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;
78 p.recomputeFundamentalQuadric();
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 float volume() {
93 double area = t.area();
94 Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
95 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
96 double height = Math.abs(t.norm().dot(origin_to_centroid));
97 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
102 public class BindingGroup {
103 public HashSet<E> es = new HashSet<E>();
104 public BindingGroup() { }
105 public BindingGroup(E e) {
108 public void add(E e) {
109 if (e.bg != null) { merge(e.bg); return; }
113 public void merge(BindingGroup bg) {
121 public Vec diagonal() { return pointset.diagonal(); }
122 public Point centroid() { return pointset.centroid(); }
123 public Vert nearest(Point p) { return pointset.nearest(p); }
125 public final class Vert extends HasPoint {
127 E e; // some edge *leaving* this point
129 Vert bound_to = this;
131 /** the nearest vertex in the "score_against" mesh */
132 Vert nearest_in_other_mesh;
133 /** the number of vertices in the other mesh for which this is the nearest_in_other_mesh */
135 /** the total error quadric (contributions from all vertices in other mesh for which this is nearest) */
136 Matrix quadric = Matrix.ZERO;
138 Matrix binding = new Matrix();
140 boolean inserted = false;
142 public Matrix errorQuadric() { return quadric; }
144 private Matrix fundamentalQuadric = null;
145 public Matrix fundamentalQuadric() {
146 if (fundamentalQuadric == null) recomputeFundamentalQuadric();
147 return fundamentalQuadric;
150 public Point getPoint() { return p; }
151 private Vert(Point p) {
153 if (pointset.get(p) != null) throw new Error();
156 public float score() { return oldscore; }
158 public void recomputeFundamentalQuadric() {
160 Matrix m = Matrix.ZERO;
164 m = m.plus(t.norm().fundamentalQuadric(t.centroid()));
166 } while(e != this.e);
167 fundamentalQuadric = m;
171 public void unscore() {
172 if (nearest_in_other_mesh == null) return;
173 if (fundamentalQuadric == null) return;
174 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.minus(fundamentalQuadric);
175 nearest_in_other_mesh.quadric_count--;
176 if (nearest_in_other_mesh.quadric_count==0)
177 nearest_in_other_mesh.quadric = Matrix.ZERO;
178 nearest_in_other_mesh = null;
181 public void rescore() {
182 if (score_against == null) return;
187 if (nearest_in_other_mesh != null) unscore();
188 if (nearest_in_other_mesh == null) {
189 nearest_in_other_mesh = score_against.nearest(p);
191 // don't attract to vertices that face the other way
192 if (nearest_in_other_mesh.e == null || nearest_in_other_mesh.norm().dot(norm()) < 0) {
193 nearest_in_other_mesh = null;
195 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.plus(fundamentalQuadric());
196 nearest_in_other_mesh.quadric_count++;
202 if (quadric_count==0) s1 = 0;
203 else s1 = p.distance(quadric_x/quadric_count, quadric_y/quadric_count, quadric_z/quadric_count);
204 s2 = quadric==null ? 0 : po.p.distance(quadric.p);
205 oldscore = (float)(s1 + s2);
207 oldscore = quadric.preAndPostMultiply(p);
212 /** does NOT update bound pairs! */
213 public boolean transform(Matrix m) {
216 if (pointset.get(this.p)==null) throw new Error();
217 pointset.remove(this);
218 float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
219 float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
220 float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
221 this.p = new Point(newx, newy, newz);
223 } catch (Exception e) {
224 throw new RuntimeException(e);
226 fundamentalQuadric = fundamentalQuadric();
229 // recompute fundamental quadrics of all vertices sharing a face
233 e.p2.recomputeFundamentalQuadric();
235 } while(e != this.e);
241 for(E e = this.e; ;) {
242 if (e.intersects(t)) { good = false; break; }
244 if (e == this.e) break;
249 if (t==this.t) continue;
250 if (this.intersects(t)) good = false;
255 public boolean move(Vec v) {
256 Matrix m = new Matrix(v);
260 good &= p.transform(m);
261 v = v.times(binding); // bleh wrong
267 public E getFreeIncident() {
268 E ret = getFreeIncident(e, e);
269 if (ret != null) return ret;
270 ret = getFreeIncident(e.pair.next, e.pair.next);
271 if (ret == null) throw new Error("unable to find free incident to " + this);
