge */
374 public final class E implements Comparable<E> {
376 public final Vertex p1, p2;
377 T t; // triangle to our "left"
378 E prev; // previous half-edge
379 E next; // next half-edge
380 E pair; // partner half-edge
381 public BindingGroup bind_peers = new BindingGroup(this);
382 public BindingGroup bind_to = bind_peers.other();
383 boolean shattered = false;
385 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
386 public float comparator() {
387 Vertex nearest = score_against.nearest(midpoint());
388 return (float)Math.max(length(), midpoint().distance(nearest.p));
390 public int compareTo(E e) {
391 return e.comparator() > comparator() ? 1 : -1;
393 public void bindEdge(E e) { bind_to.add(e); }
394 public void dobind() { bind_to.dobind(this); }
396 public Point shatter() { return shatter(midpoint(), null, null); }
397 public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
398 if (shattered || destroyed) return mid;
405 int old_colorclass = t==null ? 0 : t.colorclass;
406 if (bg1==null) bg1 = new BindingGroup();
407 if (bg2==null) bg2 = new BindingGroup();
408 BindingGroup old_bind_to = bind_to;
409 bind_peers.shatter(bg1, bg2);
410 old_bind_to.shatter(bg2.other(), bg1.other());
414 newT(r.p, p1.p, mid, null, old_colorclass);
415 newT(r.p, mid, p2.p, null, old_colorclass);
416 bg1.add(p1.getE(mid));
417 bg2.add(p2.getE(mid).pair);
421 public boolean destroyed = false;
422 public void destroy() {
423 if (destroyed) return;
425 pair.destroyed = true;
427 if (t != null) t.destroy();
430 if (pair.t != null) pair.t.destroy();
433 if (next.t != null) next.t.destroy();
434 if (prev.t != null) prev.t.destroy();
438 if (pair.next.t != null) pair.next.t.destroy();
439 if (pair.prev.t != null) pair.next.t.destroy();
445 this.bind_peers = null;
446 pair.bind_peers = null;
447 pair.prev.next = next;
448 next.prev = pair.prev;
449 prev.next = pair.next;
451 if (p1.e == this) p1.e = prev.next;
452 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
455 private void sync() {
456 this.prev.next = this;
457 this.next.prev = this;
458 this.pair.pair = this;
459 bind_peers.add(this);
460 if (this.next.p1 != p2) throw new Error();
461 if (this.prev.p2 != p1) throw new Error();
462 if (this.p1.e == null) this.p1.e = this;
463 if (!added) added = true;
465 private boolean added = false;
467 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
469 public double crossAngle() {
470 Vec v1 = t.norm().times(-1);
471 Vec v2 = pair.t.norm().times(-1);
472 return Math.acos(v1.norm().dot(v2.norm()));
475 /** angle between this half-edge and the next */
476 public double angle() {
477 Vec v1 = next.p2.p.minus(p2.p);
478 Vec v2 = this.p1.p.minus(p2.p);
479 return Math.acos(v1.norm().dot(v2.norm()));
482 public void makeAdjacent(E e) {
483 if (this.next == e) return;
484 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
485 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
487 E freeIncident = p2.getFreeIncident(e, this);
489 e.prev.next = freeIncident.next;
490 freeIncident.next.prev = e.prev;
492 freeIncident.next = this.next;
493 this.next.prev = freeIncident;
502 /** creates an isolated edge out in the middle of space */
503 public E(Point p1, Point p2) {
504 if (vertices.get(p1) != null) throw new Error();
505 if (vertices.get(p2) != null) throw new Error();
506 this.p1 = new Vertex(p1);
507 this.p2 = new Vertex(p2);
508 this.prev = this.next = this.pair = new E(this, this, this);
510 this.p2.e = this.pair;
514 /** adds a new half-edge from prev.p2 to p2 */
515 public E(E prev, Point p) {
517 p2 = vertices.get(p);
518 if (p2 == null) p2 = new Vertex(p);
522 if (p2.getE(p1) != null) throw new Error();
524 this.next = this.pair = new E(this, this, prev.next);
526 E q = p2.getFreeIncident();
528 this.next.prev = this;
530 this.prev.next = this;
531 this.pair = new E(q, this, z);
533 if (p2.e==null) p2.e = this.pair;
537 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
538 public E(E prev, E pair, E next) {
546 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); }
547 public boolean has(Vertex v) { return v==p1 || v==p2; }
548 public float length() { return p1.p.minus(p2.p).mag(); }
549 public String toString() { return p1+"->"+p2; }
553 public E makeE(Point p1, Point p2) {
554 Vertex v1 = vertices.get(p1);
555 Vertex v2 = vertices.get(p2);
556 if (v1 != null && v2 != null) {
558 if (e != null) return e;
560 if (e != null) return e;
562 if (v1 != null) return new E(v1.getFreeIncident(), p2);
563 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
564 return new E(p1, p2);
566 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
568 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
569 float dot = norm.dot(norm2);
570 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
571 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
573 E e12 = makeE(p1, p2);
574 E e23 = makeE(p2, p3);
575 E e31 = makeE(p3, p1);
576 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
577 e12.makeAdjacent(e23);
578 e23.makeAdjacent(e31);
579 e31.makeAdjacent(e12);
581 T ret = e12.makeT(colorclass);
582 if (e12.t == null) throw new Error();
583 if (e23.t == null) throw new Error();
584 if (e31.t == null) throw new Error();
589 /** [UNIQUE] a triangle (face) */
590 public final class T extends Triangle {
592 public final int color;
593 public final int colorclass;
595 public void removeFromRTree() { triangles.remove(this); }
596 public void addToRTree() { triangles.insert(this); }
598 public void destroy() { triangles.remove(this); }
600 T(E e1, int colorclass) {
604 if (e1==e2 || e1==e3) throw new Error();
605 if (e3.next!=e1) throw new Error();
606 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
609 e1.next.next.t = this;
611 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
613 int color = Math.abs(random.nextInt());
616 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
617 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
618 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
622 this.colorclass = colorclass;
625 public E e1() { return e1; }
626 public E e2() { return e1.next; }
627 public E e3() { return e1.prev; }
628 public Vertex v1() { return e1.p1; }
629 public Vertex v2() { return e1.p2; }
630 public Vertex v3() { return e1.next.p2; }
631 public Point p1() { return e1.p1.p; }
632 public Point p2() { return e1.p2.p; }
633 public Point p3() { return e1.next.p2.p; }
634 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
635 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
637 public boolean shouldBeDrawn() {
638 if (e1().bind_to.set.size() == 0) return false;
639 if (e2().bind_to.set.size() == 0) return false;
640 if (e3().bind_to.set.size() == 0) return false;