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>();
21 public ArrayList<T> ts = new ArrayList<T>();
23 public Iterator<T> iterator() { return ts.iterator(); }
25 public Point origin() { return new Point(0, 0, 0); }
27 public Mesh score_against = null;
28 public double score = 0;
29 public float score() { return (float)score; }
31 public void unbind() {
33 for(Mesh.T t : this) {
41 for(Mesh.T t : this) {
47 public int numedges = 0;
48 public float avgedge = 0;
50 public float rescore() {
53 HashSet<Vert> done = new HashSet<Vert>();
55 for(Vert p : new Vert[] { t.p1(), t.p2(), t.p3() }) {
56 if (done.contains(p)) continue;
61 for(Vert p : new Vert[] { t.p1(), t.p2(), t.p3() })
65 for(Vert p : new Vert[] { t.p1(), t.p2(), t.p3() })
67 return (float)(dist/num);
70 public void transform(Matrix m) {
71 ArrayList<Vert> set = new ArrayList<Vert>();
72 set.addAll(ps.values());
73 for(Vert v : set) v.transform(m);
76 public Vec diagonal() {
77 float min_x = Float.MAX_VALUE;
78 float min_y = Float.MAX_VALUE;
79 float min_z = Float.MAX_VALUE;
80 float max_x = Float.MIN_VALUE;
81 float max_y = Float.MIN_VALUE;
82 float max_z = Float.MIN_VALUE;
83 for(Point p : ps.keySet()) {
84 if (p.x < min_x) min_x = p.x;
85 if (p.y < min_y) min_y = p.y;
86 if (p.z < min_z) min_z = p.z;
87 if (p.x > max_x) max_x = p.x;
88 if (p.y > max_y) max_y = p.y;
89 if (p.z > max_z) max_z = p.z;
91 return new Vec(max_x - min_x, max_y - min_y, max_z - min_z);
94 public Point centroid() {
95 float min_x = Float.MAX_VALUE;
96 float min_y = Float.MAX_VALUE;
97 float min_z = Float.MAX_VALUE;
98 float max_x = Float.MIN_VALUE;
99 float max_y = Float.MIN_VALUE;
100 float max_z = Float.MIN_VALUE;
101 for(Point p : ps.keySet()) {
102 if (p.x < min_x) min_x = p.x;
103 if (p.y < min_y) min_y = p.y;
104 if (p.z < min_z) min_z = p.z;
105 if (p.x > max_x) max_x = p.x;
106 if (p.y > max_y) max_y = p.y;
107 if (p.z > max_z) max_z = p.z;
109 return new Point((float)(max_x + min_x)/2,
110 (float)(max_y + min_y)/2,
111 (float)(max_z + min_z)/2);
114 public T newT(Vert p12, Vert p23, Vert p31, Vec norm) {
115 Vec norm2 = p31.p.minus(p12.p).cross(p23.p.minus(p12.p));
116 float dot = norm.dot(norm2);
117 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within epsilon of each other: "+norm+" "+norm2);
118 if (dot < 0) { Vert p = p12; p12=p23; p23 = p; }
119 return newT(p12, p23, p31);
122 public float volume() {
125 double area = t.area();
126 Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
127 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
128 double height = Math.abs(t.norm().dot(origin_to_centroid));
129 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
134 public Vert nearest(Point p) {
136 try { results = kd.nearest(new double[]{p.x,p.y,p.z},1); } catch (Exception e) { throw new Error(e); }
137 return (Vert)results[0];
140 public T newT(Vert p1, Vert p2, Vert p3) {
141 E e12 = p1.makeE(p2);
142 E e23 = p2.makeE(p3);
143 E e31 = p3.makeE(p1);
144 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
145 e12.makeAdjacent(e23);
146 e23.makeAdjacent(e31);
147 e31.makeAdjacent(e12);
150 if (e12.t == null) throw new Error();
151 if (e23.t == null) throw new Error();
152 if (e31.t == null) throw new Error();
156 public class BindingGroup {
157 public HashSet<E> es = new HashSet<E>();
158 public BindingGroup() { }
159 public BindingGroup(E e) {
162 public void add(E e) {
163 if (e.bg != null) { merge(e.bg); return; }
167 public void merge(BindingGroup bg) {