275 public E getFreeIncident(E start, E before) {
278 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null) return e.pair;
280 } while(e != before);
284 public E getE(Point p2) {
285 Vert v = pointset.get(p2);
286 if (v==null) return null;
289 public E getE(Vert p2) {
292 if (e==null) return null;
293 if (e.p1 == this && e.p2 == p2) return e;
299 public boolean isBoundTo(Vert p) {
302 if (px==this) return true;
308 public void unbind() { bound_to = this; binding = new Matrix(); }
309 public void bind(Vert p) { bind(p, new Matrix()); }
310 public void bind(Vert p, Matrix binding) {
311 if (isBoundTo(p)) return;
312 Vert temp_bound_to = p.bound_to;
313 Matrix temp_binding = p.binding;
314 p.bound_to = this.bound_to;
315 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
316 this.bound_to = temp_bound_to;
317 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
320 Vec norm = new Vec(0, 0, 0);
323 if (e.t != null) norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
325 } while(e != this.e);
330 /** [UNIQUE] an edge */
331 public final class E implements Comparable<E> {
333 public final Vert p1, p2;
334 T t; // triangle to our "left"
335 E prev; // previous half-edge
336 E next; // next half-edge
337 E pair; // partner half-edge
338 public BindingGroup bg = new BindingGroup(this);
339 boolean shattered = false;
341 public int compareTo(E e) { return e.length() > length() ? 1 : -1; }
343 public void bind(E e) { bind(e, new Matrix()); }
344 public void bind(E e, Matrix m) { e.bg.add(this); }
346 public void dobind() {
347 if (bg==null) return;
349 if (ex==this) continue;
355 public Point shatter() { return shatter(midpoint(), null, null); }
356 public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
357 if (shattered) return mid;
364 if (bg1==null) bg1 = new BindingGroup();
365 if (bg2==null) bg2 = new BindingGroup();
366 for(E e : bg.es) e.shatter(e.midpoint(), bg1, bg2);
370 newT(r.p, p1.p, mid, null);
371 newT(r.p, mid, p2.p, null);
372 bg1.add(p1.getE(mid));
373 bg2.add(p2.getE(mid).pair);
377 public boolean destroyed = false;
378 public void destroy() {
379 if (destroyed) return;
381 pair.destroyed = true;
382 if (next.t != null) next.t.destroy();
383 if (prev.t != null) prev.t.destroy();
390 pair.prev.next = next;
391 next.prev = pair.prev;
392 prev.next = pair.next;
394 if (p1.e == this) p1.e = prev.next;
395 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
396 avgedge -= this.length();
397 avgedge -= pair.length();
402 private void sync() {
403 this.prev.next = this;
404 this.next.prev = this;
405 this.pair.pair = this;
406 if (this.next.p1 != p2) throw new Error();
407 if (this.prev.p2 != p1) throw new Error();
408 if (this.p1.e == null) this.p1.e = this;
415 private boolean added = false;
417 public T makeT() { return t==null ? (t = new T(this)) : t; }
419 /** angle between this half-edge and the next */
420 public double angle() {
421 Vec v1 = next.p2.p.minus(p2.p);
422 Vec v2 = this.p1.p.minus(p2.p);
423 return Math.acos(v1.norm().dot(v2.norm()));
426 public void makeAdjacent(E e) {
427 if (this.next == e) return;
428 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
429 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
431 E freeIncident = p2.getFreeIncident(e, this);
433 e.prev.next = freeIncident.next;
434 freeIncident.next.prev = e.prev;
436 freeIncident.next = this.next;
437 this.next.prev = freeIncident;
446 /** creates an isolated edge out in the middle of space */
447 public E(Point p1, Point p2) {
448 if (pointset.get(p1) != null) throw new Error();
449 if (pointset.get(p2) != null) throw new Error();
450 this.p1 = new Vert(p1);
451 this.p2 = new Vert(p2);
452 this.prev = this.next = this.pair = new E(this, this, this);
454 this.p2.e = this.pair;
458 /** adds a new half-edge from prev.p2 to p2 */
459 public E(E prev, Point p) {
461 p2 = pointset.get(p);
462 if (p2 == null) p2 = new Vert(p);
466 if (p2.getE(p1) != null) throw new Error();
468 this.next = this.pair = new E(this, this, prev.next);
470 E q = p2.getFreeIncident();
472 this.next.prev = this;
474 this.prev.next = this;
475 this.pair = new E(q, this, z);
477 if (p2.e==null) p2.e = this.pair;
481 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
482 public E(E prev, E pair, E next) {
490 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); }
