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 private KDTree kd = new KDTree(3);
16 public static float EPSILON = (float)0.0001;
17 public static Random random = new Random();
19 private HashMap<Point,Vert> ps = new HashMap<Point,Vert>();
20 //public HashSet<E> es = new HashSet<E>();
22 public Iterable<E> edges() {
25 public Iterator<E> iterator() {
27 HashSet<E> hse = new HashSet<E>();
28 for(T t : Mesh.this) {
36 return hse.iterator();
40 public Iterator<T> iterator() {
41 for(Vert v : ps.values()) {
42 if (v.e != null && v.e.t != null) return new FaceIterator(v);
44 return new FaceIterator();
47 public Point origin() { return new Point(0, 0, 0); }
49 public Mesh score_against = null;
50 public double score = 0;
51 public float score() { return (float)score; }
53 public int numedges = 0;
54 public float avgedge = 0;
56 public void unbind() {
57 for(Mesh.T t : this) {
65 for(Mesh.T t : this) {
72 public float rescore() {
75 HashSet<Vert> done = new HashSet<Vert>();
77 for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() }) {
78 if (done.contains(p)) continue;
83 for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() })
87 for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() })
89 return (float)(dist/num);
92 public void transform(Matrix m) {
93 ArrayList<Vert> set = new ArrayList<Vert>();
94 set.addAll(ps.values());
95 for(Vert v : set) v.transform(m);
98 public Vec diagonal() {
99 float min_x = Float.MAX_VALUE;
100 float min_y = Float.MAX_VALUE;
101 float min_z = Float.MAX_VALUE;
102 float max_x = Float.MIN_VALUE;
103 float max_y = Float.MIN_VALUE;
104 float max_z = Float.MIN_VALUE;
105 for(Point p : ps.keySet()) {
106 if (p.x < min_x) min_x = p.x;
107 if (p.y < min_y) min_y = p.y;
108 if (p.z < min_z) min_z = p.z;
109 if (p.x > max_x) max_x = p.x;
110 if (p.y > max_y) max_y = p.y;
111 if (p.z > max_z) max_z = p.z;
113 return new Vec(max_x - min_x, max_y - min_y, max_z - min_z);
116 public Point centroid() {
117 float min_x = Float.MAX_VALUE;
118 float min_y = Float.MAX_VALUE;
119 float min_z = Float.MAX_VALUE;
120 float max_x = Float.MIN_VALUE;
121 float max_y = Float.MIN_VALUE;
122 float max_z = Float.MIN_VALUE;
123 for(Point p : ps.keySet()) {
124 if (p.x < min_x) min_x = p.x;
125 if (p.y < min_y) min_y = p.y;
126 if (p.z < min_z) min_z = p.z;
127 if (p.x > max_x) max_x = p.x;
128 if (p.y > max_y) max_y = p.y;
129 if (p.z > max_z) max_z = p.z;
131 return new Point((float)(max_x + min_x)/2,
132 (float)(max_y + min_y)/2,
133 (float)(max_z + min_z)/2);
136 public float volume() {
139 double area = t.area();
140 Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
141 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
142 double height = Math.abs(t.norm().dot(origin_to_centroid));
143 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
148 public Vert nearest(Point p) {
150 try { results = kd.nearest(new double[]{p.x,p.y,p.z},1); } catch (Exception e) { throw new Error(e); }
151 return (Vert)results[0];
154 public class BindingGroup {
155 public HashSet<E> es = new HashSet<E>();
156 public BindingGroup() { }
157 public BindingGroup(E e) {
160 public void add(E e) {
161 if (e.bg != null) { merge(e.bg); return; }
165 public void merge(BindingGroup bg) {
173 public Vert register(Point p) { Vert v = ps.get(p); return v==null ? new Vert(p) : v; }
174 public final class Vert {
176 private Vert(Point p) {
178 if (ps.get(p) != null) throw new Error();