175 public Vert register(Point p) { Vert v = ps.get(p); return v==null ? new Vert(p) : v; }
176 public final class Vert {
178 private Vert(Point p) {
180 if (ps.get(p) != null) throw new Error();
181 ps.put(this.p, this);
183 public void kdremove() {
184 if (!inserted) return;
186 try { kd.delete(new double[]{p.x,p.y,p.z}); } catch (Exception e) { }
188 public void kdinsert() {
189 if (inserted) return;
191 try { kd.insert(new double[]{p.x,p.y,p.z},this); } catch (Exception e) { throw new Error(e); }
194 public float score() { return oldscore; }
195 public void unscore() {
196 if (watch == null) return;
197 watch.watch_x -= p.x;
198 watch.watch_y -= p.y;
199 watch.watch_z -= p.z;
201 if (watch.watch_count==0) {
208 public Vert partner() { return watch==null ? this : watch; }
209 public Vert watchback() { return watch_count==0 ? partner() :
210 register(new Point(watch_x/watch_count, watch_y/watch_count, watch_z/watch_count)); }
211 public void rescore() {
212 if (score_against == null) return;
217 if (watch != null) unscore();
220 watch = score_against.nearest(po.p);
222 // don't attract to vertices that face the other way
223 if (watch.norm().dot(norm()) < 0) {
226 watch.watch_x += po.p.x;
227 watch.watch_y += po.p.y;
228 watch.watch_z += po.p.z;
234 if (watch_count==0) s1 = 0;
235 else s1 = p.distance(watch_x/watch_count, watch_y/watch_count, watch_z/watch_count);
236 s2 = watch==null ? 0 : po.p.distance(watch.p);
237 oldscore = (float)(s1 + s2);
242 /** does NOT update bound pairs! */
243 public boolean transform(Matrix m) {
244 // FIXME: screws up kdtree
245 // FIXME: screws up hashmap
248 if (ps.get(this.p)==null) throw new Error();
250 float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
251 float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
252 float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
253 this.p = new Point(newx, newy, newz);
254 // FIXME: what if we move onto exactly where another point is?
255 ps.put(this.p,(Vert)this);
256 } catch (Exception e) {
257 throw new RuntimeException(e);
263 for(E e = this.e; ;) {
264 if (e.intersects(t)) { good = false; break; }
266 if (e == this.e) break;
271 if (t==this.t) continue;
272 if (this.intersects(t)) good = false;
277 public boolean move(Vec v) {
278 Matrix m = new Matrix(v);
282 good &= p.transform(m);
283 v = v.times(binding); // bleh wrong
289 public E makeE(Vert p2) {
291 if (e != null) return e;
293 if (this.e == null && p2.e == null) return this.e = new E(this, p2);
294 if (this.e == null && p2.e != null) return p2.makeE(this).pair;
295 return new E(getFreeIncident(), p2);
298 public E getFreeIncident() {
299 E ret = getFreeIncident(e, e);
300 if (ret != null) return ret;
301 ret = getFreeIncident(e.pair.next, e.pair.next);
302 if (ret == null) throw new Error("unable to find free incident to " + this);
306 public E getFreeIncident(E start, E before) {
309 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null) return e.pair;
311 } while(e != before);
315 public E getE(Vert p2) {
318 if (e==null) return null;
319 if (e.p1 == this && e.p2 == p2) return e;
325 public boolean isBoundTo(Vert p) {
328 if (px==this) return true;
334 public void unbind() { bound_to = this; binding = new Matrix(); }
335 public void bind(Vert p) { bind(p, new Matrix()); }
336 public void bind(Vert p, Matrix binding) {
337 if (isBoundTo(p)) return;
338 Vert temp_bound_to = p.bound_to;
339 Matrix temp_binding = p.binding;
340 p.bound_to = this.bound_to;
