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 PointSet<Vert> pointset = new PointSet<Vert>();
19 public Iterable<Vert> vertices() { return pointset; }
21 public Iterable<E> edges() {
24 public Iterator<E> iterator() {
26 HashSet<E> hse = new HashSet<E>();
27 for(T t : Mesh.this) {
35 return hse.iterator();
39 public Iterator<T> iterator() {
41 for(Vert v : pointset)
42 if (v.e != null && v.e.t != null)
43 return new FaceIterator(v);
44 return new FaceIterator();
48 public HashSet<T> ts = new HashSet<T>();
50 public Mesh score_against = null;
51 public double score = 0;
52 public float score() { return (float)score; }
54 public int numedges = 0;
55 public float avgedge = 0;
57 public void rebindPoints() {
59 for(Mesh.T t : this) {
64 // ask edges to re-implement their bindings
65 for(Mesh.T t : this) {
72 public void unApplyQuadricToNeighborAll() {
73 HashSet<Vert> done = new HashSet<Vert>();
75 for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() }) {
76 if (done.contains(p)) continue;
78 p.unApplyQuadricToNeighbor();
81 public void recomputeAllFundamentalQuadrics() {
82 HashSet<Vert> done = new HashSet<Vert>();
84 for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() }) {
85 if (done.contains(p)) continue;
87 p.recomputeFundamentalQuadric();
90 public float applyQuadricToNeighborAll() {
93 HashSet<Vert> done = new HashSet<Vert>();
95 for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() }) {
96 if (done.contains(p)) continue;
98 p.applyQuadricToNeighbor();
101 return (float)(dist/num);
104 public void transform(Matrix m) {
105 ArrayList<Vert> set = new ArrayList<Vert>();
106 for (Vert v : pointset)
108 for(Vert v : set) v.transform(m);
111 public float volume() {
114 double area = t.area();
115 Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
116 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
117 double height = Math.abs(t.norm().dot(origin_to_centroid));
118 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
123 public void rebuildPointSet() { pointset.rebuild(); }
124 public Vec diagonal() { return pointset.diagonal(); }
125 public Point centroid() { return pointset.centroid(); }
126 public Vert nearest(Point p) { return pointset.nearest(p); }
128 public final class Vert extends HasPoint {
130 E e; // some edge *leaving* this point
132 /** the nearest vertex in the "score_against" mesh */
133 Vert nearest_in_other_mesh;
134 /** the number of vertices in the other mesh for which this is the nearest_in_other_mesh */
136 /** the total error quadric (contributions from all vertices in other mesh for which this is nearest) */
137 Matrix quadric = Matrix.ZERO;
139 Vert bound_to = this;
140 Matrix binding = new Matrix();
142 boolean quadricStale = false;
144 public Matrix errorQuadric() { return quadric; }
145 public Point getPoint() { return p; }
146 public float score() { return oldscore; }
148 private Matrix fundamentalQuadric = null;
149 public Matrix fundamentalQuadric() {
150 if (fundamentalQuadric == null) recomputeFundamentalQuadric();
151 return fundamentalQuadric;
154 private Vert(Point p) {
156 if (pointset.get(p) != null) throw new Error();
160 private void glNormal(GL gl) {
