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 rebindPoints() {
55 for(Mesh.T t : this) {
60 // ask edges to re-implement their bindings
61 for(Mesh.T t : this) {
68 public void unApplyQuadricToNeighborAll() {
69 HashSet<Vert> done = new HashSet<Vert>();
71 for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() }) {
72 if (done.contains(p)) continue;
74 p.unApplyQuadricToNeighbor();
77 public void recomputeAllFundamentalQuadrics() {
78 HashSet<Vert> done = new HashSet<Vert>();
80 for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() }) {
81 if (done.contains(p)) continue;
83 p.recomputeFundamentalQuadric();
86 public float applyQuadricToNeighborAll() {
89 HashSet<Vert> done = new HashSet<Vert>();
91 for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() }) {
92 if (done.contains(p)) continue;
94 p.applyQuadricToNeighbor();
97 return (float)(dist/num);
100 public void transform(Matrix m) {
101 ArrayList<Vert> set = new ArrayList<Vert>();
102 for (Vert v : pointset)
104 for(Vert v : set) v.transform(m);
107 public float volume() {
110 double area = t.area();
111 Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
112 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
113 double height = Math.abs(t.norm().dot(origin_to_centroid));
114 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
119 public void rebuildPointSet() { pointset.rebuild(); }
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 /** the nearest vertex in the "score_against" mesh */
129 Vert nearest_in_other_mesh;
130 /** the number of vertices in the other mesh for which this is the nearest_in_other_mesh */
132 /** the total error quadric (contributions from all vertices in other mesh for which this is nearest) */
133 Matrix quadric = Matrix.ZERO;
135 Vert bound_to = this;
136 Matrix binding = new Matrix();
138 boolean quadricStale = false;
140 public Matrix errorQuadric() { return quadric; }
141 public Point getPoint() { return p; }
142 public float score() { return oldscore; }
144 private Matrix fundamentalQuadric = null;
145 public Matrix fundamentalQuadric() {
146 if (fundamentalQuadric == null) recomputeFundamentalQuadric();
147 return fundamentalQuadric;
150 private Vert(Point p) {
152 if (pointset.get(p) != null) throw new Error();
156 public void recomputeFundamentalQuadric() {
157 if (!quadricStale && fundamentalQuadric != null) return;
158 quadricStale = false;
159 unApplyQuadricToNeighbor();
160 Matrix m = Matrix.ZERO;
164 m = m.plus(t.norm().fundamentalQuadric(t.centroid()));
166 } while(e != this.e);
167 fundamentalQuadric = m;
168 applyQuadricToNeighbor();
171 public void unApplyQuadricToNeighbor() {
172 if (nearest_in_other_mesh == null) return;
173 if (fundamentalQuadric == null) return;
174 nearest_in_other_mesh.unComputeError();
175 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.minus(fundamentalQuadric);
176 nearest_in_other_mesh.quadric_count--;
177 if (nearest_in_other_mesh.quadric_count==0)
178 nearest_in_other_mesh.quadric = Matrix.ZERO;
179 nearest_in_other_mesh.computeError();
180 nearest_in_other_mesh = null;
183 public void applyQuadricToNeighbor() {
184 if (score_against == null) return;
186 Vert new_nearest = score_against.nearest(p);
187 if (nearest_in_other_mesh != null && new_nearest == nearest_in_other_mesh) return;
189 if (nearest_in_other_mesh != null) unApplyQuadricToNeighbor();
190 if (nearest_in_other_mesh != null) throw new Error();
192 nearest_in_other_mesh = new_nearest;
194 // don't attract to vertices that face the other way
195 if (nearest_in_other_mesh.e == null || nearest_in_other_mesh.norm().dot(norm()) < 0) {
196 nearest_in_other_mesh = null;
198 nearest_in_other_mesh.unComputeError();
199 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.plus(fundamentalQuadric());
200 nearest_in_other_mesh.quadric_count++;
201 nearest_in_other_mesh.computeError();
206 public void reComputeError() {
210 public void unComputeError() {
214 public void computeError() {
215 oldscore = quadric_count == 0 ? 0 : (quadric.preAndPostMultiply(p) / quadric_count);
219 /** does NOT update bound pairs! */
220 public boolean transform(Matrix m) {
221 unApplyQuadricToNeighbor();
223 if (pointset.get(this.p)==null) throw new Error();
224 pointset.remove(this);
225 float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
226 float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
227 float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
228 this.p = new Point(newx, newy, newz);
230 } catch (Exception e) {
231 throw new RuntimeException(e);
233 applyQuadricToNeighbor();
235 // should recompute fundamental quadrics of all vertices sharing a face, but we defer...
