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) {
236 if (nearest_in_other_mesh == null) {
237 if (score_against != null) {
238 Vert ne = score_against.nearest(p);
239 oldscore = ne.fundamentalQuadric().preAndPostMultiply(p) * 100 * 10;
244 oldscore = nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p) * 100 * 10;
247 oldscore = (quadric.preAndPostMultiply(p) * 100) / quadric_count;
256 double ang = Math.abs(e.crossAngle());
257 if (ang > Math.PI) throw new Error();
260 aspects += e.t.aspect()*e.t.aspect();
263 float minangle = (float)(Math.PI * 0.3);
265 oldscore += (ang - minangle);
268 } while (e != this.e);
269 //if (numaspects > 0) oldscore += (aspects / numaspects);
271 //System.out.println(oldscore);
272 //oldscore = oldscore*oldscore;
276 /** does NOT update bound pairs! */
277 public boolean transform(Matrix m) {
278 unApplyQuadricToNeighbor();
280 if (pointset.get(this.p)==null) throw new Error();
281 pointset.remove(this);
282 float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
283 float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
284 float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
285 this.p = new Point(newx, newy, newz);
287 } catch (Exception e) {
288 throw new RuntimeException(e);
290 applyQuadricToNeighbor();
292 // should recompute fundamental quadrics of all vertices sharing a face, but we defer...
295 e.p2.quadricStale = true;
297 } while(e != this.e);
299 // FIXME: intersection test needed?
302 for(T t : Mesh.this) {
306 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { good = false; break; }
308 //if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { good = false; break; }
309 //if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { good = false; break; }
310 //if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { good = false; break; }
313 } while(e != this.e);
316 reComputeErrorAround();
320 public boolean move(Vec v) {
321 Matrix m = new Matrix(v);
325 good &= p.transform(m);
331 public E getFreeIncident() {
332 E ret = getFreeIncident(e, e);
333 if (ret != null) return ret;
334 ret = getFreeIncident(e.pair.next, e.pair.next);
335 if (ret == null) throw new Error("unable to find free incident to " + this);
339 public E getFreeIncident(E start, E before) {
342 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null) return e.pair;
344 } while(e != before);
348 public E getE(Point p2) {
349 Vert v = pointset.get(p2);
350 if (v==null) return null;
353 public E getE(Vert p2) {
356 if (e==null) return null;
357 if (e.p1 == this && e.p2 == p2) return e;
364 Vec norm = new Vec(0, 0, 0);
367 if (e.t != null) norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
369 } while(e != this.e);
373 public boolean isBoundTo(Vert p) {
376 if (px==this) return true;
381 public void unbind() { bound_to = this; binding = new Matrix(); }
382 public void bind(Vert p) { bind(p, new Matrix()); }
383 public void bind(Vert p, Matrix binding) {
384 if (isBoundTo(p)) return;
385 Vert temp_bound_to = p.bound_to;
386 Matrix temp_binding = p.binding;
387 p.bound_to = this.bound_to;
388 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
389 this.bound_to = temp_bound_to;
390 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
394 public class BindingGroup {
395 private HashSet<E> set = new HashSet<E>();
396 public BindingGroup bind_others;
397 public BindingGroup other() { return bind_others; }
398 public BindingGroup(BindingGroup bind_others) { this.bind_others = bind_others; }
399 public BindingGroup() { this.bind_others = new BindingGroup(this); }
400 public BindingGroup(E e) { this(); set.add(e); }
401 public void add(E e) {
402 if (set.contains(e)) return;
404 BindingGroup e_bind_peers = e.bind_peers;
405 BindingGroup e_bind_to = e.bind_to;
407 e.bind_to = bind_others;
408 for (E epeer : e_bind_peers.set) add(epeer);
409 for (E eother : e_bind_to.set) bind_others.add(eother);
411 for(E eother : bind_others.set) {
412 if (e.next.bind_to.set.contains(eother.prev)) {
413 e.next.next.bindEdge(eother.prev.prev);
415 if (e.prev.bind_to.set.contains(eother.next)) {
416 e.prev.prev.bindEdge(eother.next.next);
421 public void dobind(E e) {
422 for(E ebound : set) {
423 e.p1.bind(ebound.p2);
424 e.p2.bind(ebound.p1);
427 public void shatter(BindingGroup bg1, BindingGroup bg2) {
429 e.shatter(e.midpoint(), bg1, bg2);