491 public boolean has(Vert v) { return v==p1 || v==p2; }
492 public float length() { return p1.p.minus(p2.p).mag(); }
493 public String toString() { return p1+"->"+p2; }
495 public boolean intersects(T t) {
496 double A0=t.v1().p.x, A1=t.v1().p.y, A2=t.v1().p.z;
497 double B0=t.v2().p.x, B1=t.v2().p.y, B2=t.v2().p.z;
498 double C0=t.v3().p.x, C1=t.v3().p.y, C2=t.v3().p.z;
499 double j0=p1.p.x, j1=p1.p.y, j2=p1.p.z;
500 double k0=p2.p.x, k1=p2.p.y, k2=p2.p.z;
508 double R00, R01, R02, R03,
522 /* c = a × b */
523 c0 = a1 * b2 - a2 * b1;
524 c1 = a2 * b0 - a0 * b2;
525 c2 = a0 * b1 - a1 * b0;
527 /* M^(-1) = (1/det(M)) * adj(M) */
528 in_det = 1 / (c0 * c0 + c1 * c1 + c2 * c2);
529 R00 = (b1 * c2 - b2 * c1) * in_det;
530 R01 = (b2 * c0 - b0 * c2) * in_det;
531 R02 = (b0 * c1 - b1 * c0) * in_det;
532 R10 = (c1 * a2 - c2 * a1) * in_det;
533 R11 = (c2 * a0 - c0 * a2) * in_det;
534 R12 = (c0 * a1 - c1 * a0) * in_det;
540 R03 = -(R00 * A0 + R01 * A1 + R02 * A2);
541 R13 = -(R10 * A0 + R11 * A1 + R12 * A2);
542 R23 = -(R20 * A0 + R21 * A1 + R22 * A2);
544 /* fill in last row of 4x4 matrix */
548 J2 = R20 * j0 + R21 * j1 + R22 * j2 + R23;
549 K2 = R20 * k0 + R21 * k1 + R22 * k2 + R23;
550 if (J2 * K2 >= 0) return false;
552 J0 = R00 * j0 + R01 * j1 + R02 * j2 + R03;
553 K0 = R00 * k0 + R01 * k1 + R02 * k2 + R03;
554 i0 = J0 + J2 * ((K0 - J0) / (J2 - K2));
555 if (i0 < 0 || i0 > 1) return false;
557 J1 = R10 * j0 + R11 * j1 + R12 * j2 + R13;
558 K1 = R10 * k0 + R11 * k1 + R12 * k2 + R13;
559 i1 = J1 + J2 * ((K1 - J1) / (J2 - K2));
560 if (i1 < 0 || i1 > 1 || i0 + i1 > 1) return false;
566 public E makeE(Point p1, Point p2) {
567 Vert v1 = pointset.get(p1);
568 Vert v2 = pointset.get(p2);
569 if (v1 != null && v2 != null) {
571 if (e != null) return e;
573 if (e != null) return e;
575 if (v1 != null) return new E(v1.getFreeIncident(), p2);
576 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
577 return new E(p1, p2);
579 public T newT(Point p1, Point p2, Point p3, Vec norm) {
581 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
582 float dot = norm.dot(norm2);
583 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
584 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
586 E e12 = makeE(p1, p2);
587 E e23 = makeE(p2, p3);
588 E e31 = makeE(p3, p1);
589 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
590 e12.makeAdjacent(e23);
591 e23.makeAdjacent(e31);
592 e31.makeAdjacent(e12);
595 if (e12.t == null) throw new Error();
596 if (e23.t == null) throw new Error();
597 if (e31.t == null) throw new Error();
602 public class FaceIterator implements Iterator<T> {
603 private HashSet<T> visited = new HashSet<T>();
604 private LinkedList<T> next = new LinkedList<T>();
605 public FaceIterator() { }
606 public FaceIterator(Vert v) { next.addFirst(v.e.t); }
607 public boolean hasNext() { return next.peek()!=null; }
608 public void remove() { throw new Error(); }
610 T ret = next.removeFirst();
611 if (ret == null) return null;
613 T t1 = ret.e1().pair.t;
614 T t2 = ret.e2().pair.t;
615 T t3 = ret.e3().pair.t;
616 if (t1 != null && !visited.contains(t1)) next.addFirst(t1);
617 if (t2 != null && !visited.contains(t2)) next.addFirst(t2);
618 if (t3 != null && !visited.contains(t3)) next.addFirst(t3);
623 /** [UNIQUE] a triangle (face) */
624 public final class T extends Triangle {
626 public final int color;
628 public void destroy() {
635 if (e1==e2 || e1==e3) throw new Error();
636 if (e3.next!=e1) throw new Error();
637 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
640 e1.next.next.t = this;
642 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
644 int color = Math.abs(random.nextInt());
647 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
648 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
649 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
654 public E e1() { return e1; }
655 public E e2() { return e1.next; }
656 public E e3() { return e1.prev; }
657 public Vert v1() { return e1.p1; }
658 public Vert v2() { return e1.p2; }
659 public Vert v3() { return e1.next.p2; }
660 public Point p1() { return e1.p1.p; }
661 public Point p2() { return e1.p2.p; }
662 public Point p3() { return e1.next.p2.p; }
663 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
664 public boolean has(Vert v) { return v1()==v || v2()==v || v3()==v; }