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 HashSet<Vertex> done = new HashSet<Vertex>();
52 for(Vertex p : new Vertex[] { t.v1(), t.v2(), t.v3() }) {
53 if (done.contains(p)) continue;
55 p.unApplyQuadricToNeighbor();
58 public void recomputeAllFundamentalQuadrics() {
59 HashSet<Vertex> done = new HashSet<Vertex>();
61 for(Vertex p : new Vertex[] { t.v1(), t.v2(), t.v3() }) {
62 if (done.contains(p)) continue;
64 p.recomputeFundamentalQuadric();
67 public float applyQuadricToNeighborAll() {
70 HashSet<Vertex> done = new HashSet<Vertex>();
72 for(Vertex p : new Vertex[] { t.v1(), t.v2(), t.v3() }) {
73 if (done.contains(p)) continue;
75 p.applyQuadricToNeighbor();
78 return (float)(dist/num);
81 public void transform(Matrix m) {
82 ArrayList<Vertex> set = new ArrayList<Vertex>();
83 for(Vertex v : vertices) set.add(v);
84 for(Vertex v : set) v.transform(m);
87 public void rebuild() { /*vertices.rebuild();*/ }
88 public Vec diagonal() { return vertices.diagonal(); }
89 public Point centroid() { return vertices.centroid(); }
90 public Vertex nearest(Point p) { return vertices.nearest(p); }
92 /** compute the volume of the mesh */
93 public float volume() {
96 double area = t.area();
97 Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
98 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
99 double height = Math.abs(t.norm().dot(origin_to_centroid));
100 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
106 // Vertexices //////////////////////////////////////////////////////////////////////////////
108 /** a vertex in the mesh */
109 public final class Vertex extends HasPoint implements Visitor<T> {
110 public String toString() { return p.toString(); }
112 E e; // some edge *leaving* this point
114 /** the nearest vertex in the "score_against" mesh */
115 Vertex nearest_in_other_mesh;
116 /** the number of vertices in the other mesh for which this is the nearest_in_other_mesh */
118 /** the total error quadric (contributions from all vertices in other mesh for which this is nearest) */
119 Matrix quadric = Matrix.ZERO;
121 Vertex bound_to = this;
122 Matrix binding = Matrix.ONE;
124 boolean quadricStale = false;
126 public Matrix errorQuadric() { return quadric; }
127 public Point getPoint() { return p; }
128 public float score() { return oldscore; }
130 private Matrix fundamentalQuadric = null;
131 public Matrix fundamentalQuadric() {
132 if (fundamentalQuadric == null) recomputeFundamentalQuadric();
133 return fundamentalQuadric;
136 private Vertex(Point p) {
138 if (vertices.get(p) != null) throw new Error();
142 private void glNormal(GL gl) {
144 gl.glNormal3f(norm.x, norm.y, norm.z);
147 public void recomputeFundamentalQuadric() {
148 if (!quadricStale && fundamentalQuadric != null) return;
149 quadricStale = false;
150 unApplyQuadricToNeighbor();
151 Matrix m = Matrix.ZERO;
153 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
155 m = m.plus(t.norm().fundamentalQuadric(t.centroid()));
158 fundamentalQuadric = m.times(1/(float)count);
159 applyQuadricToNeighbor();
162 public void unApplyQuadricToNeighbor() {
163 if (nearest_in_other_mesh == null) return;
164 if (fundamentalQuadric == null) return;
165 nearest_in_other_mesh.unComputeError();
166 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.minus(fundamentalQuadric);
167 nearest_in_other_mesh.quadric_count--;
168 if (nearest_in_other_mesh.quadric_count==0)
169 nearest_in_other_mesh.quadric = Matrix.ZERO;
170 nearest_in_other_mesh.computeError();
171 nearest_in_other_mesh = null;
174 public void applyQuadricToNeighbor() {
175 if (score_against == null) return;
177 Vertex new_nearest = score_against.nearest(p);
178 if (nearest_in_other_mesh != null && new_nearest == nearest_in_other_mesh) return;
180 if (nearest_in_other_mesh != null) unApplyQuadricToNeighbor();
181 if (nearest_in_other_mesh != null) throw new Error();
183 nearest_in_other_mesh = new_nearest;
185 // don't attract to vertices that face the other way
186 if (nearest_in_other_mesh.e == null || nearest_in_other_mesh.norm().dot(norm()) < 0) {