341 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
342 this.bound_to = temp_bound_to;
343 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
346 Vec norm = new Vec(0, 0, 0);
349 if (e.t != null) norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
351 } while(e != this.e);
355 Vert bound_to = this;
361 E e; // some edge *leaving* this point
362 Matrix binding = new Matrix();
364 boolean inserted = false;
367 /** [UNIQUE] an edge */
368 public final class E implements Comparable<E> {
370 public boolean intersects(T t) {
371 double A0=t.p1().p.x, A1=t.p1().p.y, A2=t.p1().p.z;
372 double B0=t.p2().p.x, B1=t.p2().p.y, B2=t.p2().p.z;
373 double C0=t.p3().p.x, C1=t.p3().p.y, C2=t.p3().p.z;
374 double j0=p1.p.x, j1=p1.p.y, j2=p1.p.z;
375 double k0=p2.p.x, k1=p2.p.y, k2=p2.p.z;
383 double R00, R01, R02, R03,
397 /* c = a × b */
398 c0 = a1 * b2 - a2 * b1;
399 c1 = a2 * b0 - a0 * b2;
400 c2 = a0 * b1 - a1 * b0;
402 /* M^(-1) = (1/det(M)) * adj(M) */
403 in_det = 1 / (c0 * c0 + c1 * c1 + c2 * c2);
404 R00 = (b1 * c2 - b2 * c1) * in_det;
405 R01 = (b2 * c0 - b0 * c2) * in_det;
406 R02 = (b0 * c1 - b1 * c0) * in_det;
407 R10 = (c1 * a2 - c2 * a1) * in_det;
408 R11 = (c2 * a0 - c0 * a2) * in_det;
409 R12 = (c0 * a1 - c1 * a0) * in_det;
415 R03 = -(R00 * A0 + R01 * A1 + R02 * A2);
416 R13 = -(R10 * A0 + R11 * A1 + R12 * A2);
417 R23 = -(R20 * A0 + R21 * A1 + R22 * A2);
419 /* fill in last row of 4x4 matrix */
423 J2 = R20 * j0 + R21 * j1 + R22 * j2 + R23;
424 K2 = R20 * k0 + R21 * k1 + R22 * k2 + R23;
425 if (J2 * K2 >= 0) return false;
427 J0 = R00 * j0 + R01 * j1 + R02 * j2 + R03;
428 K0 = R00 * k0 + R01 * k1 + R02 * k2 + R03;
429 i0 = J0 + J2 * ((K0 - J0) / (J2 - K2));
430 if (i0 < 0 || i0 > 1) return false;
432 J1 = R10 * j0 + R11 * j1 + R12 * j2 + R13;
433 K1 = R10 * k0 + R11 * k1 + R12 * k2 + R13;
434 i1 = J1 + J2 * ((K1 - J1) / (J2 - K2));
435 if (i1 < 0 || i1 > 1 || i0 + i1 > 1) return false;
440 public int compareTo(E e) {
441 return e.length() > length() ? 1 : -1;
444 public final Vert p1, p2;
445 T t; // triangle to our "left"
446 E prev; // previous half-edge
447 E next; // next half-edge
448 E pair; // partner half-edge
451 public BindingGroup bg = new BindingGroup(this);
453 public void bind(E e) { bind(e, new Matrix()); }
454 public void bind(E e, Matrix m) { e.bg.add(this); }
456 public void dobind() {
457 if (bg==null) return;
459 if (ex==this) continue;
465 boolean shattered = false;
466 public Vert shatter() { return shatter(register(midpoint()), null, null); }
467 public Vert shatter(Vert mid, BindingGroup bg1, BindingGroup bg2) {
468 if (shattered) return mid;
475 if (bg1==null) bg1 = new BindingGroup();
476 if (bg2==null) bg2 = new BindingGroup();
477 for(E e : bg.es) e.shatter(register(e.midpoint()), bg1, bg2);
483 bg1.add(p1.getE(mid));
484 bg2.add(mid.getE(p2));
488 public boolean destroyed = false;
489 public void destroy() {
490 if (destroyed) return;
492 pair.destroyed = true;
493 if (next.t != null) next.t.destroy();
494 if (prev.t != null) prev.t.destroy();
495 if (pair.next.t != null) ts.remove(pair.next.t);
496 if (pair.prev.t != null) ts.remove(pair.prev.t);
503 pair.prev.next = next;
504 next.prev = pair.prev;
505 prev.next = pair.next;
507 if (p1.e == this) p1.e = prev.next;
508 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
511 avgedge -= this.length();
512 avgedge -= pair.length();
517 private void sync() {
518 this.prev.next = this;
519 this.next.prev = this;
520 this.pair.pair = this;
