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;
156 m = m.plus(t.norm().fundamentalQuadric(t.centroid()));
159 } while(e != this.e);
160 fundamentalQuadric = m.times(1/(float)count);
161 applyQuadricToNeighbor();
164 public void unApplyQuadricToNeighbor() {
165 if (nearest_in_other_mesh == null) return;
166 if (fundamentalQuadric == null) return;
167 nearest_in_other_mesh.unComputeError();
168 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.minus(fundamentalQuadric);
169 nearest_in_other_mesh.quadric_count--;
170 if (nearest_in_other_mesh.quadric_count==0)
171 nearest_in_other_mesh.quadric = Matrix.ZERO;
172 nearest_in_other_mesh.computeError();
173 nearest_in_other_mesh = null;
176 public void applyQuadricToNeighbor() {
177 if (score_against == null) return;
179 Vertex new_nearest = score_against.nearest(p);
180 if (nearest_in_other_mesh != null && new_nearest == nearest_in_other_mesh) return;
182 if (nearest_in_other_mesh != null) unApplyQuadricToNeighbor();
183 if (nearest_in_other_mesh != null) throw new Error();
185 nearest_in_other_mesh = new_nearest;
187 // don't attract to vertices that face the other way
188 if (nearest_in_other_mesh.e == null || nearest_in_other_mesh.norm().dot(norm()) < 0) {
189 nearest_in_other_mesh = null;
191 nearest_in_other_mesh.unComputeError();
192 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.plus(fundamentalQuadric());
193 nearest_in_other_mesh.quadric_count++;
194 nearest_in_other_mesh.computeError();
199 public void reComputeErrorAround() {
201 if (nearest_in_other_mesh != null) nearest_in_other_mesh.reComputeError();
204 e.p2.reComputeError();
206 } while (e != this.e);
208 public void reComputeError() {
212 public void unComputeError() {
216 public void computeError() {
217 if (quadric_count == 0) {
218 if (immutableVertices) {
219 } else if (nearest_in_other_mesh == null) {
220 if (score_against != null) {
221 Vertex ne = score_against.nearest(p);
222 oldscore = ne.fundamentalQuadric().preAndPostMultiply(p) * 100 * 10;
227 oldscore = nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p) * 100 * 10;
230 oldscore = (quadric.preAndPostMultiply(p) * 100) / quadric_count;
239 //double ang = Math.abs(e.crossAngle());
240 double ang = Math.abs(e.crossAngle());
241 if (ang > Math.PI) throw new Error();
245 aspects += e.t.aspect()*e.t.aspect();
249 float minangle = (float)(Math.PI * 0.8);
251 oldscore += (ang - minangle);
254 } while (e != this.e);
255 if (numaspects > 0) oldscore += (aspects / numaspects);
257 //System.out.println(oldscore);
258 //oldscore = oldscore*oldscore;
262 private void removeTrianglesFromRTree() {
265 if (e.t != null) e.t.removeFromRTree();
267 } while(e != this.e);
269 private void addTrianglesToRTree() {
272 if (e.t != null) e.t.addToRTree();
274 } while(e != this.e);
277 /** does NOT update bound pairs! */
278 public boolean transform(Matrix m) {
279 if (immutableVertices) throw new Error();
280 unApplyQuadricToNeighbor();
283 if (vertices.get(this.p)==null) throw new Error();
284 vertices.remove(this);
285 removeTrianglesFromRTree();
286 float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
287 float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
288 float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
289 this.p = new Point(newx, newy, newz);
290 addTrianglesToRTree();
292 } catch (Exception e) {
293 throw new RuntimeException(e);
295 applyQuadricToNeighbor();
297 // FIXME: intersection test needed?
300 // should recompute fundamental quadrics of all vertices sharing a face, but we defer...
