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); }
19 private HashMap<Point,Vert> verts = new HashMap<Point,Vert>();
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 Point origin() { return new Point(0, 0, 0); }
48 public Mesh score_against = null;
49 public double score = 0;
50 public float score() { return (float)score; }
52 public int numedges = 0;
53 public float avgedge = 0;
55 public void unbind() {
56 for(Mesh.T t : this) {
64 for(Mesh.T t : this) {
71 public float rescore() {
74 HashSet<Vert> done = new HashSet<Vert>();
76 for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() }) {
77 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() })
90 return (float)(dist/num);
93 public void transform(Matrix m) {
94 ArrayList<Vert> set = new ArrayList<Vert>();
95 for (Vert v : pointset)
97 for(Vert v : set) v.transform(m);
100 public Vec diagonal() {
101 float min_x = Float.MAX_VALUE;
102 float min_y = Float.MAX_VALUE;
103 float min_z = Float.MAX_VALUE;
104 float max_x = Float.MIN_VALUE;
105 float max_y = Float.MIN_VALUE;
106 float max_z = Float.MIN_VALUE;
107 for(Point p : verts.keySet()) {
108 if (p.x < min_x) min_x = p.x;
109 if (p.y < min_y) min_y = p.y;
110 if (p.z < min_z) min_z = p.z;
111 if (p.x > max_x) max_x = p.x;
112 if (p.y > max_y) max_y = p.y;
113 if (p.z > max_z) max_z = p.z;
115 return new Vec(max_x - min_x, max_y - min_y, max_z - min_z);
118 public Point centroid() {
119 float min_x = Float.MAX_VALUE;
120 float min_y = Float.MAX_VALUE;
121 float min_z = Float.MAX_VALUE;
122 float max_x = Float.MIN_VALUE;
123 float max_y = Float.MIN_VALUE;
124 float max_z = Float.MIN_VALUE;
125 for(Point p : verts.keySet()) {
126 if (p.x < min_x) min_x = p.x;
127 if (p.y < min_y) min_y = p.y;
128 if (p.z < min_z) min_z = p.z;
129 if (p.x > max_x) max_x = p.x;
130 if (p.y > max_y) max_y = p.y;
131 if (p.z > max_z) max_z = p.z;
133 return new Point((float)(max_x + min_x)/2,
134 (float)(max_y + min_y)/2,
135 (float)(max_z + min_z)/2);
138 public float volume() {
141 double area = t.area();
142 Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
143 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
144 double height = Math.abs(t.norm().dot(origin_to_centroid));
145 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
151 public class BindingGroup {
152 public HashSet<E> es = new HashSet<E>();
153 public BindingGroup() { }
154 public BindingGroup(E e) {
157 public void add(E e) {
158 if (e.bg != null) { merge(e.bg); return; }
162 public void merge(BindingGroup bg) {
170 public Vert register(Point p) { Vert v = verts.get(p); return v==null ? new Vert(p) : v; }
171 public final class Vert extends HasPoint {
173 public Point getPoint() { return p; }
174 private Vert(Point p) {
176 if (verts.get(p) != null) throw new Error();
177 verts.put(this.p, this);
180 public void reinsert() {
181 pointset.remove(this);
184 public void kdremove() {
185 if (!inserted) return;
187 pointset.remove(this);
189 public void kdinsert() {
190 if (inserted) return;
195 public float score() { return oldscore; }
196 public void unscore() {
197 if (watch == null) return;
198 watch.watch_x -= p.x;
199 watch.watch_y -= p.y;
200 watch.watch_z -= p.z;
202 if (watch.watch_count==0) {
209 public Vert partner() { return watch==null ? this : watch; }
210 public Vert watchback() { return watch_count==0 ? partner() :
211 register(new Point(watch_x/watch_count, watch_y/watch_count, watch_z/watch_count)); }
212 public void rescore() {
213 if (score_against == null) return;
218 if (watch != null) unscore();
221 watch = score_against.nearest(po.p);
223 // don't attract to vertices that face the other way
224 if (watch.e == null || watch.norm().dot(norm()) < 0) {
227 watch.watch_x += po.p.x;
228 watch.watch_y += po.p.y;
229 watch.watch_z += po.p.z;
235 if (watch_count==0) s1 = 0;
236 else s1 = p.distance(watch_x/watch_count, watch_y/watch_count, watch_z/watch_count);
237 s2 = watch==null ? 0 : po.p.distance(watch.p);
238 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 (verts.get(this.p)==null) throw new Error();
249 verts.remove(this.p);
250 pointset.remove(this);
251 float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
252 float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
253 float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
254 this.p = new Point(newx, newy, newz);
255 // FIXME: what if we move onto exactly where another point is?