162 gl.glNormal3f(norm.x, norm.y, norm.z);
165 public void recomputeFundamentalQuadric() {
166 //if (!quadricStale && fundamentalQuadric != null) return;
167 quadricStale = false;
168 unApplyQuadricToNeighbor();
169 Matrix m = Matrix.ZERO;
174 m = m.plus(t.norm().fundamentalQuadric(t.centroid()));
177 } while(e != this.e);
178 fundamentalQuadric = m.times(1/(float)count);
179 applyQuadricToNeighbor();
182 public void unApplyQuadricToNeighbor() {
183 if (nearest_in_other_mesh == null) return;
184 if (fundamentalQuadric == null) return;
185 nearest_in_other_mesh.unComputeError();
186 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.minus(fundamentalQuadric);
187 nearest_in_other_mesh.quadric_count--;
188 if (nearest_in_other_mesh.quadric_count==0)
189 nearest_in_other_mesh.quadric = Matrix.ZERO;
190 nearest_in_other_mesh.computeError();
191 nearest_in_other_mesh = null;
194 public void applyQuadricToNeighbor() {
195 if (score_against == null) return;
197 Vert new_nearest = score_against.nearest(p);
198 if (nearest_in_other_mesh != null && new_nearest == nearest_in_other_mesh) return;
200 if (nearest_in_other_mesh != null) unApplyQuadricToNeighbor();
201 if (nearest_in_other_mesh != null) throw new Error();
203 nearest_in_other_mesh = new_nearest;
205 // don't attract to vertices that face the other way
206 if (nearest_in_other_mesh.e == null || nearest_in_other_mesh.norm().dot(norm()) < 0) {
207 nearest_in_other_mesh = null;
209 nearest_in_other_mesh.unComputeError();
210 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.plus(fundamentalQuadric());
211 nearest_in_other_mesh.quadric_count++;
212 nearest_in_other_mesh.computeError();
217 public void reComputeErrorAround() {
219 if (nearest_in_other_mesh != null) nearest_in_other_mesh.reComputeError();
222 e.p2.reComputeError();
224 } while (e != this.e);
226 public void reComputeError() {
230 public void unComputeError() {
234 public void computeError() {
235 if (quadric_count == 0) {
238 else if (nearest_in_other_mesh == null) {
239 if (score_against != null) {
240 Vert ne = score_against.nearest(p);
241 oldscore = ne.fundamentalQuadric().preAndPostMultiply(p) * 100 * 10;
246 oldscore = nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p) * 100 * 10;
249 oldscore = (quadric.preAndPostMultiply(p) * 100) /*/ quadric_count*/;
258 double ang = Math.abs(e.crossAngle());
259 if (ang > Math.PI) throw new Error();
263 aspects += e.t.aspect()*e.t.aspect();
267 float minangle = (float)(Math.PI * 0.8);
269 oldscore += (ang - minangle);
272 } while (e != this.e);
273 if (numaspects > 0) oldscore += (aspects / numaspects);
275 //System.out.println(oldscore);
276 //oldscore = oldscore*oldscore;
280 /** does NOT update bound pairs! */
281 public boolean transform(Matrix m) {
282 unApplyQuadricToNeighbor();
284 if (pointset.get(this.p)==null) throw new Error();
285 pointset.remove(this);
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);
291 } catch (Exception e) {
292 throw new RuntimeException(e);
294 applyQuadricToNeighbor();
296 // should recompute fundamental quadrics of all vertices sharing a face, but we defer...
299 e.p2.quadricStale = true;
301 } while(e != this.e);
303 // FIXME: intersection test needed?