304 if (Math.abs(e.crossAngle()) > (Math.PI * 0.9) ||
305 Math.abs(e.next.crossAngle()) > (Math.PI * 0.9)) {
308 if (e.t.aspect() < 0.1) {
312 e.p2.quadricStale = true;
314 } while(e != this.e);
316 if (!ignorecollision && good) triangles.range(new Segment(oldp, this.p), this);
320 reComputeErrorAround();
324 public void visit(T t) {
328 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { good = false; }
330 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { good = false; }
331 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { good = false; }
332 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { good = false; }
335 } while(e != Vertex.this.e);
337 private boolean good;
339 public boolean move(Vec v) {
340 Matrix m = Matrix.translate(v);
344 good &= p.transform(m);
350 public E getFreeIncident() {
351 E ret = getFreeIncident(e, e);
352 if (ret != null) return ret;
353 ret = getFreeIncident(e.pair.next, e.pair.next);
357 System.out.println(ex + " " + ex.t);
360 throw new Error("unable to find free incident to " + this);
365 public E getFreeIncident(E start, E before) {
368 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null) return e.pair;
370 } while(e != before);
374 public E getE(Point p2) {
375 Vertex v = vertices.get(p2);
376 if (v==null) return null;
379 public E getE(Vertex p2) {
382 if (e==null) return null;
383 if (e.p1 == this && e.p2 == p2) return e;
390 Vec norm = new Vec(0, 0, 0);
393 if (e.t != null) norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
395 } while(e != this.e);
399 public boolean isBoundTo(Vertex p) {
402 if (px==this) return true;
407 public void unbind() { bound_to = this; binding = Matrix.ONE; }
408 public void bind(Vertex p) { bind(p, Matrix.ONE); }
409 public void bind(Vertex p, Matrix binding) {
410 if (isBoundTo(p)) return;
411 Vertex temp_bound_to = p.bound_to;
412 Matrix temp_binding = p.binding;
413 p.bound_to = this.bound_to;
414 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
415 this.bound_to = temp_bound_to;
416 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
420 public class BindingGroup {
421 private HashSet<E> set = new HashSet<E>();
422 public BindingGroup bind_others;
423 public BindingGroup other() { return bind_others; }
424 public BindingGroup(BindingGroup bind_others) { this.bind_others = bind_others; }
425 public BindingGroup() { this.bind_others = new BindingGroup(this); }
426 public BindingGroup(E e) { this(); set.add(e); }
427 public void add(E e) {
428 if (set.contains(e)) return;
430 BindingGroup e_bind_peers = e.bind_peers;
431 BindingGroup e_bind_to = e.bind_to;
433 e.bind_to = bind_others;
434 for (E epeer : e_bind_peers.set) add(epeer);
435 for (E eother : e_bind_to.set) bind_others.add(eother);
437 for(E eother : bind_others.set) {
438 if (e.next.bind_to.set.contains(eother.prev)) {
439 e.next.next.bindEdge(eother.prev.prev);
441 if (e.prev.bind_to.set.contains(eother.next)) {
442 e.prev.prev.bindEdge(eother.next.next);
447 public void dobind(E e) {
448 for(E ebound : set) {
449 e.p1.bind(ebound.p2);
450 e.p2.bind(ebound.p1);
453 public void shatter(BindingGroup bg1, BindingGroup bg2) {
455 e.shatter(e.midpoint(), bg1, bg2);
460 /** [UNIQUE] an edge */
461 public final class E implements Comparable<E> {
463 public final Vertex p1, p2;
464 T t; // triangle to our "left"
465 E prev; // previous half-edge
466 E next; // next half-edge
467 E pair; // partner half-edge
468 public BindingGroup bind_peers = new BindingGroup(this);
469 public BindingGroup bind_to = bind_peers.other();
470 boolean shattered = false;
472 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
473 public float comparator() {
474 Vertex nearest = score_against.nearest(midpoint());
475 //if (t==null) return length();
477 double ang = Math.abs(crossAngle());
478 float minangle = (float)(Math.PI * 0.9);
483 if ((length() * length()) / t.area() > 10)
484 return (float)(length()*Math.sqrt(t.area()));
485 return length()*t.area();
487 return (float)Math.max(length(), midpoint().distance(nearest.p));
490 public int compareTo(E e) {
491 return e.comparator() > comparator() ? 1 : -1;
493 public void bindEdge(E e) { bind_to.add(e); }
494 public void dobind() { bind_to.dobind(this); }
496 public Point shatter() { return shatter(midpoint(), null, null); }
497 public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
498 if (shattered || destroyed) return mid;
505 int old_colorclass = t==null ? 0 : t.colorclass;
506 if (bg1==null) bg1 = new BindingGroup();
507 if (bg2==null) bg2 = new BindingGroup();
508 BindingGroup old_bind_to = bind_to;
509 bind_peers.shatter(bg1, bg2);
510 old_bind_to.shatter(bg2.other(), bg1.other());
514 newT(r.p, p1.p, mid, null, old_colorclass);
515 newT(r.p, mid, p2.p, null, old_colorclass);
516 bg1.add(p1.getE(mid));
517 bg2.add(p2.getE(mid).pair);
521 public boolean destroyed = false;
522 public void destroy() {
523 if (destroyed) return;
525 pair.destroyed = true;
527 if (t != null) t.destroy();
530 if (pair.t != null) pair.t.destroy();
533 if (next.t != null) next.t.destroy();
534 if (prev.t != null) prev.t.destroy();