257 verts.put(this.p,(Vert)this);
258 } catch (Exception e) {
259 throw new RuntimeException(e);
265 for(E e = this.e; ;) {
266 if (e.intersects(t)) { good = false; break; }
268 if (e == this.e) break;
273 if (t==this.t) continue;
274 if (this.intersects(t)) good = false;
279 public boolean move(Vec v) {
280 Matrix m = new Matrix(v);
284 good &= p.transform(m);
285 v = v.times(binding); // bleh wrong
291 public E makeE(Vert p2) {
293 if (e != null) return e;
295 if (this.e == null && p2.e == null) return this.e = new E(this, p2);
296 if (this.e == null && p2.e != null) return p2.makeE(this).pair;
297 return new E(getFreeIncident(), p2);
300 public E getFreeIncident() {
301 E ret = getFreeIncident(e, e);
302 if (ret != null) return ret;
303 ret = getFreeIncident(e.pair.next, e.pair.next);
304 if (ret == null) throw new Error("unable to find free incident to " + this);
308 public E getFreeIncident(E start, E before) {
311 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null) return e.pair;
313 } while(e != before);
317 public E getE(Vert p2) {
320 if (e==null) return null;
321 if (e.p1 == this && e.p2 == p2) return e;
327 public boolean isBoundTo(Vert p) {
330 if (px==this) return true;
336 public void unbind() { bound_to = this; binding = new Matrix(); }
337 public void bind(Vert p) { bind(p, new Matrix()); }
338 public void bind(Vert p, Matrix binding) {
339 if (isBoundTo(p)) return;
340 Vert temp_bound_to = p.bound_to;
341 Matrix temp_binding = p.binding;
342 p.bound_to = this.bound_to;
343 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
344 this.bound_to = temp_bound_to;
345 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
348 Vec norm = new Vec(0, 0, 0);
351 if (e.t != null) norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
353 } while(e != this.e);
357 Vert bound_to = this;
363 E e; // some edge *leaving* this point
364 Matrix binding = new Matrix();
366 boolean inserted = false;
369 /** [UNIQUE] an edge */
370 public final class E implements Comparable<E> {
372 public boolean intersects(T t) {
373 double A0=t.v1().p.x, A1=t.v1().p.y, A2=t.v1().p.z;
374 double B0=t.v2().p.x, B1=t.v2().p.y, B2=t.v2().p.z;
375 double C0=t.v3().p.x, C1=t.v3().p.y, C2=t.v3().p.z;
376 double j0=p1.p.x, j1=p1.p.y, j2=p1.p.z;
377 double k0=p2.p.x, k1=p2.p.y, k2=p2.p.z;
385 double R00, R01, R02, R03,
399 /* c = a × b */
400 c0 = a1 * b2 - a2 * b1;
401 c1 = a2 * b0 - a0 * b2;
402 c2 = a0 * b1 - a1 * b0;
404 /* M^(-1) = (1/det(M)) * adj(M) */
405 in_det = 1 / (c0 * c0 + c1 * c1 + c2 * c2);
406 R00 = (b1 * c2 - b2 * c1) * in_det;
407 R01 = (b2 * c0 - b0 * c2) * in_det;
408 R02 = (b0 * c1 - b1 * c0) * in_det;
409 R10 = (c1 * a2 - c2 * a1) * in_det;
410 R11 = (c2 * a0 - c0 * a2) * in_det;
411 R12 = (c0 * a1 - c1 * a0) * in_det;
417 R03 = -(R00 * A0 + R01 * A1 + R02 * A2);
418 R13 = -(R10 * A0 + R11 * A1 + R12 * A2);
419 R23 = -(R20 * A0 + R21 * A1 + R22 * A2);
421 /* fill in last row of 4x4 matrix */
425 J2 = R20 * j0 + R21 * j1 + R22 * j2 + R23;
426 K2 = R20 * k0 + R21 * k1 + R22 * k2 + R23;
427 if (J2 * K2 >= 0) return false;
429 J0 = R00 * j0 + R01 * j1 + R02 * j2 + R03;
430 K0 = R00 * k0 + R01 * k1 + R02 * k2 + R03;
431 i0 = J0 + J2 * ((K0 - J0) / (J2 - K2));
432 if (i0 < 0 || i0 > 1) return false;
434 J1 = R10 * j0 + R11 * j1 + R12 * j2 + R13;
435 K1 = R10 * k0 + R11 * k1 + R12 * k2 + R13;
436 i1 = J1 + J2 * ((K1 - J1) / (J2 - K2));
437 if (i1 < 0 || i1 > 1 || i0 + i1 > 1) return false;
442 public int compareTo(E e) {
443 return e.length() > length() ? 1 : -1;
446 public final Vert p1, p2;
447 T t; // triangle to our "left"
448 E prev; // previous half-edge
449 E next; // next half-edge
450 E pair; // partner half-edge
453 public BindingGroup bg = new BindingGroup(this);
455 public void bind(E e) { bind(e, new Matrix()); }
456 public void bind(E e, Matrix m) { e.bg.add(this); }
458 public void dobind() {
459 if (bg==null) return;
461 if (ex==this) continue;
467 boolean shattered = false;
468 public Vert shatter() { return shatter(register(midpoint()), null, null); }
469 public Vert shatter(Vert mid, BindingGroup bg1, BindingGroup bg2) {
470 if (shattered) return mid;
477 if (bg1==null) bg1 = new BindingGroup();
478 if (bg2==null) bg2 = new BindingGroup();
479 for(E e : bg.es) e.shatter(register(e.midpoint()), bg1, bg2);
483 newT(r, p1, mid, null);
484 newT(r, mid, p2, null);
485 bg1.add(p1.getE(mid));
486 bg2.add(mid.getE(p2));
490 public boolean destroyed = false;