306 for(T t : Mesh.this) {
310 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { good = false; break; }
312 //if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { good = false; break; }
313 //if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { good = false; break; }
314 //if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { good = false; break; }
317 } while(e != this.e);
320 reComputeErrorAround();
324 public boolean move(Vec v) {
325 Matrix m = new Matrix(v);
329 good &= p.transform(m);
335 public E getFreeIncident() {
336 E ret = getFreeIncident(e, e);
337 if (ret != null) return ret;
338 ret = getFreeIncident(e.pair.next, e.pair.next);
339 if (ret == null) throw new Error("unable to find free incident to " + this);
343 public E getFreeIncident(E start, E before) {
346 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null) return e.pair;
348 } while(e != before);
352 public E getE(Point p2) {
353 Vert v = pointset.get(p2);
354 if (v==null) return null;
357 public E getE(Vert p2) {
360 if (e==null) return null;
361 if (e.p1 == this && e.p2 == p2) return e;
368 Vec norm = new Vec(0, 0, 0);
371 if (e.t != null) norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
373 } while(e != this.e);
377 public boolean isBoundTo(Vert p) {
380 if (px==this) return true;
385 public void unbind() { bound_to = this; binding = new Matrix(); }
386 public void bind(Vert p) { bind(p, new Matrix()); }
387 public void bind(Vert p, Matrix binding) {
388 if (isBoundTo(p)) return;
389 Vert temp_bound_to = p.bound_to;
390 Matrix temp_binding = p.binding;
391 p.bound_to = this.bound_to;
392 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
393 this.bound_to = temp_bound_to;
394 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
398 public class BindingGroup {
399 private HashSet<E> set = new HashSet<E>();
400 public BindingGroup bind_others;
401 public BindingGroup other() { return bind_others; }
402 public BindingGroup(BindingGroup bind_others) { this.bind_others = bind_others; }
403 public BindingGroup() { this.bind_others = new BindingGroup(this); }
404 public BindingGroup(E e) { this(); set.add(e); }
405 public void add(E e) {
406 if (set.contains(e)) return;
408 BindingGroup e_bind_peers = e.bind_peers;
409 BindingGroup e_bind_to = e.bind_to;
411 e.bind_to = bind_others;
412 for (E epeer : e_bind_peers.set) add(epeer);
413 for (E eother : e_bind_to.set) bind_others.add(eother);
415 for(E eother : bind_others.set) {
416 if (e.next.bind_to.set.contains(eother.prev)) {
417 e.next.next.bindEdge(eother.prev.prev);
419 if (e.prev.bind_to.set.contains(eother.next)) {
420 e.prev.prev.bindEdge(eother.next.next);
425 public void dobind(E e) {
426 for(E ebound : set) {
427 e.p1.bind(ebound.p2);
428 e.p2.bind(ebound.p1);
431 public void shatter(BindingGroup bg1, BindingGroup bg2) {
433 e.shatter(e.midpoint(), bg1, bg2);
438 /** [UNIQUE] an edge */
439 public final class E implements Comparable<E> {
441 public final Vert p1, p2;
442 T t; // triangle to our "left"
443 E prev; // previous half-edge
444 E next; // next half-edge
445 E pair; // partner half-edge
446 public BindingGroup bind_peers = new BindingGroup(this);
447 public BindingGroup bind_to = bind_peers.other();
448 boolean shattered = false;
450 public float comparator() {
451 if (t==null) return length();
452 if ((length() * length()) / t.area() > 10)
453 return (float)(length()*Math.sqrt(t.area()));
454 return length()*t.area();
456 public int compareTo(E e) {
457 return e.comparator() > comparator() ? 1 : -1;
459 public void bindEdge(E e) { bind_to.add(e); }
460 public void dobind() { bind_to.dobind(this); }
462 public Point shatter() { return shatter(midpoint(), null, null); }
463 public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
464 if (shattered || destroyed) return mid;
471 int old_colorclass = t==null ? 0 : t.colorclass;