521 if (this.next.p1 != p2) throw new Error();
522 if (this.prev.p2 != p1) throw new Error();
523 if (this.p1.e == null) this.p1.e = this;
531 private boolean added = false;
533 public T makeT() { return t==null ? (t = new T(this)) : t; }
535 /** angle between this half-edge and the next */
536 public double angle() {
537 Vec v1 = next.p2.p.minus(p2.p);
538 Vec v2 = this.p1.p.minus(p2.p);
539 return Math.acos(v1.norm().dot(v2.norm()));
542 public void makeAdjacent(E e) {
543 if (this.next == e) return;
544 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
545 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
547 E freeIncident = p2.getFreeIncident(e, this);
549 e.prev.next = freeIncident.next;
550 freeIncident.next.prev = e.prev;
552 freeIncident.next = this.next;
553 this.next.prev = freeIncident;
562 /** creates an isolated edge out in the middle of space */
563 public E(Vert p1, Vert p2) {
564 if (p1==p2) throw new Error("attempt to create edge with single vertex: " + p1);
567 this.prev = this.next = this.pair = new E(this, this, this);
571 /** adds a new half-edge from prev.p2 to p2 */
572 public E(E prev, Vert p2) {
576 if (p2.getE(p1) != null) throw new Error();
578 this.next = this.pair = new E(this, this, prev.next);
580 E q = p2.getFreeIncident();
582 this.next.prev = this;
584 this.prev.next = this;
585 this.pair = new E(q, this, z);
590 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
591 public E(E prev, E pair, E next) {
599 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); }
600 public boolean has(Vert v) { return v==p1 || v==p2; }
601 public float length() { return p1.p.minus(p2.p).mag(); }
602 public String toString() { return p1+"->"+p2; }
605 /** [UNIQUE] a triangle (face) */
606 public final class T {
608 public final int color;
610 public void destroy() {
614 public Vert nearest(Point p) {
615 float d1 = p1().p.distance(p);
616 float d2 = p2().p.distance(p);
617 float d3 = p3().p.distance(p);
618 if (d1 < d2 && d1 < d3) return p1();
619 if (d2 < d3) return p2();
627 if (e1==e2 || e1==e3) throw new Error();
628 if (e3.next!=e1) throw new Error();
629 if (e1.t!=null || e2.t!=null || e3.t!=null)
630 throw new Error("non-manifold surface or disagreeing normals");
633 e1.next.next.t = this;
635 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
637 int color = Math.abs(random.nextInt());
640 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
641 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
642 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
654 public Vert p1() { return e1.p1; }
655 public Vert p2() { return e1.p2; }
656 public Vert p3() { return e1.next.p2; }
657 public E e1() { return e1; }
658 public E e2() { return e1.next; }
659 public E e3() { return e1.prev; }
660 public Vec norm() { return p2().p.minus(p1().p).cross(p3().p.minus(p1().p)).norm(); }
661 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
662 public boolean has(Vert v) { return p1()==v || p2()==v || p3()==v; }
664 public float area() {
665 return (float)Math.abs(0.5 * e1().length() * new Vec(p1().p, p2().p).norm().dot(new Vec(p2().p, p3().p)));
668 public void glVertices(GL gl) {
674 public Point centroid() { return new Point((p1().p.x+p2().p.x+p3().p.x)/3,
675 (p1().p.y+p2().p.y+p3().p.y)/3,
676 (p1().p.z+p2().p.z+p3().p.z)/3); }
677 public float diameter() {
678 // FIXME: what is this supposed to be?
679 return Math.max(Math.max(e1().length(), e2().length()), e3().length()) / 2;