434 /** [UNIQUE] an edge */
435 public final class E implements Comparable<E> {
437 public final Vert p1, p2;
438 T t; // triangle to our "left"
439 E prev; // previous half-edge
440 E next; // next half-edge
441 E pair; // partner half-edge
442 public BindingGroup bind_peers = new BindingGroup(this);
443 public BindingGroup bind_to = bind_peers.other();
444 boolean shattered = false;
446 public float comparator() {
447 if (t==null) return length();
448 if ((length() * length()) / t.area() > 10)
449 return (float)(length()*Math.sqrt(t.area()));
450 return length()*t.area();
452 public int compareTo(E e) {
453 return e.comparator() > comparator() ? 1 : -1;
455 public void bindEdge(E e) { bind_to.add(e); }
456 public void dobind() { bind_to.dobind(this); }
458 public Point shatter() { return shatter(midpoint(), null, null); }
459 public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
460 if (shattered || destroyed) return mid;
467 int old_colorclass = t==null ? 0 : t.colorclass;
468 if (bg1==null) bg1 = new BindingGroup();
469 if (bg2==null) bg2 = new BindingGroup();
470 BindingGroup old_bind_to = bind_to;
471 bind_peers.shatter(bg1, bg2);
472 old_bind_to.shatter(bg2.other(), bg1.other());
476 newT(r.p, p1.p, mid, null, old_colorclass);
477 newT(r.p, mid, p2.p, null, old_colorclass);
478 bg1.add(p1.getE(mid));
479 bg2.add(p2.getE(mid).pair);
483 public boolean destroyed = false;
484 public void destroy() {
485 if (destroyed) return;
487 pair.destroyed = true;
489 if (t != null) t.destroy();
492 if (pair.t != null) pair.t.destroy();
495 if (next.t != null) next.t.destroy();
496 if (prev.t != null) prev.t.destroy();
500 if (pair.next.t != null) pair.next.t.destroy();
501 if (pair.prev.t != null) pair.next.t.destroy();
507 this.bind_peers = null;
508 pair.bind_peers = null;
509 pair.prev.next = next;
510 next.prev = pair.prev;
511 prev.next = pair.next;
513 if (p1.e == this) p1.e = prev.next;
514 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
515 avgedge -= this.length();
516 avgedge -= pair.length();
521 private void sync() {
522 this.prev.next = this;
523 this.next.prev = this;
524 this.pair.pair = this;
525 bind_peers.add(this);
526 if (this.next.p1 != p2) throw new Error();
527 if (this.prev.p2 != p1) throw new Error();
528 if (this.p1.e == null) this.p1.e = this;
535 private boolean added = false;
537 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
539 public double crossAngle() {
540 Vec v1 = t.norm().times(-1);
541 Vec v2 = pair.t.norm().times(-1);
542 return Math.acos(v1.norm().dot(v2.norm()));
545 /** angle between this half-edge and the next */
546 public double angle() {
547 Vec v1 = next.p2.p.minus(p2.p);
548 Vec v2 = this.p1.p.minus(p2.p);
549 return Math.acos(v1.norm().dot(v2.norm()));
552 public void makeAdjacent(E e) {
553 if (this.next == e) return;
554 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
555 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
557 E freeIncident = p2.getFreeIncident(e, this);
559 e.prev.next = freeIncident.next;
560 freeIncident.next.prev = e.prev;
562 freeIncident.next = this.next;
563 this.next.prev = freeIncident;
572 /** creates an isolated edge out in the middle of space */
573 public E(Point p1, Point p2) {
574 if (pointset.get(p1) != null) throw new Error();
575 if (pointset.get(p2) != null) throw new Error();
576 this.p1 = new Vert(p1);
577 this.p2 = new Vert(p2);
578 this.prev = this.next = this.pair = new E(this, this, this);
580 this.p2.e = this.pair;
584 /** adds a new half-edge from prev.p2 to p2 */
585 public E(E prev, Point p) {
587 p2 = pointset.get(p);
588 if (p2 == null) p2 = new Vert(p);
592 if (p2.getE(p1) != null) throw new Error();
594 this.next = this.pair = new E(this, this, prev.next);
596 E q = p2.getFreeIncident();
598 this.next.prev = this;
600 this.prev.next = this;
601 this.pair = new E(q, this, z);
603 if (p2.e==null) p2.e = this.pair;
607 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
608 public E(E prev, E pair, E next) {
616 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); }
617 public boolean has(Vert v) { return v==p1 || v==p2; }
618 public float length() { return p1.p.minus(p2.p).mag(); }
619 public String toString() { return p1+"->"+p2; }
621 public boolean intersects(T t) {
622 double A0=t.v1().p.x, A1=t.v1().p.y, A2=t.v1().p.z;