472 if (bg1==null) bg1 = new BindingGroup();
473 if (bg2==null) bg2 = new BindingGroup();
474 BindingGroup old_bind_to = bind_to;
475 bind_peers.shatter(bg1, bg2);
476 old_bind_to.shatter(bg2.other(), bg1.other());
480 newT(r.p, p1.p, mid, null, old_colorclass);
481 newT(r.p, mid, p2.p, null, old_colorclass);
482 bg1.add(p1.getE(mid));
483 bg2.add(p2.getE(mid).pair);
487 public boolean destroyed = false;
488 public void destroy() {
489 if (destroyed) return;
491 pair.destroyed = true;
493 if (t != null) t.destroy();
496 if (pair.t != null) pair.t.destroy();
499 if (next.t != null) next.t.destroy();
500 if (prev.t != null) prev.t.destroy();
504 if (pair.next.t != null) pair.next.t.destroy();
505 if (pair.prev.t != null) pair.next.t.destroy();
511 this.bind_peers = null;
512 pair.bind_peers = null;
513 pair.prev.next = next;
514 next.prev = pair.prev;
515 prev.next = pair.next;
517 if (p1.e == this) p1.e = prev.next;
518 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
519 avgedge -= this.length();
520 avgedge -= pair.length();
525 private void sync() {
526 this.prev.next = this;
527 this.next.prev = this;
528 this.pair.pair = this;
529 bind_peers.add(this);
530 if (this.next.p1 != p2) throw new Error();
531 if (this.prev.p2 != p1) throw new Error();
532 if (this.p1.e == null) this.p1.e = this;
539 private boolean added = false;
541 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
543 public double crossAngle() {
544 Vec v1 = t.norm().times(-1);
545 Vec v2 = pair.t.norm().times(-1);
546 return Math.acos(v1.norm().dot(v2.norm()));
549 /** angle between this half-edge and the next */
550 public double angle() {
551 Vec v1 = next.p2.p.minus(p2.p);
552 Vec v2 = this.p1.p.minus(p2.p);
553 return Math.acos(v1.norm().dot(v2.norm()));
556 public void makeAdjacent(E e) {
557 if (this.next == e) return;
558 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
559 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
561 E freeIncident = p2.getFreeIncident(e, this);
563 e.prev.next = freeIncident.next;
564 freeIncident.next.prev = e.prev;
566 freeIncident.next = this.next;
567 this.next.prev = freeIncident;
576 /** creates an isolated edge out in the middle of space */
577 public E(Point p1, Point p2) {
578 if (pointset.get(p1) != null) throw new Error();
579 if (pointset.get(p2) != null) throw new Error();
580 this.p1 = new Vert(p1);
581 this.p2 = new Vert(p2);
582 this.prev = this.next = this.pair = new E(this, this, this);
584 this.p2.e = this.pair;
588 /** adds a new half-edge from prev.p2 to p2 */
589 public E(E prev, Point p) {
591 p2 = pointset.get(p);
592 if (p2 == null) p2 = new Vert(p);
596 if (p2.getE(p1) != null) throw new Error();
598 this.next = this.pair = new E(this, this, prev.next);
600 E q = p2.getFreeIncident();
602 this.next.prev = this;
604 this.prev.next = this;
605 this.pair = new E(q, this, z);
607 if (p2.e==null) p2.e = this.pair;
611 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
612 public E(E prev, E pair, E next) {
620 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); }
621 public boolean has(Vert v) { return v==p1 || v==p2; }
622 public float length() { return p1.p.minus(p2.p).mag(); }
623 public String toString() { return p1+"->"+p2; }
625 public boolean intersects(T t) {
626 double A0=t.v1().p.x, A1=t.v1().p.y, A2=t.v1().p.z;
627 double B0=t.v2().p.x, B1=t.v2().p.y, B2=t.v2().p.z;
628 double C0=t.v3().p.x, C1=t.v3().p.y, C2=t.v3().p.z;
629 double j0=p1.p.x, j1=p1.p.y, j2=p1.p.z;
630 double k0=p2.p.x, k1=p2.p.y, k2=p2.p.z;
638 double R00, R01, R02, R03,
652 /* c = a × b */
653 c0 = a1 * b2 - a2 * b1;
654 c1 = a2 * b0 - a0 * b2;
655 c2 = a0 * b1 - a1 * b0;
657 /* M^(-1) = (1/det(M)) * adj(M) */
658 in_det = 1 / (c0 * c0 + c1 * c1 + c2 * c2);
659 R00 = (b1 * c2 - b2 * c1) * in_det;
660 R01 = (b2 * c0 - b0 * c2) * in_det;
661 R02 = (b0 * c1 - b1 * c0) * in_det;
