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 float EPSILON = (float)0.0001;
15 public static 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() {
40 for(Vert v : pointset)
41 if (v.e != null && v.e.t != null)
42 return new FaceIterator(v);
43 return new FaceIterator();
46 public Mesh score_against = null;
47 public double score = 0;
48 public float score() { return (float)score; }
50 public int numedges = 0;
51 public float avgedge = 0;
53 public void unbind() {
54 for(Mesh.T t : this) {
62 for(Mesh.T t : this) {
69 public float rescore() {
72 HashSet<Vert> done = new HashSet<Vert>();
74 for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() }) {
75 if (done.contains(p)) continue;
79 return (float)(dist/num);
82 public void transform(Matrix m) {
83 ArrayList<Vert> set = new ArrayList<Vert>();
84 for (Vert v : pointset)
86 for(Vert v : set) v.transform(m);
89 public float volume() {
92 double area = t.area();
93 Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
94 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
95 double height = Math.abs(t.norm().dot(origin_to_centroid));
96 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
102 public class BindingGroup {
103 public HashSet<E> es = new HashSet<E>();
104 public BindingGroup() { }
105 public BindingGroup(E e) {
108 public void add(E e) {
109 if (e.bg != null) { merge(e.bg); return; }
113 public void merge(BindingGroup bg) {
121 public Vec diagonal() { return pointset.diagonal(); }
122 public Point centroid() { return pointset.centroid(); }
123 public Vert nearest(Point p) { return pointset.nearest(p); }
125 public final class Vert extends HasPoint {
127 E e; // some edge *leaving* this point
129 Vert bound_to = this;
135 Matrix binding = new Matrix();
137 boolean inserted = false;
139 public Point getPoint() { return p; }
140 private Vert(Point p) {
143 //if (e==null) throw new Error();
144 if (pointset.get(p) != null) throw new Error();
147 public float score() { return oldscore; }
148 public void unscore() {
149 if (watch == null) return;
150 watch.watch_x -= p.x;
151 watch.watch_y -= p.y;
152 watch.watch_z -= p.z;
154 if (watch.watch_count==0) {
161 public Vert partner() { return watch==null ? this : watch; }
162 public Point watchback() { return watch_count==0 ? partner().p :
163 new Point(watch_x/watch_count, watch_y/watch_count, watch_z/watch_count); }
164 public void rescore() {
165 if (score_against == null) return;
170 if (watch != null) unscore();
173 watch = score_against.nearest(po.p);
175 // don't attract to vertices that face the other way
176 if (watch.e == null || watch.norm().dot(norm()) < 0) {
179 watch.watch_x += po.p.x;
180 watch.watch_y += po.p.y;
181 watch.watch_z += po.p.z;
187 if (watch_count==0) s1 = 0;
188 else s1 = p.distance(watch_x/watch_count, watch_y/watch_count, watch_z/watch_count);
189 s2 = watch==null ? 0 : po.p.distance(watch.p);
190 oldscore = (float)(s1 + s2);
194 /** does NOT update bound pairs! */
195 public boolean transform(Matrix m) {
196 // FIXME: screws up kdtree
197 // FIXME: screws up hashmap
200 if (pointset.get(this.p)==null) throw new Error();
201 pointset.remove(this);
202 float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
203 float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
204 float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
205 this.p = new Point(newx, newy, newz);
206 // FIXME: what if we move onto exactly where another point is?
