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 final float EPSILON = (float)0.0001;
15 public static final 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;
101 public class BindingGroup {
102 public HashSet<E> es = new HashSet<E>();
103 public BindingGroup() { }
104 public BindingGroup(E e) {
107 public void add(E e) {
108 if (e.bg != null) { merge(e.bg); return; }
112 public void merge(BindingGroup bg) {
120 public Vec diagonal() { return pointset.diagonal(); }
121 public Point centroid() { return pointset.centroid(); }
122 public Vert nearest(Point p) { return pointset.nearest(p); }
124 public final class Vert extends HasPoint {
126 E e; // some edge *leaving* this point
128 Vert bound_to = this;
130 /** the nearest vertex in the "score_against" mesh */
131 Vert nearest_in_other_mesh;
132 /** the number of vertices in the other mesh for which this is the nearest_in_other_mesh */
134 /** the total error quadric (contributions from all vertices in other mesh for which this is nearest) */
135 Matrix quadric = Matrix.ZERO;
137 Matrix binding = new Matrix();
139 boolean inserted = false;
141 public Matrix errorQuadric() { return quadric; }
143 private Matrix fundamentalQuadric = null;
144 public Matrix fundamentalQuadric() {
145 if (fundamentalQuadric == null) recomputeFundamentalQuadric();
146 return fundamentalQuadric;
149 public Point getPoint() { return p; }
150 private Vert(Point p) {
152 if (pointset.get(p) != null) throw new Error();
155 public float score() { return oldscore; }
157 public void recomputeFundamentalQuadric() {
159 Matrix m = Matrix.ZERO;
163 m = m.plus(t.norm().fundamentalQuadric(t.centroid()));
165 } while(e != this.e);
166 fundamentalQuadric = m;
170 public void unscore() {
171 if (nearest_in_other_mesh == null) return;
172 if (fundamentalQuadric == null) return;
173 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.minus(fundamentalQuadric);
174 nearest_in_other_mesh.quadric_count--;
175 if (nearest_in_other_mesh.quadric_count==0)
176 nearest_in_other_mesh.quadric = Matrix.ZERO;
177 nearest_in_other_mesh = null;
180 public void rescore() {
181 if (score_against == null) return;
186 if (nearest_in_other_mesh != null) unscore();
187 if (nearest_in_other_mesh == null) {
188 nearest_in_other_mesh = score_against.nearest(p);
190 // don't attract to vertices that face the other way
191 if (nearest_in_other_mesh.e == null || nearest_in_other_mesh.norm().dot(norm()) < 0) {
192 nearest_in_other_mesh = null;
194 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.plus(fundamentalQuadric());
195 nearest_in_other_mesh.quadric_count++;
201 if (quadric_count==0) s1 = 0;
202 else s1 = p.distance(quadric_x/quadric_count, quadric_y/quadric_count, quadric_z/quadric_count);
203 s2 = quadric==null ? 0 : po.p.distance(quadric.p);
204 oldscore = (float)(s1 + s2);
206 oldscore = quadric.preAndPostMultiply(p);
211 /** does NOT update bound pairs! */
212 public boolean transform(Matrix m) {
215 if (pointset.get(this.p)==null) throw new Error();
216 pointset.remove(this);
217 float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
218 float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
219 float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
220 this.p = new Point(newx, newy, newz);
222 } catch (Exception e) {
223 throw new RuntimeException(e);
225 fundamentalQuadric = fundamentalQuadric();
228 // recompute fundamental quadrics of all vertices sharing a face
231 e.t.v1().recomputeFundamentalQuadric();
232 e.t.v2().recomputeFundamentalQuadric();
233 e.t.v3().recomputeFundamentalQuadric();
235 } while(e != this.e);
240 for(E e = this.e; ;) {
241 if (e.intersects(t)) { good = false; break; }
243 if (e == this.e) break;
248 if (t==this.t) continue;
249 if (this.intersects(t)) good = false;
254 public boolean move(Vec v) {
255 Matrix m = new Matrix(v);
259 good &= p.transform(m);
260 v = v.times(binding); // bleh wrong
266 public E getFreeIncident() {
267 E ret = getFreeIncident(e, e);
268 if (ret != null) return ret;
269 ret = getFreeIncident(e.pair.next, e.pair.next);
270 if (ret == null) throw new Error("unable to find free incident to " + this);
274 public E getFreeIncident(E start, E before) {
277 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null) return e.pair;
