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>();
18 public Vert nearest(Point p) { return pointset.nearest(p); }
20 public Iterable<E> edges() {
23 public Iterator<E> iterator() {
25 HashSet<E> hse = new HashSet<E>();
26 for(T t : Mesh.this) {
34 return hse.iterator();
38 public Iterator<T> iterator() {
39 for(Vert v : pointset)
40 if (v.e != null && v.e.t != null)
41 return new FaceIterator(v);
42 return new FaceIterator();
45 public Point origin() { return new Point(0, 0, 0); }
47 public Mesh score_against = null;
48 public double score = 0;
49 public float score() { return (float)score; }
51 public int numedges = 0;
52 public float avgedge = 0;
54 public void unbind() {
55 for(Mesh.T t : this) {
63 for(Mesh.T t : this) {
70 public float rescore() {
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;
80 return (float)(dist/num);
83 public void transform(Matrix m) {
84 ArrayList<Vert> set = new ArrayList<Vert>();
85 for (Vert v : pointset)
87 for(Vert v : set) v.transform(m);
90 public Vec diagonal() { return pointset.diagonal(); }
91 public Point centroid() { return pointset.centroid(); }
93 public float volume() {
96 double area = t.area();
97 Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
98 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
99 double height = Math.abs(t.norm().dot(origin_to_centroid));
100 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
106 public class BindingGroup {
107 public HashSet<E> es = new HashSet<E>();
108 public BindingGroup() { }
109 public BindingGroup(E e) {
112 public void add(E e) {
113 if (e.bg != null) { merge(e.bg); return; }
117 public void merge(BindingGroup bg) {
125 public Vert register(Point p) { Vert v = pointset.get(p); return v==null ? new Vert(p) : v; }
126 public final class Vert extends HasPoint {
128 public Point getPoint() { return p; }
129 private Vert(Point p) {
131 if (pointset.get(p) != null) throw new Error();
134 public float score() { return oldscore; }
135 public void unscore() {
136 if (watch == null) return;
137 watch.watch_x -= p.x;
138 watch.watch_y -= p.y;
139 watch.watch_z -= p.z;
141 if (watch.watch_count==0) {
148 public Vert partner() { return watch==null ? this : watch; }
149 public Vert watchback() { return watch_count==0 ? partner() :
150 register(new Point(watch_x/watch_count, watch_y/watch_count, watch_z/watch_count)); }
151 public void rescore() {
152 if (score_against == null) return;
157 if (watch != null) unscore();
160 watch = score_against.nearest(po.p);
162 // don't attract to vertices that face the other way
163 if (watch.e == null || watch.norm().dot(norm()) < 0) {
166 watch.watch_x += po.p.x;
167 watch.watch_y += po.p.y;
168 watch.watch_z += po.p.z;
174 if (watch_count==0) s1 = 0;
175 else s1 = p.distance(watch_x/watch_count, watch_y/watch_count, watch_z/watch_count);
176 s2 = watch==null ? 0 : po.p.distance(watch.p);
177 oldscore = (float)(s1 + s2);
181 /** does NOT update bound pairs! */
182 public boolean transform(Matrix m) {
183 // FIXME: screws up kdtree
184 // FIXME: screws up hashmap
187 if (pointset.get(this.p)==null) throw new Error();
188 pointset.remove(this);
189 float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
190 float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
191 float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
192 this.p = new Point(newx, newy, newz);
193 // FIXME: what if we move onto exactly where another point is?
