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 void unscore() {
70 HashSet<Vert> done = new HashSet<Vert>();
72 for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() }) {
73 if (done.contains(p)) continue;
78 public void fundamental() {
79 HashSet<Vert> done = new HashSet<Vert>();
81 for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() }) {
82 if (done.contains(p)) continue;
84 p.recomputeFundamentalQuadric();
87 public float rescore() {
90 HashSet<Vert> done = new HashSet<Vert>();
92 for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() }) {
93 if (done.contains(p)) continue;
98 return (float)(dist/num);
101 public void transform(Matrix m) {
102 ArrayList<Vert> set = new ArrayList<Vert>();
103 for (Vert v : pointset)
105 for(Vert v : set) v.transform(m);
108 public float volume() {
111 double area = t.area();
112 Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
113 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
114 double height = Math.abs(t.norm().dot(origin_to_centroid));
115 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
120 public class BindingGroup {
121 public HashSet<E> es = new HashSet<E>();
122 public BindingGroup() { }
123 public BindingGroup(E e) {
126 public void add(E e) {
127 if (e.bg != null) { merge(e.bg); return; }
131 public void merge(BindingGroup bg) {
139 public Vec diagonal() { return pointset.diagonal(); }
140 public Point centroid() { return pointset.centroid(); }
141 public Vert nearest(Point p) { return pointset.nearest(p); }
143 public final class Vert extends HasPoint {
145 E e; // some edge *leaving* this point
147 Vert bound_to = this;
149 /** the nearest vertex in the "score_against" mesh */
150 Vert nearest_in_other_mesh;
151 /** the number of vertices in the other mesh for which this is the nearest_in_other_mesh */
153 /** the total error quadric (contributions from all vertices in other mesh for which this is nearest) */
154 Matrix quadric = Matrix.ZERO;
156 Matrix binding = new Matrix();
158 boolean inserted = false;
160 public Matrix errorQuadric() { return quadric; }
162 private Matrix fundamentalQuadric = null;
163 public Matrix fundamentalQuadric() {
164 if (fundamentalQuadric == null) recomputeFundamentalQuadric();
165 return fundamentalQuadric;
168 public Point getPoint() { return p; }
169 private Vert(Point p) {
171 if (pointset.get(p) != null) throw new Error();
174 public float score() { return oldscore; }
176 public void recomputeFundamentalQuadric() {
178 Matrix m = Matrix.ZERO;
182 m = m.plus(t.norm().fundamentalQuadric(t.centroid()));
184 } while(e != this.e);
185 fundamentalQuadric = m;
189 public void unscore() {
190 if (nearest_in_other_mesh == null) return;
191 if (fundamentalQuadric == null) return;
192 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.minus(fundamentalQuadric);
193 nearest_in_other_mesh.quadric_count--;
194 if (nearest_in_other_mesh.quadric_count==0)
195 nearest_in_other_mesh.quadric = Matrix.ZERO;
196 nearest_in_other_mesh = null;
199 public void rescore() {
200 if (score_against == null) return;
205 if (nearest_in_other_mesh != null) unscore();
206 if (nearest_in_other_mesh == null) {
207 nearest_in_other_mesh = score_against.nearest(p);
209 // don't attract to vertices that face the other way
210 if (nearest_in_other_mesh.e == null || nearest_in_other_mesh.norm().dot(norm()) < 0) {
211 nearest_in_other_mesh = null;
213 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.plus(fundamentalQuadric());
214 nearest_in_other_mesh.quadric_count++;
220 if (quadric_count==0) s1 = 0;
221 else s1 = p.distance(quadric_x/quadric_count, quadric_y/quadric_count, quadric_z/quadric_count);
222 s2 = quadric==null ? 0 : po.p.distance(quadric.p);
223 oldscore = (float)(s1 + s2);
225 oldscore = quadric_count == 0 ? 0 : (quadric.preAndPostMultiply(p) / quadric_count);
230 /** does NOT update bound pairs! */
231 public boolean transform(Matrix m) {
234 if (pointset.get(this.p)==null) throw new Error();
235 pointset.remove(this);
236 float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