179 ps.put(this.p, this);
181 public void kdremove() {
182 if (!inserted) return;
184 try { kd.delete(new double[]{p.x,p.y,p.z}); } catch (Exception e) { }
186 public void kdinsert() {
187 if (inserted) return;
189 try { kd.insert(new double[]{p.x,p.y,p.z},this); } catch (Exception e) { throw new Error(e); }
192 public float score() { return oldscore; }
193 public void unscore() {
194 if (watch == null) return;
195 watch.watch_x -= p.x;
196 watch.watch_y -= p.y;
197 watch.watch_z -= p.z;
199 if (watch.watch_count==0) {
206 public Vert partner() { return watch==null ? this : watch; }
207 public Vert watchback() { return watch_count==0 ? partner() :
208 register(new Point(watch_x/watch_count, watch_y/watch_count, watch_z/watch_count)); }
209 public void rescore() {
210 if (score_against == null) return;
215 if (watch != null) unscore();
218 watch = score_against.nearest(po.p);
220 // don't attract to vertices that face the other way
221 if (watch.norm().dot(norm()) < 0) {
224 watch.watch_x += po.p.x;
225 watch.watch_y += po.p.y;
226 watch.watch_z += po.p.z;
232 if (watch_count==0) s1 = 0;
233 else s1 = p.distance(watch_x/watch_count, watch_y/watch_count, watch_z/watch_count);
234 s2 = watch==null ? 0 : po.p.distance(watch.p);
235 oldscore = (float)(s1 + s2);
239 /** does NOT update bound pairs! */
240 public boolean transform(Matrix m) {
241 // FIXME: screws up kdtree
242 // FIXME: screws up hashmap
245 if (ps.get(this.p)==null) throw new Error();
247 float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
248 float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
249 float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
250 this.p = new Point(newx, newy, newz);
251 // FIXME: what if we move onto exactly where another point is?
252 ps.put(this.p,(Vert)this);
253 } catch (Exception e) {
254 throw new RuntimeException(e);
260 for(E e = this.e; ;) {
261 if (e.intersects(t)) { good = false; break; }
263 if (e == this.e) break;
268 if (t==this.t) continue;
269 if (this.intersects(t)) good = false;
274 public boolean move(Vec v) {
275 Matrix m = new Matrix(v);
279 good &= p.transform(m);
280 v = v.times(binding); // bleh wrong
286 public E makeE(Vert p2) {
288 if (e != null) return e;
290 if (this.e == null && p2.e == null) return this.e = new E(this, p2);
291 if (this.e == null && p2.e != null) return p2.makeE(this).pair;
292 return new E(getFreeIncident(), p2);
295 public E getFreeIncident() {
296 E ret = getFreeIncident(e, e);
297 if (ret != null) return ret;
298 ret = getFreeIncident(e.pair.next, e.pair.next);
299 if (ret == null) throw new Error("unable to find free incident to " + this);
303 public E getFreeIncident(E start, E before) {
306 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null) return e.pair;
308 } while(e != before);
312 public E getE(Vert p2) {
315 if (e==null) return null;
316 if (e.p1 == this && e.p2 == p2) return e;
322 public boolean isBoundTo(Vert p) {
325 if (px==this) return true;
331 public void unbind() { bound_to = this; binding = new Matrix(); }
332 public void bind(Vert p) { bind(p, new Matrix()); }
333 public void bind(Vert p, Matrix binding) {
334 if (isBoundTo(p)) return;
335 Vert temp_bound_to = p.bound_to;
336 Matrix temp_binding = p.binding;
337 p.bound_to = this.bound_to;
338 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
339 this.bound_to = temp_bound_to;
340 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
343 Vec norm = new Vec(0, 0, 0);