195 } catch (Exception e) {
196 throw new RuntimeException(e);
202 for(E e = this.e; ;) {
203 if (e.intersects(t)) { good = false; break; }
205 if (e == this.e) break;
210 if (t==this.t) continue;
211 if (this.intersects(t)) good = false;
216 public boolean move(Vec v) {
217 Matrix m = new Matrix(v);
221 good &= p.transform(m);
222 v = v.times(binding); // bleh wrong
228 public E makeE(Vert p2) {
230 if (e != null) return e;
232 if (this.e == null && p2.e == null) return this.e = new E(this, p2);
233 if (this.e == null && p2.e != null) return p2.makeE(this).pair;
234 return new E(getFreeIncident(), p2);
237 public E getFreeIncident() {
238 E ret = getFreeIncident(e, e);
239 if (ret != null) return ret;
240 ret = getFreeIncident(e.pair.next, e.pair.next);
241 if (ret == null) throw new Error("unable to find free incident to " + this);
245 public E getFreeIncident(E start, E before) {
248 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null) return e.pair;
250 } while(e != before);
254 public E getE(Vert p2) {
257 if (e==null) return null;
258 if (e.p1 == this && e.p2 == p2) return e;
264 public boolean isBoundTo(Vert p) {
267 if (px==this) return true;
273 public void unbind() { bound_to = this; binding = new Matrix(); }
274 public void bind(Vert p) { bind(p, new Matrix()); }
275 public void bind(Vert p, Matrix binding) {
276 if (isBoundTo(p)) return;
277 Vert temp_bound_to = p.bound_to;
278 Matrix temp_binding = p.binding;
279 p.bound_to = this.bound_to;
280 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
281 this.bound_to = temp_bound_to;
282 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
285 Vec norm = new Vec(0, 0, 0);
288 if (e.t != null) norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
290 } while(e != this.e);
294 Vert bound_to = this;
300 E e; // some edge *leaving* this point
301 Matrix binding = new Matrix();
303 boolean inserted = false;
306 /** [UNIQUE] an edge */
307 public final class E implements Comparable<E> {
309 public boolean intersects(T t) {
310 double A0=t.v1().p.x, A1=t.v1().p.y, A2=t.v1().p.z;
311 double B0=t.v2().p.x, B1=t.v2().p.y, B2=t.v2().p.z;
312 double C0=t.v3().p.x, C1=t.v3().p.y, C2=t.v3().p.z;
313 double j0=p1.p.x, j1=p1.p.y, j2=p1.p.z;
314 double k0=p2.p.x, k1=p2.p.y, k2=p2.p.z;
322 double R00, R01, R02, R03,
336 /* c = a × b */
337 c0 = a1 * b2 - a2 * b1;
338 c1 = a2 * b0 - a0 * b2;
339 c2 = a0 * b1 - a1 * b0;
341 /* M^(-1) = (1/det(M)) * adj(M) */
342 in_det = 1 / (c0 * c0 + c1 * c1 + c2 * c2);
343 R00 = (b1 * c2 - b2 * c1) * in_det;
344 R01 = (b2 * c0 - b0 * c2) * in_det;
345 R02 = (b0 * c1 - b1 * c0) * in_det;
346 R10 = (c1 * a2 - c2 * a1) * in_det;
347 R11 = (c2 * a0 - c0 * a2) * in_det;
348 R12 = (c0 * a1 - c1 * a0) * in_det;
354 R03 = -(R00 * A0 + R01 * A1 + R02 * A2);
355 R13 = -(R10 * A0 + R11 * A1 + R12 * A2);
356 R23 = -(R20 * A0 + R21 * A1 + R22 * A2);
358 /* fill in last row of 4x4 matrix */
362 J2 = R20 * j0 + R21 * j1 + R22 * j2 + R23;
363 K2 = R20 * k0 + R21 * k1 + R22 * k2 + R23;
364 if (J2 * K2 >= 0) return false;
366 J0 = R00 * j0 + R01 * j1 + R02 * j2 + R03;
367 K0 = R00 * k0 + R01 * k1 + R02 * k2 + R03;
368 i0 = J0 + J2 * ((K0 - J0) / (J2 - K2));
369 if (i0 < 0 || i0 > 1) return false;
371 J1 = R10 * j0 + R11 * j1 + R12 * j2 + R13;
372 K1 = R10 * k0 + R11 * k1 + R12 * k2 + R13;
373 i1 = J1 + J2 * ((K1 - J1) / (J2 - K2));
374 if (i1 < 0 || i1 > 1 || i0 + i1 > 1) return false;
379 public int compareTo(E e) {
380 return e.length() > length() ? 1 : -1;
383 public final Vert p1, p2;
384 T t; // triangle to our "left"
385 E prev; // previous half-edge
386 E next; // next half-edge
387 E pair; // partner half-edge
390 public BindingGroup bg = new BindingGroup(this);
392 public void bind(E e) { bind(e, new Matrix()); }
393 public void bind(E e, Matrix m) { e.bg.add(this); }
395 public void dobind() {
396 if (bg==null) return;
398 if (ex==this) continue;
404 boolean shattered = false;
405 public Vert shatter() { return shatter(register(midpoint()), null, null); }
406 public Vert shatter(Vert mid, BindingGroup bg1, BindingGroup bg2) {
407 if (shattered) return mid;
414 if (bg1==null) bg1 = new BindingGroup();
415 if (bg2==null) bg2 = new BindingGroup();
416 for(E e : bg.es) e.shatter(register(e.midpoint()), bg1, bg2);
420 newT(r, p1, mid, null);
421 newT(r, mid, p2, null);
422 bg1.add(p1.getE(mid));
423 bg2.add(mid.getE(p2));
427 public boolean destroyed = false;
428 public void destroy() {
429 if (destroyed) return;
431 pair.destroyed = true;