623 double B0=t.v2().p.x, B1=t.v2().p.y, B2=t.v2().p.z;
624 double C0=t.v3().p.x, C1=t.v3().p.y, C2=t.v3().p.z;
625 double j0=p1.p.x, j1=p1.p.y, j2=p1.p.z;
626 double k0=p2.p.x, k1=p2.p.y, k2=p2.p.z;
634 double R00, R01, R02, R03,
648 /* c = a × b */
649 c0 = a1 * b2 - a2 * b1;
650 c1 = a2 * b0 - a0 * b2;
651 c2 = a0 * b1 - a1 * b0;
653 /* M^(-1) = (1/det(M)) * adj(M) */
654 in_det = 1 / (c0 * c0 + c1 * c1 + c2 * c2);
655 R00 = (b1 * c2 - b2 * c1) * in_det;
656 R01 = (b2 * c0 - b0 * c2) * in_det;
657 R02 = (b0 * c1 - b1 * c0) * in_det;
658 R10 = (c1 * a2 - c2 * a1) * in_det;
659 R11 = (c2 * a0 - c0 * a2) * in_det;
660 R12 = (c0 * a1 - c1 * a0) * in_det;
666 R03 = -(R00 * A0 + R01 * A1 + R02 * A2);
667 R13 = -(R10 * A0 + R11 * A1 + R12 * A2);
668 R23 = -(R20 * A0 + R21 * A1 + R22 * A2);
670 /* fill in last row of 4x4 matrix */
674 J2 = R20 * j0 + R21 * j1 + R22 * j2 + R23;
675 K2 = R20 * k0 + R21 * k1 + R22 * k2 + R23;
676 if (J2 * K2 >= 0) return false;
678 J0 = R00 * j0 + R01 * j1 + R02 * j2 + R03;
679 K0 = R00 * k0 + R01 * k1 + R02 * k2 + R03;
680 i0 = J0 + J2 * ((K0 - J0) / (J2 - K2));
681 if (i0 < 0 || i0 > 1) return false;
683 J1 = R10 * j0 + R11 * j1 + R12 * j2 + R13;
684 K1 = R10 * k0 + R11 * k1 + R12 * k2 + R13;
685 i1 = J1 + J2 * ((K1 - J1) / (J2 - K2));
686 if (i1 < 0 || i1 > 1 || i0 + i1 > 1) return false;
692 public E makeE(Point p1, Point p2) {
693 Vert v1 = pointset.get(p1);
694 Vert v2 = pointset.get(p2);
695 if (v1 != null && v2 != null) {
697 if (e != null) return e;
699 if (e != null) return e;
701 if (v1 != null) return new E(v1.getFreeIncident(), p2);
702 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
703 return new E(p1, p2);
705 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
707 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
708 float dot = norm.dot(norm2);
709 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
710 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
712 E e12 = makeE(p1, p2);
713 E e23 = makeE(p2, p3);
714 E e31 = makeE(p3, p1);
715 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
716 e12.makeAdjacent(e23);
717 e23.makeAdjacent(e31);
718 e31.makeAdjacent(e12);
720 T ret = e12.makeT(colorclass);
721 if (e12.t == null) throw new Error();
722 if (e23.t == null) throw new Error();
723 if (e31.t == null) throw new Error();
728 public class FaceIterator implements Iterator<T> {
729 private HashSet<T> visited = new HashSet<T>();
730 private LinkedList<T> next = new LinkedList<T>();
731 public FaceIterator() { }
732 public FaceIterator(Vert v) { next.addFirst(v.e.t); }
733 public boolean hasNext() { return next.peek()!=null; }
734 public void remove() { throw new Error(); }
736 T ret = next.removeFirst();
737 if (ret == null) return null;
739 T t1 = ret.e1().pair.t;
740 T t2 = ret.e2().pair.t;
741 T t3 = ret.e3().pair.t;
742 if (t1 != null && !visited.contains(t1)) next.addFirst(t1);
743 if (t2 != null && !visited.contains(t2)) next.addFirst(t2);
744 if (t3 != null && !visited.contains(t3)) next.addFirst(t3);
749 /** [UNIQUE] a triangle (face) */
750 public final class T extends Triangle {
752 public final int color;
753 public final int colorclass;
755 public void destroy() {
759 T(E e1, int colorclass) {
763 if (e1==e2 || e1==e3) throw new Error();
764 if (e3.next!=e1) throw new Error();
765 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
768 e1.next.next.t = this;
770 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
772 int color = Math.abs(random.nextInt());
775 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
776 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
777 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
781 this.colorclass = colorclass;
784 public E e1() { return e1; }
785 public E e2() { return e1.next; }
786 public E e3() { return e1.prev; }
787 public Vert v1() { return e1.p1; }
788 public Vert v2() { return e1.p2; }
789 public Vert v3() { return e1.next.p2; }
790 public Point p1() { return e1.p1.p; }
791 public Point p2() { return e1.p2.p; }
792 public Point p3() { return e1.next.p2.p; }
793 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
794 public boolean has(Vert v) { return v1()==v || v2()==v || v3()==v; }
796 public void glVertices(GL gl) {
798 if (e1().bind_to.set.size() == 0) return;
799 if (e2().bind_to.set.size() == 0) return;
800 if (e3().bind_to.set.size() == 0) return;