279 } while(e != before);
283 public E getE(Point p2) {
284 Vert v = pointset.get(p2);
285 if (v==null) return null;
288 public E getE(Vert p2) {
291 if (e==null) return null;
292 if (e.p1 == this && e.p2 == p2) return e;
298 public boolean isBoundTo(Vert p) {
301 if (px==this) return true;
307 public void unbind() { bound_to = this; binding = new Matrix(); }
308 public void bind(Vert p) { bind(p, new Matrix()); }
309 public void bind(Vert p, Matrix binding) {
310 if (isBoundTo(p)) return;
311 Vert temp_bound_to = p.bound_to;
312 Matrix temp_binding = p.binding;
313 p.bound_to = this.bound_to;
314 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
315 this.bound_to = temp_bound_to;
316 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
319 Vec norm = new Vec(0, 0, 0);
322 if (e.t != null) norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
324 } while(e != this.e);
329 /** [UNIQUE] an edge */
330 public final class E implements Comparable<E> {
332 public final Vert p1, p2;
333 T t; // triangle to our "left"
334 E prev; // previous half-edge
335 E next; // next half-edge
336 E pair; // partner half-edge
337 public BindingGroup bg = new BindingGroup(this);
338 boolean shattered = false;
340 public int compareTo(E e) { return e.length() > length() ? 1 : -1; }
342 public void bind(E e) { bind(e, new Matrix()); }
343 public void bind(E e, Matrix m) { e.bg.add(this); }
345 public void dobind() {
346 if (bg==null) return;
348 if (ex==this) continue;
354 public Point shatter() { return shatter(midpoint(), null, null); }
355 public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
356 if (shattered) return mid;
363 if (bg1==null) bg1 = new BindingGroup();
364 if (bg2==null) bg2 = new BindingGroup();
365 for(E e : bg.es) e.shatter(e.midpoint(), bg1, bg2);
369 newT(r.p, p1.p, mid, null);
370 newT(r.p, mid, p2.p, null);
371 bg1.add(p1.getE(mid));
372 bg2.add(p2.getE(mid).pair);
376 public boolean destroyed = false;
377 public void destroy() {
378 if (destroyed) return;
380 pair.destroyed = true;
381 if (next.t != null) next.t.destroy();
382 if (prev.t != null) prev.t.destroy();
389 pair.prev.next = next;
390 next.prev = pair.prev;
391 prev.next = pair.next;
393 if (p1.e == this) p1.e = prev.next;
394 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
395 avgedge -= this.length();
396 avgedge -= pair.length();
401 private void sync() {
402 this.prev.next = this;
403 this.next.prev = this;
404 this.pair.pair = this;
405 if (this.next.p1 != p2) throw new Error();
406 if (this.prev.p2 != p1) throw new Error();
407 if (this.p1.e == null) this.p1.e = this;
414 private boolean added = false;
416 public T makeT() { return t==null ? (t = new T(this)) : t; }
418 /** angle between this half-edge and the next */
419 public double angle() {
420 Vec v1 = next.p2.p.minus(p2.p);
421 Vec v2 = this.p1.p.minus(p2.p);
422 return Math.acos(v1.norm().dot(v2.norm()));
425 public void makeAdjacent(E e) {
426 if (this.next == e) return;
427 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
428 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
430 E freeIncident = p2.getFreeIncident(e, this);
432 e.prev.next = freeIncident.next;
433 freeIncident.next.prev = e.prev;
435 freeIncident.next = this.next;
436 this.next.prev = freeIncident;
445 /** creates an isolated edge out in the middle of space */
446 public E(Point p1, Point p2) {
447 if (pointset.get(p1) != null) throw new Error();
448 if (pointset.get(p2) != null) throw new Error();
449 this.p1 = new Vert(p1);
450 this.p2 = new Vert(p2);
451 this.prev = this.next = this.pair = new E(this, this, this);
453 this.p2.e = this.pair;
457 /** adds a new half-edge from prev.p2 to p2 */
458 public E(E prev, Point p) {
460 p2 = pointset.get(p);
461 if (p2 == null) p2 = new Vert(p);
465 if (p2.getE(p1) != null) throw new Error();
467 this.next = this.pair = new E(this, this, prev.next);
469 E q = p2.getFreeIncident();
471 this.next.prev = this;
473 this.prev.next = this;
474 this.pair = new E(q, this, z);
476 if (p2.e==null) p2.e = this.pair;
480 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
481 public E(E prev, E pair, E next) {
489 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); }
490 public boolean has(Vert v) { return v==p1 || v==p2; }