208 } catch (Exception e) {
209 throw new RuntimeException(e);
215 for(E e = this.e; ;) {
216 if (e.intersects(t)) { good = false; break; }
218 if (e == this.e) break;
223 if (t==this.t) continue;
224 if (this.intersects(t)) good = false;
229 public boolean move(Vec v) {
230 Matrix m = new Matrix(v);
234 good &= p.transform(m);
235 v = v.times(binding); // bleh wrong
241 public E getFreeIncident() {
242 E ret = getFreeIncident(e, e);
243 if (ret != null) return ret;
244 ret = getFreeIncident(e.pair.next, e.pair.next);
245 if (ret == null) throw new Error("unable to find free incident to " + this);
249 public E getFreeIncident(E start, E before) {
252 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null) return e.pair;
254 } while(e != before);
258 public E getE(Point p2) {
259 Vert v = pointset.get(p2);
260 if (v==null) return null;
263 public E getE(Vert p2) {
266 if (e==null) return null;
267 if (e.p1 == this && e.p2 == p2) return e;
273 public boolean isBoundTo(Vert p) {
276 if (px==this) return true;
282 public void unbind() { bound_to = this; binding = new Matrix(); }
283 public void bind(Vert p) { bind(p, new Matrix()); }
284 public void bind(Vert p, Matrix binding) {
285 if (isBoundTo(p)) return;
286 Vert temp_bound_to = p.bound_to;
287 Matrix temp_binding = p.binding;
288 p.bound_to = this.bound_to;
289 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
290 this.bound_to = temp_bound_to;
291 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
294 Vec norm = new Vec(0, 0, 0);
297 if (e.t != null) norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
299 } while(e != this.e);
304 /** [UNIQUE] an edge */
305 public final class E implements Comparable<E> {
307 public final Vert p1, p2;
308 T t; // triangle to our "left"
309 E prev; // previous half-edge
310 E next; // next half-edge
311 E pair; // partner half-edge
312 public BindingGroup bg = new BindingGroup(this);
314 public int compareTo(E e) { return e.length() > length() ? 1 : -1; }
316 public void bind(E e) { bind(e, new Matrix()); }
317 public void bind(E e, Matrix m) { e.bg.add(this); }
319 public void dobind() {
320 if (bg==null) return;
322 if (ex==this) continue;
328 boolean shattered = false;
329 public Point shatter() { return shatter(midpoint(), null, null); }
330 public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
331 if (shattered) return mid;
338 if (bg1==null) bg1 = new BindingGroup();
339 if (bg2==null) bg2 = new BindingGroup();
340 for(E e : bg.es) e.shatter(e.midpoint(), bg1, bg2);
344 newT(r.p, p1.p, mid, null);
345 newT(r.p, mid, p2.p, null);
346 bg1.add(p1.getE(mid));
347 bg2.add(p2.getE(mid).pair);
351 public boolean destroyed = false;
352 public void destroy() {
353 if (destroyed) return;
355 pair.destroyed = true;
356 if (next.t != null) next.t.destroy();
357 if (prev.t != null) prev.t.destroy();
364 pair.prev.next = next;
365 next.prev = pair.prev;
366 prev.next = pair.next;
368 if (p1.e == this) p1.e = prev.next;
369 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
370 avgedge -= this.length();
371 avgedge -= pair.length();
376 private void sync() {
377 this.prev.next = this;
378 this.next.prev = this;
379 this.pair.pair = this;
380 if (this.next.p1 != p2) throw new Error();
381 if (this.prev.p2 != p1) throw new Error();
382 if (this.p1.e == null) this.p1.e = this;
389 private boolean added = false;
391 public T makeT() { return t==null ? (t = new T(this)) : t; }
393 /** angle between this half-edge and the next */
394 public double angle() {
395 Vec v1 = next.p2.p.minus(p2.p);
396 Vec v2 = this.p1.p.minus(p2.p);
397 return Math.acos(v1.norm().dot(v2.norm()));
400 public void makeAdjacent(E e) {
401 if (this.next == e) return;
402 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
403 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
405 E freeIncident = p2.getFreeIncident(e, this);
407 e.prev.next = freeIncident.next;
408 freeIncident.next.prev = e.prev;
410 freeIncident.next = this.next;
411 this.next.prev = freeIncident;
420 /** creates an isolated edge out in the middle of space */
421 public E(Point p1, Point p2) {
422 if (pointset.get(p1) != null) throw new Error();
423 if (pointset.get(p2) != null) throw new Error();
424 this.p1 = new Vert(p1);
425 this.p2 = new Vert(p2);
426 this.prev = this.next = this.pair = new E(this, this, this);
428 this.p2.e = this.pair;
432 /** adds a new half-edge from prev.p2 to p2 */
433 public E(E prev, Point p) {
435 p2 = pointset.get(p);
436 if (p2 == null) p2 = new Vert(p);
440 if (p2.getE(p1) != null) throw new Error();
442 this.next = this.pair = new E(this, this, prev.next);