346 if (e.t != null) norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
348 } while(e != this.e);
352 Vert bound_to = this;
358 E e; // some edge *leaving* this point
359 Matrix binding = new Matrix();
361 boolean inserted = false;
364 /** [UNIQUE] an edge */
365 public final class E implements Comparable<E> {
367 public boolean intersects(T t) {
368 double A0=t.v1().p.x, A1=t.v1().p.y, A2=t.v1().p.z;
369 double B0=t.v2().p.x, B1=t.v2().p.y, B2=t.v2().p.z;
370 double C0=t.v3().p.x, C1=t.v3().p.y, C2=t.v3().p.z;
371 double j0=p1.p.x, j1=p1.p.y, j2=p1.p.z;
372 double k0=p2.p.x, k1=p2.p.y, k2=p2.p.z;
380 double R00, R01, R02, R03,
394 /* c = a × b */
395 c0 = a1 * b2 - a2 * b1;
396 c1 = a2 * b0 - a0 * b2;
397 c2 = a0 * b1 - a1 * b0;
399 /* M^(-1) = (1/det(M)) * adj(M) */
400 in_det = 1 / (c0 * c0 + c1 * c1 + c2 * c2);
401 R00 = (b1 * c2 - b2 * c1) * in_det;
402 R01 = (b2 * c0 - b0 * c2) * in_det;
403 R02 = (b0 * c1 - b1 * c0) * in_det;
404 R10 = (c1 * a2 - c2 * a1) * in_det;
405 R11 = (c2 * a0 - c0 * a2) * in_det;
406 R12 = (c0 * a1 - c1 * a0) * in_det;
412 R03 = -(R00 * A0 + R01 * A1 + R02 * A2);
413 R13 = -(R10 * A0 + R11 * A1 + R12 * A2);
414 R23 = -(R20 * A0 + R21 * A1 + R22 * A2);
416 /* fill in last row of 4x4 matrix */
420 J2 = R20 * j0 + R21 * j1 + R22 * j2 + R23;
421 K2 = R20 * k0 + R21 * k1 + R22 * k2 + R23;
422 if (J2 * K2 >= 0) return false;
424 J0 = R00 * j0 + R01 * j1 + R02 * j2 + R03;
425 K0 = R00 * k0 + R01 * k1 + R02 * k2 + R03;
426 i0 = J0 + J2 * ((K0 - J0) / (J2 - K2));
427 if (i0 < 0 || i0 > 1) return false;
429 J1 = R10 * j0 + R11 * j1 + R12 * j2 + R13;
430 K1 = R10 * k0 + R11 * k1 + R12 * k2 + R13;
431 i1 = J1 + J2 * ((K1 - J1) / (J2 - K2));
432 if (i1 < 0 || i1 > 1 || i0 + i1 > 1) return false;
437 public int compareTo(E e) {
438 return e.length() > length() ? 1 : -1;
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
448 public BindingGroup bg = new BindingGroup(this);
450 public void bind(E e) { bind(e, new Matrix()); }
451 public void bind(E e, Matrix m) { e.bg.add(this); }
453 public void dobind() {
454 if (bg==null) return;
456 if (ex==this) continue;
462 boolean shattered = false;
463 public Vert shatter() { return shatter(register(midpoint()), null, null); }
464 public Vert shatter(Vert mid, BindingGroup bg1, BindingGroup bg2) {
465 if (shattered) return mid;
472 if (bg1==null) bg1 = new BindingGroup();
473 if (bg2==null) bg2 = new BindingGroup();
474 for(E e : bg.es) e.shatter(register(e.midpoint()), bg1, bg2);
478 newT(r, p1, mid, null);
479 newT(r, mid, p2, null);
480 bg1.add(p1.getE(mid));
481 bg2.add(mid.getE(p2));
485 public boolean destroyed = false;
486 public void destroy() {
487 if (destroyed) return;
489 pair.destroyed = true;
490 if (next.t != null) next.t.destroy();
491 if (prev.t != null) prev.t.destroy();
498 pair.prev.next = next;
499 next.prev = pair.prev;
500 prev.next = pair.next;
502 if (p1.e == this) p1.e = prev.next;
503 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
504 avgedge -= this.length();
505 avgedge -= pair.length();
510 private void sync() {
511 this.prev.next = this;
512 this.next.prev = this;
513 this.pair.pair = this;
514 if (this.next.p1 != p2) throw new Error();
515 if (this.prev.p2 != p1) throw new Error();
516 if (this.p1.e == null) this.p1.e = this;
523 private boolean added = false;
525 public T makeT() { return t==null ? (t = new T(this)) : t; }
527 /** angle between this half-edge and the next */