491 public void destroy() {
492 if (destroyed) return;
494 pair.destroyed = true;
495 if (next.t != null) next.t.destroy();
496 if (prev.t != null) prev.t.destroy();
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;
509 avgedge -= this.length();
510 avgedge -= pair.length();
515 private void sync() {
516 this.prev.next = this;
517 this.next.prev = this;
518 this.pair.pair = this;
519 if (this.next.p1 != p2) throw new Error();
520 if (this.prev.p2 != p1) throw new Error();
521 if (this.p1.e == null) this.p1.e = this;
528 private boolean added = false;
530 public T makeT() { return t==null ? (t = new T(this)) : t; }
532 /** angle between this half-edge and the next */
533 public double angle() {
534 Vec v1 = next.p2.p.minus(p2.p);
535 Vec v2 = this.p1.p.minus(p2.p);
536 return Math.acos(v1.norm().dot(v2.norm()));
539 public void makeAdjacent(E e) {
540 if (this.next == e) return;
541 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
542 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
544 E freeIncident = p2.getFreeIncident(e, this);
546 e.prev.next = freeIncident.next;
547 freeIncident.next.prev = e.prev;
549 freeIncident.next = this.next;
550 this.next.prev = freeIncident;
559 /** creates an isolated edge out in the middle of space */
560 public E(Vert p1, Vert p2) {
561 if (p1==p2) throw new Error("attempt to create edge with single vertex: " + p1);
564 this.prev = this.next = this.pair = new E(this, this, this);
568 /** adds a new half-edge from prev.p2 to p2 */
569 public E(E prev, Vert p2) {
573 if (p2.getE(p1) != null) throw new Error();
575 this.next = this.pair = new E(this, this, prev.next);
577 E q = p2.getFreeIncident();
579 this.next.prev = this;
581 this.prev.next = this;
582 this.pair = new E(q, this, z);
587 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
588 public E(E prev, E pair, E next) {
596 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); }
597 public boolean has(Vert v) { return v==p1 || v==p2; }
598 public float length() { return p1.p.minus(p2.p).mag(); }
599 public String toString() { return p1+"->"+p2; }
602 public T newT(Vert p1, Vert p2, Vert p3, Vec norm) {
604 Vec norm2 = p3.p.minus(p1.p).cross(p2.p.minus(p1.p));
605 float dot = norm.dot(norm2);
606 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
607 if (dot < 0) { Vert p = p1; p1=p2; p2 = p; }
609 E e12 = p1.makeE(p2);
610 E e23 = p2.makeE(p3);
611 E e31 = p3.makeE(p1);
612 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
613 e12.makeAdjacent(e23);
614 e23.makeAdjacent(e31);
615 e31.makeAdjacent(e12);
618 if (e12.t == null) throw new Error();
619 if (e23.t == null) throw new Error();
620 if (e31.t == null) throw new Error();
625 public class FaceIterator implements Iterator<T> {
626 private HashSet<T> visited = new HashSet<T>();
627 private LinkedList<T> next = new LinkedList<T>();
628 public FaceIterator() { }
629 public FaceIterator(Vert v) { next.addFirst(v.e.t); }
630 public boolean hasNext() { return next.peek()!=null; }
631 public void remove() { throw new Error(); }
633 T ret = next.removeFirst();
634 if (ret == null) return null;
636 T t1 = ret.e1().pair.t;
637 T t2 = ret.e2().pair.t;
638 T t3 = ret.e3().pair.t;
639 if (t1 != null && !visited.contains(t1)) next.addFirst(t1);
640 if (t2 != null && !visited.contains(t2)) next.addFirst(t2);
641 if (t3 != null && !visited.contains(t3)) next.addFirst(t3);
646 /** [UNIQUE] a triangle (face) */
647 public final class T extends Triangle {
649 public final int color;
651 public void destroy() {
658 if (e1==e2 || e1==e3) throw new Error();
659 if (e3.next!=e1) throw new Error();
660 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
663 e1.next.next.t = this;
665 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
667 int color = Math.abs(random.nextInt());
670 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
671 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
672 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
681 public E e1() { return e1; }
682 public E e2() { return e1.next; }
683 public E e3() { return e1.prev; }
684 public Vert v1() { return e1.p1; }
685 public Vert v2() { return e1.p2; }
686 public Vert v3() { return e1.next.p2; }
687 public Point p1() { return e1.p1.p; }
688 public Point p2() { return e1.p2.p; }
689 public Point p3() { return e1.next.p2.p; }
690 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
691 public boolean has(Vert v) { return v1()==v || v2()==v || v3()==v; }