432 if (next.t != null) next.t.destroy();
433 if (prev.t != null) prev.t.destroy();
440 pair.prev.next = next;
441 next.prev = pair.prev;
442 prev.next = pair.next;
444 if (p1.e == this) p1.e = prev.next;
445 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
446 avgedge -= this.length();
447 avgedge -= pair.length();
452 private void sync() {
453 this.prev.next = this;
454 this.next.prev = this;
455 this.pair.pair = this;
456 if (this.next.p1 != p2) throw new Error();
457 if (this.prev.p2 != p1) throw new Error();
458 if (this.p1.e == null) this.p1.e = this;
465 private boolean added = false;
467 public T makeT() { return t==null ? (t = new T(this)) : t; }
469 /** angle between this half-edge and the next */
470 public double angle() {
471 Vec v1 = next.p2.p.minus(p2.p);
472 Vec v2 = this.p1.p.minus(p2.p);
473 return Math.acos(v1.norm().dot(v2.norm()));
476 public void makeAdjacent(E e) {
477 if (this.next == e) return;
478 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
479 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
481 E freeIncident = p2.getFreeIncident(e, this);
483 e.prev.next = freeIncident.next;
484 freeIncident.next.prev = e.prev;
486 freeIncident.next = this.next;
487 this.next.prev = freeIncident;
496 /** creates an isolated edge out in the middle of space */
497 public E(Vert p1, Vert p2) {
498 if (p1==p2) throw new Error("attempt to create edge with single vertex: " + p1);
501 this.prev = this.next = this.pair = new E(this, this, this);
505 /** adds a new half-edge from prev.p2 to p2 */
506 public E(E prev, Vert p2) {
510 if (p2.getE(p1) != null) throw new Error();
512 this.next = this.pair = new E(this, this, prev.next);
514 E q = p2.getFreeIncident();
516 this.next.prev = this;
518 this.prev.next = this;
519 this.pair = new E(q, this, z);
524 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
525 public E(E prev, E pair, E next) {
533 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); }
534 public boolean has(Vert v) { return v==p1 || v==p2; }
535 public float length() { return p1.p.minus(p2.p).mag(); }
536 public String toString() { return p1+"->"+p2; }
539 public T newT(Vert p1, Vert p2, Vert p3, Vec norm) {
541 Vec norm2 = p3.p.minus(p1.p).cross(p2.p.minus(p1.p));
542 float dot = norm.dot(norm2);
543 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
544 if (dot < 0) { Vert p = p1; p1=p2; p2 = p; }
546 E e12 = p1.makeE(p2);
547 E e23 = p2.makeE(p3);
548 E e31 = p3.makeE(p1);
549 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
550 e12.makeAdjacent(e23);
551 e23.makeAdjacent(e31);
552 e31.makeAdjacent(e12);
555 if (e12.t == null) throw new Error();
556 if (e23.t == null) throw new Error();
557 if (e31.t == null) throw new Error();
562 public class FaceIterator implements Iterator<T> {
563 private HashSet<T> visited = new HashSet<T>();
564 private LinkedList<T> next = new LinkedList<T>();
565 public FaceIterator() { }
566 public FaceIterator(Vert v) { next.addFirst(v.e.t); }
567 public boolean hasNext() { return next.peek()!=null; }
568 public void remove() { throw new Error(); }
570 T ret = next.removeFirst();
571 if (ret == null) return null;
573 T t1 = ret.e1().pair.t;
574 T t2 = ret.e2().pair.t;
575 T t3 = ret.e3().pair.t;
576 if (t1 != null && !visited.contains(t1)) next.addFirst(t1);
577 if (t2 != null && !visited.contains(t2)) next.addFirst(t2);
578 if (t3 != null && !visited.contains(t3)) next.addFirst(t3);
583 /** [UNIQUE] a triangle (face) */
584 public final class T extends Triangle {
586 public final int color;
588 public void destroy() {
595 if (e1==e2 || e1==e3) throw new Error();
596 if (e3.next!=e1) throw new Error();
597 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
600 e1.next.next.t = this;
602 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
604 int color = Math.abs(random.nextInt());
607 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
608 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
609 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
614 public E e1() { return e1; }
615 public E e2() { return e1.next; }
616 public E e3() { return e1.prev; }
617 public Vert v1() { return e1.p1; }
618 public Vert v2() { return e1.p2; }
619 public Vert v3() { return e1.next.p2; }
620 public Point p1() { return e1.p1.p; }
621 public Point p2() { return e1.p2.p; }
622 public Point p3() { return e1.next.p2.p; }
623 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
624 public boolean has(Vert v) { return v1()==v || v2()==v || v3()==v; }