491 public float length() { return p1.p.minus(p2.p).mag(); }
492 public String toString() { return p1+"->"+p2; }
494 public boolean intersects(T t) {
495 double A0=t.v1().p.x, A1=t.v1().p.y, A2=t.v1().p.z;
496 double B0=t.v2().p.x, B1=t.v2().p.y, B2=t.v2().p.z;
497 double C0=t.v3().p.x, C1=t.v3().p.y, C2=t.v3().p.z;
498 double j0=p1.p.x, j1=p1.p.y, j2=p1.p.z;
499 double k0=p2.p.x, k1=p2.p.y, k2=p2.p.z;
507 double R00, R01, R02, R03,
521 /* c = a × b */
522 c0 = a1 * b2 - a2 * b1;
523 c1 = a2 * b0 - a0 * b2;
524 c2 = a0 * b1 - a1 * b0;
526 /* M^(-1) = (1/det(M)) * adj(M) */
527 in_det = 1 / (c0 * c0 + c1 * c1 + c2 * c2);
528 R00 = (b1 * c2 - b2 * c1) * in_det;
529 R01 = (b2 * c0 - b0 * c2) * in_det;
530 R02 = (b0 * c1 - b1 * c0) * in_det;
531 R10 = (c1 * a2 - c2 * a1) * in_det;
532 R11 = (c2 * a0 - c0 * a2) * in_det;
533 R12 = (c0 * a1 - c1 * a0) * in_det;
539 R03 = -(R00 * A0 + R01 * A1 + R02 * A2);
540 R13 = -(R10 * A0 + R11 * A1 + R12 * A2);
541 R23 = -(R20 * A0 + R21 * A1 + R22 * A2);
543 /* fill in last row of 4x4 matrix */
547 J2 = R20 * j0 + R21 * j1 + R22 * j2 + R23;
548 K2 = R20 * k0 + R21 * k1 + R22 * k2 + R23;
549 if (J2 * K2 >= 0) return false;
551 J0 = R00 * j0 + R01 * j1 + R02 * j2 + R03;
552 K0 = R00 * k0 + R01 * k1 + R02 * k2 + R03;
553 i0 = J0 + J2 * ((K0 - J0) / (J2 - K2));
554 if (i0 < 0 || i0 > 1) return false;
556 J1 = R10 * j0 + R11 * j1 + R12 * j2 + R13;
557 K1 = R10 * k0 + R11 * k1 + R12 * k2 + R13;
558 i1 = J1 + J2 * ((K1 - J1) / (J2 - K2));
559 if (i1 < 0 || i1 > 1 || i0 + i1 > 1) return false;
565 public E makeE(Point p1, Point p2) {
566 Vert v1 = pointset.get(p1);
567 Vert v2 = pointset.get(p2);
568 if (v1 != null && v2 != null) {
570 if (e != null) return e;
572 if (e != null) return e;
574 if (v1 != null) return new E(v1.getFreeIncident(), p2);
575 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
576 return new E(p1, p2);
578 public T newT(Point p1, Point p2, Point p3, Vec norm) {
580 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
581 float dot = norm.dot(norm2);
582 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
583 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
585 E e12 = makeE(p1, p2);
586 E e23 = makeE(p2, p3);
587 E e31 = makeE(p3, p1);
588 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
589 e12.makeAdjacent(e23);
590 e23.makeAdjacent(e31);
591 e31.makeAdjacent(e12);
594 if (e12.t == null) throw new Error();
595 if (e23.t == null) throw new Error();
596 if (e31.t == null) throw new Error();
601 public class FaceIterator implements Iterator<T> {
602 private HashSet<T> visited = new HashSet<T>();
603 private LinkedList<T> next = new LinkedList<T>();
604 public FaceIterator() { }
605 public FaceIterator(Vert v) { next.addFirst(v.e.t); }
606 public boolean hasNext() { return next.peek()!=null; }
607 public void remove() { throw new Error(); }
609 T ret = next.removeFirst();
610 if (ret == null) return null;
612 T t1 = ret.e1().pair.t;
613 T t2 = ret.e2().pair.t;
614 T t3 = ret.e3().pair.t;
615 if (t1 != null && !visited.contains(t1)) next.addFirst(t1);
616 if (t2 != null && !visited.contains(t2)) next.addFirst(t2);
617 if (t3 != null && !visited.contains(t3)) next.addFirst(t3);
622 /** [UNIQUE] a triangle (face) */
623 public final class T extends Triangle {
625 public final int color;
627 public void destroy() {
634 if (e1==e2 || e1==e3) throw new Error();
635 if (e3.next!=e1) throw new Error();
636 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
639 e1.next.next.t = this;
641 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
643 int color = Math.abs(random.nextInt());
646 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
647 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
648 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
653 public E e1() { return e1; }
654 public E e2() { return e1.next; }
655 public E e3() { return e1.prev; }
656 public Vert v1() { return e1.p1; }
657 public Vert v2() { return e1.p2; }
658 public Vert v3() { return e1.next.p2; }
659 public Point p1() { return e1.p1.p; }
660 public Point p2() { return e1.p2.p; }
661 public Point p3() { return e1.next.p2.p; }
662 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
663 public boolean has(Vert v) { return v1()==v || v2()==v || v3()==v; }