237 float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
238 float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
239 this.p = new Point(newx, newy, newz);
241 } catch (Exception e) {
242 throw new RuntimeException(e);
244 fundamentalQuadric = fundamentalQuadric();
247 // recompute fundamental quadrics of all vertices sharing a face
251 e.p2.recomputeFundamentalQuadric();
253 } while(e != this.e);
259 for(E e = this.e; ;) {
260 if (e.intersects(t)) { good = false; break; }
262 if (e == this.e) break;
267 if (t==this.t) continue;
268 if (this.intersects(t)) good = false;
273 public boolean move(Vec v) {
274 Matrix m = new Matrix(v);
278 good &= p.transform(m);
279 v = v.times(binding); // bleh wrong
285 public E getFreeIncident() {
286 E ret = getFreeIncident(e, e);
287 if (ret != null) return ret;
288 ret = getFreeIncident(e.pair.next, e.pair.next);
289 if (ret == null) throw new Error("unable to find free incident to " + this);
293 public E getFreeIncident(E start, E before) {
296 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null) return e.pair;
298 } while(e != before);
302 public E getE(Point p2) {
303 Vert v = pointset.get(p2);
304 if (v==null) return null;
307 public E getE(Vert p2) {
310 if (e==null) return null;
311 if (e.p1 == this && e.p2 == p2) return e;
317 public boolean isBoundTo(Vert p) {
320 if (px==this) return true;
326 public void unbind() { bound_to = this; binding = new Matrix(); }
327 public void bind(Vert p) { bind(p, new Matrix()); }
328 public void bind(Vert p, Matrix binding) {
329 if (isBoundTo(p)) return;
330 Vert temp_bound_to = p.bound_to;
331 Matrix temp_binding = p.binding;
332 p.bound_to = this.bound_to;
333 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
334 this.bound_to = temp_bound_to;
335 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
338 Vec norm = new Vec(0, 0, 0);
341 if (e.t != null) norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
343 } while(e != this.e);
348 /** [UNIQUE] an edge */
349 public final class E implements Comparable<E> {
351 public final Vert p1, p2;
352 T t; // triangle to our "left"
353 E prev; // previous half-edge
354 E next; // next half-edge
355 E pair; // partner half-edge
356 public BindingGroup bg = new BindingGroup(this);
357 boolean shattered = false;
359 public int compareTo(E e) { return e.length() > length() ? 1 : -1; }
361 public void bind(E e) { bind(e, new Matrix()); }
362 public void bind(E e, Matrix m) { e.bg.add(this); }
364 public void dobind() {
365 if (bg==null) return;
367 if (ex==this) continue;
373 public Point shatter() { return shatter(midpoint(), null, null); }
374 public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
375 if (shattered) return mid;
382 if (bg1==null) bg1 = new BindingGroup();
383 if (bg2==null) bg2 = new BindingGroup();
384 for(E e : bg.es) e.shatter(e.midpoint(), bg1, bg2);
388 newT(r.p, p1.p, mid, null);
389 newT(r.p, mid, p2.p, null);
390 bg1.add(p1.getE(mid));
391 bg2.add(p2.getE(mid).pair);
395 public boolean destroyed = false;
396 public void destroy() {
397 if (destroyed) return;
399 pair.destroyed = true;
400 if (next.t != null) next.t.destroy();
401 if (prev.t != null) prev.t.destroy();
408 pair.prev.next = next;
409 next.prev = pair.prev;
410 prev.next = pair.next;
412 if (p1.e == this) p1.e = prev.next;
413 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
414 avgedge -= this.length();
415 avgedge -= pair.length();
420 private void sync() {
421 this.prev.next = this;
422 this.next.prev = this;
423 this.pair.pair = this;
424 if (this.next.p1 != p2) throw new Error();
425 if (this.prev.p2 != p1) throw new Error();
426 if (this.p1.e == null) this.p1.e = this;
433 private boolean added = false;
435 public T makeT() { return t==null ? (t = new T(this)) : t; }
437 /** angle between this half-edge and the next */
438 public double angle() {
439 Vec v1 = next.p2.p.minus(p2.p);
440 Vec v2 = this.p1.p.minus(p2.p);
441 return Math.acos(v1.norm().dot(v2.norm()));
444 public void makeAdjacent(E e) {
445 if (this.next == e) return;