187 nearest_in_other_mesh = null;
189 nearest_in_other_mesh.unComputeError();
190 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.plus(fundamentalQuadric());
191 nearest_in_other_mesh.quadric_count++;
192 nearest_in_other_mesh.computeError();
197 public void reComputeErrorAround() {
199 if (nearest_in_other_mesh != null) nearest_in_other_mesh.reComputeError();
200 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
201 e.p2.reComputeError();
203 public void reComputeError() {
207 public void unComputeError() {
211 public void computeError() {
214 ? (quadric.preAndPostMultiply(p) * 100) / quadric_count
217 : nearest_in_other_mesh != null
218 ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p) * 100 * 10
219 : score_against != null
220 ? score_against.nearest(p).fundamentalQuadric().preAndPostMultiply(p) * 100 * 10
222 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
223 double ang = Math.abs(e.crossAngle());
224 if (ang > Math.PI) throw new Error();
225 float minangle = (float)(Math.PI * 0.8);
227 oldscore += (ang - minangle);
233 private void removeTrianglesFromRTree() {
234 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
235 if (e.t != null) e.t.removeFromRTree();
237 private void addTrianglesToRTree() {
238 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
239 if (e.t != null) e.t.addToRTree();
242 /** does NOT update bound pairs! */
243 public boolean transform(Matrix m) {
244 if (immutableVertices) throw new Error();
246 unApplyQuadricToNeighbor();
249 if (vertices.get(this.p)==null) throw new Error();
250 vertices.remove(this);
251 removeTrianglesFromRTree();
252 float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
253 float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
254 float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
255 this.p = new Point(newx, newy, newz);
256 addTrianglesToRTree();
259 applyQuadricToNeighbor();
263 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
264 if (Math.abs(e.crossAngle()) > (Math.PI * 0.9) || Math.abs(e.next.crossAngle()) > (Math.PI * 0.9)) good = false;
265 if (e.t.aspect() < 0.1) good = false;
266 e.p2.quadricStale = true;
269 if (!ignorecollision && good) triangles.range(oldp, this.p, (Visitor<T>)this);
271 reComputeErrorAround();
275 public void visit(T t) {
277 for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
278 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { good = false; }
280 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { good = false; }
281 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { good = false; }
282 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { good = false; }
286 private boolean good;
288 public boolean move(Vec v) {
289 Matrix m = Matrix.translate(v);
293 good &= p.transform(m);
299 public E getFreeIncident() {
300 E ret = getFreeIncident(e, e);
301 if (ret != null) return ret;
302 ret = getFreeIncident(e.pair.next, e.pair.next);
306 System.out.println(ex + " " + ex.t);
309 throw new Error("unable to find free incident to " + this);
314 public E getFreeIncident(E start, E before) {
317 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null) return e.pair;
319 } while(e != before);
323 public E getE(Point p2) {
324 Vertex v = vertices.get(p2);
325 if (v==null) return null;
328 public E getE(Vertex p2) {
331 if (e==null) return null;
332 if (e.p1 == this && e.p2 == p2) return e;
339 Vec norm = new Vec(0, 0, 0);
342 if (e.t != null) norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
344 } while(e != this.e);
348 public boolean isBoundTo(Vertex p) {
351 if (px==this) return true;
356 public void unbind() { bound_to = this; binding = Matrix.ONE; }
357 public void bind(Vertex p) { bind(p, Matrix.ONE); }
358 public void bind(Vertex p, Matrix binding) {
359 if (isBoundTo(p)) return;
360 Vertex temp_bound_to = p.bound_to;
361 Matrix temp_binding = p.binding;
362 p.bound_to = this.bound_to;
363 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
364 this.bound_to = temp_bound_to;
365 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