528 public double angle() {
529 Vec v1 = next.p2.p.minus(p2.p);
530 Vec v2 = this.p1.p.minus(p2.p);
531 return Math.acos(v1.norm().dot(v2.norm()));
534 public void makeAdjacent(E e) {
535 if (this.next == e) return;
536 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
537 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
539 E freeIncident = p2.getFreeIncident(e, this);
541 e.prev.next = freeIncident.next;
542 freeIncident.next.prev = e.prev;
544 freeIncident.next = this.next;
545 this.next.prev = freeIncident;
554 /** creates an isolated edge out in the middle of space */
555 public E(Vert p1, Vert p2) {
556 if (p1==p2) throw new Error("attempt to create edge with single vertex: " + p1);
559 this.prev = this.next = this.pair = new E(this, this, this);
563 /** adds a new half-edge from prev.p2 to p2 */
564 public E(E prev, Vert p2) {
568 if (p2.getE(p1) != null) throw new Error();
570 this.next = this.pair = new E(this, this, prev.next);
572 E q = p2.getFreeIncident();
574 this.next.prev = this;
576 this.prev.next = this;
577 this.pair = new E(q, this, z);
582 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
583 public E(E prev, E pair, E next) {
591 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); }
592 public boolean has(Vert v) { return v==p1 || v==p2; }
593 public float length() { return p1.p.minus(p2.p).mag(); }
594 public String toString() { return p1+"->"+p2; }
597 public T newT(Vert p1, Vert p2, Vert p3, Vec norm) {
599 Vec norm2 = p3.p.minus(p1.p).cross(p2.p.minus(p1.p));
600 float dot = norm.dot(norm2);
601 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within epsilon of each other: "+norm+" "+norm2);
602 if (dot < 0) { Vert p = p1; p1=p2; p2 = p; }
604 E e12 = p1.makeE(p2);
605 E e23 = p2.makeE(p3);
606 E e31 = p3.makeE(p1);
607 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
608 e12.makeAdjacent(e23);
609 e23.makeAdjacent(e31);
610 e31.makeAdjacent(e12);
613 if (e12.t == null) throw new Error();
614 if (e23.t == null) throw new Error();
615 if (e31.t == null) throw new Error();
620 public class FaceIterator implements Iterator<T> {
621 private HashSet<T> visited = new HashSet<T>();
622 private LinkedList<T> next = new LinkedList<T>();
623 public FaceIterator() { }
624 public FaceIterator(Vert v) { next.addFirst(v.e.t); }
625 public boolean hasNext() { return next.peek()!=null; }
626 public void remove() { throw new Error(); }
628 T ret = next.removeFirst();
629 if (ret == null) return null;
631 T t1 = ret.e1().pair.t;
632 T t2 = ret.e2().pair.t;
633 T t3 = ret.e3().pair.t;
634 if (t1 != null && !visited.contains(t1)) next.addFirst(t1);
635 if (t2 != null && !visited.contains(t2)) next.addFirst(t2);
636 if (t3 != null && !visited.contains(t3)) next.addFirst(t3);
641 /** [UNIQUE] a triangle (face) */
642 public final class T extends Triangle {
644 public final int color;
646 public void destroy() {
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; }
676 public E e1() { return e1; }
677 public E e2() { return e1.next; }
678 public E e3() { return e1.prev; }
679 public Vert v1() { return e1.p1; }
680 public Vert v2() { return e1.p2; }
681 public Vert v3() { return e1.next.p2; }
682 public Point p1() { return e1.p1.p; }
683 public Point p2() { return e1.p2.p; }
684 public Point p3() { return e1.next.p2.p; }
685 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
686 public boolean has(Vert v) { return v1()==v || v2()==v || v3()==v; }