238 e.p2.quadricStale = true;
240 } while(e != this.e);
243 // FIXME: intersection test needed?
247 public boolean move(Vec v) {
248 Matrix m = new Matrix(v);
252 good &= p.transform(m);
258 public E getFreeIncident() {
259 E ret = getFreeIncident(e, e);
260 if (ret != null) return ret;
261 ret = getFreeIncident(e.pair.next, e.pair.next);
262 if (ret == null) throw new Error("unable to find free incident to " + this);
266 public E getFreeIncident(E start, E before) {
269 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null) return e.pair;
271 } while(e != before);
275 public E getE(Point p2) {
276 Vert v = pointset.get(p2);
277 if (v==null) return null;
280 public E getE(Vert p2) {
283 if (e==null) return null;
284 if (e.p1 == this && e.p2 == p2) return e;
291 Vec norm = new Vec(0, 0, 0);
294 if (e.t != null) norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
296 } while(e != this.e);
300 public boolean isBoundTo(Vert p) {
303 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
321 public class BindingGroup {
322 private HashSet<E> left = new HashSet<E>();
323 private HashSet<E> right = new HashSet<E>();
324 public BindingGroup() { }
325 public BindingGroup(E e) { add(e, false); }
326 public void add(E e, boolean swap) {
328 if (e.bg == this) return; /* fixme what if it is in the "other" set? */
329 for(E ex : (!swap ? e.bg.left : e.bg.right)) {
333 for(E ex : (!swap ? e.bg.right : e.bg.left)) {
338 (!swap ? left : right).add(e);
342 public void dobind(E e) {
345 if (left.contains(e)) { v1 = e.p1; v2 = e.p2; }
346 if (right.contains(e)) { v1 = e.p2; v2 = e.p1; }
358 public void shatter(BindingGroup bg1, BindingGroup bg2) {
360 e.shatter(e.midpoint(), bg1, bg2);
364 e.shatter(e.midpoint(), bg1, bg2); // swap correct?
370 /** [UNIQUE] an edge */
371 public final class E implements Comparable<E> {
373 public final Vert p1, p2;
374 T t; // triangle to our "left"
375 E prev; // previous half-edge
376 E next; // next half-edge
377 E pair; // partner half-edge
378 public BindingGroup bg = new BindingGroup(this);
379 boolean shattered = false;
381 public int compareTo(E e) { return e.length() > length() ? 1 : -1; }
383 public void bindEdge(E e) {
384 bg.add(e.pair, false);
386 public void dobind() { if (bg != null) bg.dobind(this); }
388 public Point shatter() { return shatter(midpoint(), null, null); }
389 public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
390 if (shattered) return mid;
397 if (bg1==null) bg1 = new BindingGroup();
398 if (bg2==null) bg2 = new BindingGroup();
399 bg.shatter(bg1, bg2);
403 newT(r.p, p1.p, mid, null);
404 newT(r.p, mid, p2.p, null);
405 bg1.add(p1.getE(mid), false);
406 bg2.add(p2.getE(mid).pair, false);
410 public boolean destroyed = false;
411 public void destroy() {
412 if (destroyed) return;
414 pair.destroyed = true;
415 if (next.t != null) next.t.destroy();
416 if (prev.t != null) prev.t.destroy();
423 pair.prev.next = next;
424 next.prev = pair.prev;
425 prev.next = pair.next;
427 if (p1.e == this) p1.e = prev.next;
428 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
429 avgedge -= this.length();
430 avgedge -= pair.length();
435 private void sync() {
436 this.prev.next = this;
437 this.next.prev = this;
438 this.pair.pair = this;
439 if (this.next.p1 != p2) throw new Error();
440 if (this.prev.p2 != p1) throw new Error();
441 if (this.p1.e == null) this.p1.e = this;
448 private boolean added = false;
450 public T makeT() { return t==null ? (t = new T(this)) : t; }
452 /** angle between this half-edge and the next */
453 public double angle() {
454 Vec v1 = next.p2.p.minus(p2.p);
455 Vec v2 = this.p1.p.minus(p2.p);
456 return Math.acos(v1.norm().dot(v2.norm()));
459 public void makeAdjacent(E e) {
460 if (this.next == e) return;
461 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