369 public class BindingGroup {
370 private HashSet<E> set = new HashSet<E>();
371 public BindingGroup bind_others;
372 public BindingGroup other() { return bind_others; }
373 public BindingGroup(BindingGroup bind_others) { this.bind_others = bind_others; }
374 public BindingGroup() { this.bind_others = new BindingGroup(this); }
375 public BindingGroup(E e) { this(); set.add(e); }
376 public void add(E e) {
377 if (set.contains(e)) return;
379 BindingGroup e_bind_peers = e.bind_peers;
380 BindingGroup e_bind_to = e.bind_to;
382 e.bind_to = bind_others;
383 for (E epeer : e_bind_peers.set) add(epeer);
384 for (E eother : e_bind_to.set) bind_others.add(eother);
386 for(E eother : bind_others.set) {
387 if (e.next.bind_to.set.contains(eother.prev)) {
388 e.next.next.bindEdge(eother.prev.prev);
390 if (e.prev.bind_to.set.contains(eother.next)) {
391 e.prev.prev.bindEdge(eother.next.next);
396 public void dobind(E e) {
397 for(E ebound : set) {
398 e.p1.bind(ebound.p2);
399 e.p2.bind(ebound.p1);
402 public void shatter(BindingGroup bg1, BindingGroup bg2) {
404 e.shatter(e.midpoint(), bg1, bg2);
409 /** [UNIQUE] an edge */
410 public final class E implements Comparable<E> {
412 public final Vertex p1, p2;
413 T t; // triangle to our "left"
414 E prev; // previous half-edge
415 E next; // next half-edge
416 E pair; // partner half-edge
417 public BindingGroup bind_peers = new BindingGroup(this);
418 public BindingGroup bind_to = bind_peers.other();
419 boolean shattered = false;
421 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
422 public float comparator() {
423 Vertex nearest = score_against.nearest(midpoint());
424 //if (t==null) return length();
426 double ang = Math.abs(crossAngle());
427 float minangle = (float)(Math.PI * 0.9);
432 if ((length() * length()) / t.area() > 10)
433 return (float)(length()*Math.sqrt(t.area()));
434 return length()*t.area();
436 return (float)Math.max(length(), midpoint().distance(nearest.p));
439 public int compareTo(E e) {
440 return e.comparator() > comparator() ? 1 : -1;
442 public void bindEdge(E e) { bind_to.add(e); }
443 public void dobind() { bind_to.dobind(this); }
445 public Point shatter() { return shatter(midpoint(), null, null); }
446 public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
447 if (shattered || destroyed) return mid;
454 int old_colorclass = t==null ? 0 : t.colorclass;
455 if (bg1==null) bg1 = new BindingGroup();
456 if (bg2==null) bg2 = new BindingGroup();
457 BindingGroup old_bind_to = bind_to;
458 bind_peers.shatter(bg1, bg2);
459 old_bind_to.shatter(bg2.other(), bg1.other());
463 newT(r.p, p1.p, mid, null, old_colorclass);
464 newT(r.p, mid, p2.p, null, old_colorclass);
465 bg1.add(p1.getE(mid));
466 bg2.add(p2.getE(mid).pair);
470 public boolean destroyed = false;
471 public void destroy() {
472 if (destroyed) return;
474 pair.destroyed = true;
476 if (t != null) t.destroy();
479 if (pair.t != null) pair.t.destroy();
482 if (next.t != null) next.t.destroy();
483 if (prev.t != null) prev.t.destroy();
487 if (pair.next.t != null) pair.next.t.destroy();
488 if (pair.prev.t != null) pair.next.t.destroy();
494 this.bind_peers = null;
495 pair.bind_peers = null;
496 pair.prev.next = next;
497 next.prev = pair.prev;
498 prev.next = pair.next;
500 if (p1.e == this) p1.e = prev.next;
501 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
504 private void sync() {
505 this.prev.next = this;
506 this.next.prev = this;
507 this.pair.pair = this;
508 bind_peers.add(this);
509 if (this.next.p1 != p2) throw new Error();
510 if (this.prev.p2 != p1) throw new Error();
511 if (this.p1.e == null) this.p1.e = this;
512 if (!added) added = true;
514 private boolean added = false;
516 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
518 public double crossAngle() {
519 Vec v1 = t.norm().times(-1);
520 Vec v2 = pair.t.norm().times(-1);
521 return Math.acos(v1.norm().dot(v2.norm()));
524 /** angle between this half-edge and the next */
525 public double angle() {
526 Vec v1 = next.p2.p.minus(p2.p);