444 E q = p2.getFreeIncident();
446 this.next.prev = this;
448 this.prev.next = this;
449 this.pair = new E(q, this, z);
451 if (p2.e==null) p2.e = this.pair;
455 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
456 public E(E prev, E pair, E next) {
464 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); }
465 public boolean has(Vert v) { return v==p1 || v==p2; }
466 public float length() { return p1.p.minus(p2.p).mag(); }
467 public String toString() { return p1+"->"+p2; }
469 public boolean intersects(T t) {
470 double A0=t.v1().p.x, A1=t.v1().p.y, A2=t.v1().p.z;
471 double B0=t.v2().p.x, B1=t.v2().p.y, B2=t.v2().p.z;
472 double C0=t.v3().p.x, C1=t.v3().p.y, C2=t.v3().p.z;
473 double j0=p1.p.x, j1=p1.p.y, j2=p1.p.z;
474 double k0=p2.p.x, k1=p2.p.y, k2=p2.p.z;
482 double R00, R01, R02, R03,
496 /* c = a × b */
497 c0 = a1 * b2 - a2 * b1;
498 c1 = a2 * b0 - a0 * b2;
499 c2 = a0 * b1 - a1 * b0;
501 /* M^(-1) = (1/det(M)) * adj(M) */
502 in_det = 1 / (c0 * c0 + c1 * c1 + c2 * c2);
503 R00 = (b1 * c2 - b2 * c1) * in_det;
504 R01 = (b2 * c0 - b0 * c2) * in_det;
505 R02 = (b0 * c1 - b1 * c0) * in_det;
506 R10 = (c1 * a2 - c2 * a1) * in_det;
507 R11 = (c2 * a0 - c0 * a2) * in_det;
508 R12 = (c0 * a1 - c1 * a0) * in_det;
514 R03 = -(R00 * A0 + R01 * A1 + R02 * A2);
515 R13 = -(R10 * A0 + R11 * A1 + R12 * A2);
516 R23 = -(R20 * A0 + R21 * A1 + R22 * A2);
518 /* fill in last row of 4x4 matrix */
522 J2 = R20 * j0 + R21 * j1 + R22 * j2 + R23;
523 K2 = R20 * k0 + R21 * k1 + R22 * k2 + R23;
524 if (J2 * K2 >= 0) return false;
526 J0 = R00 * j0 + R01 * j1 + R02 * j2 + R03;
527 K0 = R00 * k0 + R01 * k1 + R02 * k2 + R03;
528 i0 = J0 + J2 * ((K0 - J0) / (J2 - K2));
529 if (i0 < 0 || i0 > 1) return false;
531 J1 = R10 * j0 + R11 * j1 + R12 * j2 + R13;
532 K1 = R10 * k0 + R11 * k1 + R12 * k2 + R13;
533 i1 = J1 + J2 * ((K1 - J1) / (J2 - K2));
534 if (i1 < 0 || i1 > 1 || i0 + i1 > 1) return false;
540 public E makeE(Point p1, Point p2) {
541 Vert v1 = pointset.get(p1);
542 Vert v2 = pointset.get(p2);
543 if (v1 != null && v2 != null) {
545 if (e != null) return e;
547 if (e != null) return e;
549 if (v1 != null) return new E(v1.getFreeIncident(), p2);
550 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
551 return new E(p1, p2);
553 public T newT(Point p1, Point p2, Point p3, Vec norm) {
555 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
556 float dot = norm.dot(norm2);
557 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
558 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
560 E e12 = makeE(p1, p2);
561 E e23 = makeE(p2, p3);
562 E e31 = makeE(p3, p1);
563 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
564 e12.makeAdjacent(e23);
565 e23.makeAdjacent(e31);
566 e31.makeAdjacent(e12);
569 if (e12.t == null) throw new Error();
570 if (e23.t == null) throw new Error();
571 if (e31.t == null) throw new Error();
576 public class FaceIterator implements Iterator<T> {
577 private HashSet<T> visited = new HashSet<T>();
578 private LinkedList<T> next = new LinkedList<T>();
579 public FaceIterator() { }
580 public FaceIterator(Vert v) { next.addFirst(v.e.t); }
581 public boolean hasNext() { return next.peek()!=null; }
582 public void remove() { throw new Error(); }
584 T ret = next.removeFirst();
585 if (ret == null) return null;
587 T t1 = ret.e1().pair.t;
588 T t2 = ret.e2().pair.t;
589 T t3 = ret.e3().pair.t;
590 if (t1 != null && !visited.contains(t1)) next.addFirst(t1);
591 if (t2 != null && !visited.contains(t2)) next.addFirst(t2);
592 if (t3 != null && !visited.contains(t3)) next.addFirst(t3);
597 /** [UNIQUE] a triangle (face) */
598 public final class T extends Triangle {
600 public final int color;
602 public void destroy() {
609 if (e1==e2 || e1==e3) throw new Error();
610 if (e3.next!=e1) throw new Error();
611 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
614 e1.next.next.t = this;
616 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
618 int color = Math.abs(random.nextInt());
621 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
622 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
623 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
628 public E e1() { return e1; }
629 public E e2() { return e1.next; }
630 public E e3() { return e1.prev; }
631 public Vert v1() { return e1.p1; }
632 public Vert v2() { return e1.p2; }
633 public Vert v3() { return e1.next.p2; }
634 public Point p1() { return e1.p1.p; }
635 public Point p2() { return e1.p2.p; }
636 public Point p3() { return e1.next.p2.p; }
637 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
638 public boolean has(Vert v) { return v1()==v || v2()==v || v3()==v; }