446 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
447 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
449 E freeIncident = p2.getFreeIncident(e, this);
451 e.prev.next = freeIncident.next;
452 freeIncident.next.prev = e.prev;
454 freeIncident.next = this.next;
455 this.next.prev = freeIncident;
464 /** creates an isolated edge out in the middle of space */
465 public E(Point p1, Point p2) {
466 if (pointset.get(p1) != null) throw new Error();
467 if (pointset.get(p2) != null) throw new Error();
468 this.p1 = new Vert(p1);
469 this.p2 = new Vert(p2);
470 this.prev = this.next = this.pair = new E(this, this, this);
472 this.p2.e = this.pair;
476 /** adds a new half-edge from prev.p2 to p2 */
477 public E(E prev, Point p) {
479 p2 = pointset.get(p);
480 if (p2 == null) p2 = new Vert(p);
484 if (p2.getE(p1) != null) throw new Error();
486 this.next = this.pair = new E(this, this, prev.next);
488 E q = p2.getFreeIncident();
490 this.next.prev = this;
492 this.prev.next = this;
493 this.pair = new E(q, this, z);
495 if (p2.e==null) p2.e = this.pair;
499 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
500 public E(E prev, E pair, E next) {
508 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); }
509 public boolean has(Vert v) { return v==p1 || v==p2; }
510 public float length() { return p1.p.minus(p2.p).mag(); }
511 public String toString() { return p1+"->"+p2; }
513 public boolean intersects(T t) {
514 double A0=t.v1().p.x, A1=t.v1().p.y, A2=t.v1().p.z;
515 double B0=t.v2().p.x, B1=t.v2().p.y, B2=t.v2().p.z;
516 double C0=t.v3().p.x, C1=t.v3().p.y, C2=t.v3().p.z;
517 double j0=p1.p.x, j1=p1.p.y, j2=p1.p.z;
518 double k0=p2.p.x, k1=p2.p.y, k2=p2.p.z;
526 double R00, R01, R02, R03,
540 /* c = a × b */
541 c0 = a1 * b2 - a2 * b1;
542 c1 = a2 * b0 - a0 * b2;
543 c2 = a0 * b1 - a1 * b0;
545 /* M^(-1) = (1/det(M)) * adj(M) */
546 in_det = 1 / (c0 * c0 + c1 * c1 + c2 * c2);
547 R00 = (b1 * c2 - b2 * c1) * in_det;
548 R01 = (b2 * c0 - b0 * c2) * in_det;
549 R02 = (b0 * c1 - b1 * c0) * in_det;
550 R10 = (c1 * a2 - c2 * a1) * in_det;
551 R11 = (c2 * a0 - c0 * a2) * in_det;
552 R12 = (c0 * a1 - c1 * a0) * in_det;
558 R03 = -(R00 * A0 + R01 * A1 + R02 * A2);
559 R13 = -(R10 * A0 + R11 * A1 + R12 * A2);
560 R23 = -(R20 * A0 + R21 * A1 + R22 * A2);
562 /* fill in last row of 4x4 matrix */
566 J2 = R20 * j0 + R21 * j1 + R22 * j2 + R23;
567 K2 = R20 * k0 + R21 * k1 + R22 * k2 + R23;
568 if (J2 * K2 >= 0) return false;
570 J0 = R00 * j0 + R01 * j1 + R02 * j2 + R03;
571 K0 = R00 * k0 + R01 * k1 + R02 * k2 + R03;
572 i0 = J0 + J2 * ((K0 - J0) / (J2 - K2));
573 if (i0 < 0 || i0 > 1) return false;
575 J1 = R10 * j0 + R11 * j1 + R12 * j2 + R13;
576 K1 = R10 * k0 + R11 * k1 + R12 * k2 + R13;
577 i1 = J1 + J2 * ((K1 - J1) / (J2 - K2));
578 if (i1 < 0 || i1 > 1 || i0 + i1 > 1) return false;
584 public E makeE(Point p1, Point p2) {
585 Vert v1 = pointset.get(p1);
586 Vert v2 = pointset.get(p2);
587 if (v1 != null && v2 != null) {
589 if (e != null) return e;
591 if (e != null) return e;
593 if (v1 != null) return new E(v1.getFreeIncident(), p2);
594 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
595 return new E(p1, p2);
597 public T newT(Point p1, Point p2, Point p3, Vec norm) {
599 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
600 float dot = norm.dot(norm2);
601 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
602 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
604 E e12 = makeE(p1, p2);
605 E e23 = makeE(p2, p3);
606 E e31 = makeE(p3, 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; }
672 public E e1() { return e1; }
673 public E e2() { return e1.next; }
674 public E e3() { return e1.prev; }
675 public Vert v1() { return e1.p1; }
676 public Vert v2() { return e1.p2; }
677 public Vert v3() { return e1.next.p2; }
678 public Point p1() { return e1.p1.p; }
679 public Point p2() { return e1.p2.p; }
680 public Point p3() { return e1.next.p2.p; }
681 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
682 public boolean has(Vert v) { return v1()==v || v2()==v || v3()==v; }