538 if (pair.next.t != null) pair.next.t.destroy();
539 if (pair.prev.t != null) pair.next.t.destroy();
545 this.bind_peers = null;
546 pair.bind_peers = null;
547 pair.prev.next = next;
548 next.prev = pair.prev;
549 prev.next = pair.next;
551 if (p1.e == this) p1.e = prev.next;
552 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
555 private void sync() {
556 this.prev.next = this;
557 this.next.prev = this;
558 this.pair.pair = this;
559 bind_peers.add(this);
560 if (this.next.p1 != p2) throw new Error();
561 if (this.prev.p2 != p1) throw new Error();
562 if (this.p1.e == null) this.p1.e = this;
563 if (!added) added = true;
565 private boolean added = false;
567 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
569 public double crossAngle() {
570 Vec v1 = t.norm().times(-1);
571 Vec v2 = pair.t.norm().times(-1);
572 return Math.acos(v1.norm().dot(v2.norm()));
575 /** angle between this half-edge and the next */
576 public double angle() {
577 Vec v1 = next.p2.p.minus(p2.p);
578 Vec v2 = this.p1.p.minus(p2.p);
579 return Math.acos(v1.norm().dot(v2.norm()));
582 public void makeAdjacent(E e) {
583 if (this.next == e) return;
584 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
585 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
587 E freeIncident = p2.getFreeIncident(e, this);
589 e.prev.next = freeIncident.next;
590 freeIncident.next.prev = e.prev;
592 freeIncident.next = this.next;
593 this.next.prev = freeIncident;
602 /** creates an isolated edge out in the middle of space */
603 public E(Point p1, Point p2) {
604 if (vertices.get(p1) != null) throw new Error();
605 if (vertices.get(p2) != null) throw new Error();
606 this.p1 = new Vertex(p1);
607 this.p2 = new Vertex(p2);
608 this.prev = this.next = this.pair = new E(this, this, this);
610 this.p2.e = this.pair;
614 /** adds a new half-edge from prev.p2 to p2 */
615 public E(E prev, Point p) {
617 p2 = vertices.get(p);
618 if (p2 == null) p2 = new Vertex(p);
622 if (p2.getE(p1) != null) throw new Error();
624 this.next = this.pair = new E(this, this, prev.next);
626 E q = p2.getFreeIncident();
628 this.next.prev = this;
630 this.prev.next = this;
631 this.pair = new E(q, this, z);
633 if (p2.e==null) p2.e = this.pair;
637 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
638 public E(E prev, E pair, E next) {
646 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); }
647 public boolean has(Vertex v) { return v==p1 || v==p2; }
648 public float length() { return p1.p.minus(p2.p).mag(); }
649 public String toString() { return p1+"->"+p2; }
653 public E makeE(Point p1, Point p2) {
654 Vertex v1 = vertices.get(p1);
655 Vertex v2 = vertices.get(p2);
656 if (v1 != null && v2 != null) {
658 if (e != null) return e;
660 if (e != null) return e;
662 if (v1 != null) return new E(v1.getFreeIncident(), p2);
663 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
664 return new E(p1, p2);
666 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
668 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
669 float dot = norm.dot(norm2);
670 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
671 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
673 E e12 = makeE(p1, p2);
674 E e23 = makeE(p2, p3);
675 E e31 = makeE(p3, p1);
676 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
677 e12.makeAdjacent(e23);
678 e23.makeAdjacent(e31);
679 e31.makeAdjacent(e12);
681 T ret = e12.makeT(colorclass);
682 if (e12.t == null) throw new Error();
683 if (e23.t == null) throw new Error();
684 if (e31.t == null) throw new Error();
689 /** [UNIQUE] a triangle (face) */
690 public final class T extends Triangle {
692 public final int color;
693 public final int colorclass;
695 public void removeFromRTree() { triangles.remove(this); }
696 public void addToRTree() { triangles.insert(this); }
698 public void destroy() { triangles.remove(this); }
700 T(E e1, int colorclass) {
704 if (e1==e2 || e1==e3) throw new Error();
705 if (e3.next!=e1) throw new Error();
706 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
709 e1.next.next.t = this;
711 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
713 int color = Math.abs(random.nextInt());
716 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
717 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
718 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
722 this.colorclass = colorclass;
725 public E e1() { return e1; }
726 public E e2() { return e1.next; }
727 public E e3() { return e1.prev; }
728 public Vertex v1() { return e1.p1; }
729 public Vertex v2() { return e1.p2; }
730 public Vertex v3() { return e1.next.p2; }
731 public Point p1() { return e1.p1.p; }
732 public Point p2() { return e1.p2.p; }
733 public Point p3() { return e1.next.p2.p; }
734 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
735 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
737 public boolean shouldBeDrawn() {
738 if (e1().bind_to.set.size() == 0) return false;
739 if (e2().bind_to.set.size() == 0) return false;
740 if (e3().bind_to.set.size() == 0) return false;