662 R10 = (c1 * a2 - c2 * a1) * in_det;
663 R11 = (c2 * a0 - c0 * a2) * in_det;
664 R12 = (c0 * a1 - c1 * a0) * in_det;
670 R03 = -(R00 * A0 + R01 * A1 + R02 * A2);
671 R13 = -(R10 * A0 + R11 * A1 + R12 * A2);
672 R23 = -(R20 * A0 + R21 * A1 + R22 * A2);
674 /* fill in last row of 4x4 matrix */
678 J2 = R20 * j0 + R21 * j1 + R22 * j2 + R23;
679 K2 = R20 * k0 + R21 * k1 + R22 * k2 + R23;
680 if (J2 * K2 >= 0) return false;
682 J0 = R00 * j0 + R01 * j1 + R02 * j2 + R03;
683 K0 = R00 * k0 + R01 * k1 + R02 * k2 + R03;
684 i0 = J0 + J2 * ((K0 - J0) / (J2 - K2));
685 if (i0 < 0 || i0 > 1) return false;
687 J1 = R10 * j0 + R11 * j1 + R12 * j2 + R13;
688 K1 = R10 * k0 + R11 * k1 + R12 * k2 + R13;
689 i1 = J1 + J2 * ((K1 - J1) / (J2 - K2));
690 if (i1 < 0 || i1 > 1 || i0 + i1 > 1) return false;
696 public E makeE(Point p1, Point p2) {
697 Vert v1 = pointset.get(p1);
698 Vert v2 = pointset.get(p2);
699 if (v1 != null && v2 != null) {
701 if (e != null) return e;
703 if (e != null) return e;
705 if (v1 != null) return new E(v1.getFreeIncident(), p2);
706 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
707 return new E(p1, p2);
709 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
711 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
712 float dot = norm.dot(norm2);
713 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
714 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
716 E e12 = makeE(p1, p2);
717 E e23 = makeE(p2, p3);
718 E e31 = makeE(p3, p1);
719 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
720 e12.makeAdjacent(e23);
721 e23.makeAdjacent(e31);
722 e31.makeAdjacent(e12);
724 T ret = e12.makeT(colorclass);
725 if (e12.t == null) throw new Error();
726 if (e23.t == null) throw new Error();
727 if (e31.t == null) throw new Error();
732 public class FaceIterator implements Iterator<T> {
733 private HashSet<T> visited = new HashSet<T>();
734 private LinkedList<T> next = new LinkedList<T>();
735 public FaceIterator() { }
736 public FaceIterator(Vert v) { next.addFirst(v.e.t); }
737 public boolean hasNext() { return next.peek()!=null; }
738 public void remove() { throw new Error(); }
740 T ret = next.removeFirst();
741 if (ret == null) return null;
743 T t1 = ret.e1().pair.t;
744 T t2 = ret.e2().pair.t;
745 T t3 = ret.e3().pair.t;
746 if (t1 != null && !visited.contains(t1)) next.addFirst(t1);
747 if (t2 != null && !visited.contains(t2)) next.addFirst(t2);
748 if (t3 != null && !visited.contains(t3)) next.addFirst(t3);
753 /** [UNIQUE] a triangle (face) */
754 public final class T extends Triangle {
756 public final int color;
757 public final int colorclass;
759 public void destroy() {
763 T(E e1, int colorclass) {
767 if (e1==e2 || e1==e3) throw new Error();
768 if (e3.next!=e1) throw new Error();
769 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
772 e1.next.next.t = this;
774 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
776 int color = Math.abs(random.nextInt());
779 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
780 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
781 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
785 this.colorclass = colorclass;
788 public E e1() { return e1; }
789 public E e2() { return e1.next; }
790 public E e3() { return e1.prev; }
791 public Vert v1() { return e1.p1; }
792 public Vert v2() { return e1.p2; }
793 public Vert v3() { return e1.next.p2; }
794 public Point p1() { return e1.p1.p; }
795 public Point p2() { return e1.p2.p; }
796 public Point p3() { return e1.next.p2.p; }
797 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
798 public boolean has(Vert v) { return v1()==v || v2()==v || v3()==v; }
800 public void glVertices(GL gl) {
802 if (e1().bind_to.set.size() == 0) return;
803 if (e2().bind_to.set.size() == 0) return;
804 if (e3().bind_to.set.size() == 0) return;
812 public boolean tilemesh = false;