527 Vec v2 = this.p1.p.minus(p2.p);
528 return Math.acos(v1.norm().dot(v2.norm()));
531 public void makeAdjacent(E e) {
532 if (this.next == e) return;
533 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
534 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
536 E freeIncident = p2.getFreeIncident(e, this);
538 e.prev.next = freeIncident.next;
539 freeIncident.next.prev = e.prev;
541 freeIncident.next = this.next;
542 this.next.prev = freeIncident;
551 /** creates an isolated edge out in the middle of space */
552 public E(Point p1, Point p2) {
553 if (vertices.get(p1) != null) throw new Error();
554 if (vertices.get(p2) != null) throw new Error();
555 this.p1 = new Vertex(p1);
556 this.p2 = new Vertex(p2);
557 this.prev = this.next = this.pair = new E(this, this, this);
559 this.p2.e = this.pair;
563 /** adds a new half-edge from prev.p2 to p2 */
564 public E(E prev, Point p) {
566 p2 = vertices.get(p);
567 if (p2 == null) p2 = new Vertex(p);
571 if (p2.getE(p1) != null) throw new Error();
573 this.next = this.pair = new E(this, this, prev.next);
575 E q = p2.getFreeIncident();
577 this.next.prev = this;
579 this.prev.next = this;
580 this.pair = new E(q, this, z);
582 if (p2.e==null) p2.e = this.pair;
586 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
587 public E(E prev, E pair, E next) {
595 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); }
596 public boolean has(Vertex v) { return v==p1 || v==p2; }
597 public float length() { return p1.p.minus(p2.p).mag(); }
598 public String toString() { return p1+"->"+p2; }
602 public E makeE(Point p1, Point p2) {
603 Vertex v1 = vertices.get(p1);
604 Vertex v2 = vertices.get(p2);
605 if (v1 != null && v2 != null) {
607 if (e != null) return e;
609 if (e != null) return e;
611 if (v1 != null) return new E(v1.getFreeIncident(), p2);
612 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
613 return new E(p1, p2);
615 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
617 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
618 float dot = norm.dot(norm2);
619 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
620 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
622 E e12 = makeE(p1, p2);
623 E e23 = makeE(p2, p3);
624 E e31 = makeE(p3, p1);
625 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
626 e12.makeAdjacent(e23);
627 e23.makeAdjacent(e31);
628 e31.makeAdjacent(e12);
630 T ret = e12.makeT(colorclass);
631 if (e12.t == null) throw new Error();
632 if (e23.t == null) throw new Error();
633 if (e31.t == null) throw new Error();
638 /** [UNIQUE] a triangle (face) */
639 public final class T extends Triangle {
641 public final int color;
642 public final int colorclass;
644 public void removeFromRTree() { triangles.remove(this); }
645 public void addToRTree() { triangles.insert(this); }
647 public void destroy() { triangles.remove(this); }
649 T(E e1, int colorclass) {
653 if (e1==e2 || e1==e3) throw new Error();
654 if (e3.next!=e1) throw new Error();
655 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
658 e1.next.next.t = this;
660 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
662 int color = Math.abs(random.nextInt());
665 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
666 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
667 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
671 this.colorclass = colorclass;
674 public E e1() { return e1; }
675 public E e2() { return e1.next; }
676 public E e3() { return e1.prev; }
677 public Vertex v1() { return e1.p1; }
678 public Vertex v2() { return e1.p2; }
679 public Vertex v3() { return e1.next.p2; }
680 public Point p1() { return e1.p1.p; }
681 public Point p2() { return e1.p2.p; }
682 public Point p3() { return e1.next.p2.p; }
683 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
684 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
686 public boolean shouldBeDrawn() {
687 if (e1().bind_to.set.size() == 0) return false;
688 if (e2().bind_to.set.size() == 0) return false;
689 if (e3().bind_to.set.size() == 0) return false;