462 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
464 E freeIncident = p2.getFreeIncident(e, this);
466 e.prev.next = freeIncident.next;
467 freeIncident.next.prev = e.prev;
469 freeIncident.next = this.next;
470 this.next.prev = freeIncident;
479 /** creates an isolated edge out in the middle of space */
480 public E(Point p1, Point p2) {
481 if (pointset.get(p1) != null) throw new Error();
482 if (pointset.get(p2) != null) throw new Error();
483 this.p1 = new Vert(p1);
484 this.p2 = new Vert(p2);
485 this.prev = this.next = this.pair = new E(this, this, this);
487 this.p2.e = this.pair;
491 /** adds a new half-edge from prev.p2 to p2 */
492 public E(E prev, Point p) {
494 p2 = pointset.get(p);
495 if (p2 == null) p2 = new Vert(p);
499 if (p2.getE(p1) != null) throw new Error();
501 this.next = this.pair = new E(this, this, prev.next);
503 E q = p2.getFreeIncident();
505 this.next.prev = this;
507 this.prev.next = this;
508 this.pair = new E(q, this, z);
510 if (p2.e==null) p2.e = this.pair;
514 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
515 public E(E prev, E pair, E next) {
523 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); }
524 public boolean has(Vert v) { return v==p1 || v==p2; }
525 public float length() { return p1.p.minus(p2.p).mag(); }
526 public String toString() { return p1+"->"+p2; }
528 public boolean intersects(T t) {
529 double A0=t.v1().p.x, A1=t.v1().p.y, A2=t.v1().p.z;
530 double B0=t.v2().p.x, B1=t.v2().p.y, B2=t.v2().p.z;
531 double C0=t.v3().p.x, C1=t.v3().p.y, C2=t.v3().p.z;
532 double j0=p1.p.x, j1=p1.p.y, j2=p1.p.z;
533 double k0=p2.p.x, k1=p2.p.y, k2=p2.p.z;
541 double R00, R01, R02, R03,
555 /* c = a × b */
556 c0 = a1 * b2 - a2 * b1;
557 c1 = a2 * b0 - a0 * b2;
558 c2 = a0 * b1 - a1 * b0;
560 /* M^(-1) = (1/det(M)) * adj(M) */
561 in_det = 1 / (c0 * c0 + c1 * c1 + c2 * c2);
562 R00 = (b1 * c2 - b2 * c1) * in_det;
563 R01 = (b2 * c0 - b0 * c2) * in_det;
564 R02 = (b0 * c1 - b1 * c0) * in_det;
565 R10 = (c1 * a2 - c2 * a1) * in_det;
566 R11 = (c2 * a0 - c0 * a2) * in_det;
567 R12 = (c0 * a1 - c1 * a0) * in_det;
573 R03 = -(R00 * A0 + R01 * A1 + R02 * A2);
574 R13 = -(R10 * A0 + R11 * A1 + R12 * A2);
575 R23 = -(R20 * A0 + R21 * A1 + R22 * A2);
577 /* fill in last row of 4x4 matrix */
581 J2 = R20 * j0 + R21 * j1 + R22 * j2 + R23;
582 K2 = R20 * k0 + R21 * k1 + R22 * k2 + R23;
583 if (J2 * K2 >= 0) return false;
585 J0 = R00 * j0 + R01 * j1 + R02 * j2 + R03;
586 K0 = R00 * k0 + R01 * k1 + R02 * k2 + R03;
587 i0 = J0 + J2 * ((K0 - J0) / (J2 - K2));
588 if (i0 < 0 || i0 > 1) return false;
590 J1 = R10 * j0 + R11 * j1 + R12 * j2 + R13;
591 K1 = R10 * k0 + R11 * k1 + R12 * k2 + R13;
592 i1 = J1 + J2 * ((K1 - J1) / (J2 - K2));
593 if (i1 < 0 || i1 > 1 || i0 + i1 > 1) return false;
599 public E makeE(Point p1, Point p2) {
600 Vert v1 = pointset.get(p1);
601 Vert v2 = pointset.get(p2);
602 if (v1 != null && v2 != null) {
604 if (e != null) return e;
606 if (e != null) return e;
608 if (v1 != null) return new E(v1.getFreeIncident(), p2);
609 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
610 return new E(p1, p2);
612 public T newT(Point p1, Point p2, Point p3, Vec norm) {
614 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
615 float dot = norm.dot(norm2);
616 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
617 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
619 E e12 = makeE(p1, p2);
620 E e23 = makeE(p2, p3);
621 E e31 = makeE(p3, p1);
622 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
623 e12.makeAdjacent(e23);
624 e23.makeAdjacent(e31);
625 e31.makeAdjacent(e12);
628 if (e12.t == null) throw new Error();
629 if (e23.t == null) throw new Error();
630 if (e31.t == null) throw new Error();
635 public class FaceIterator implements Iterator<T> {
636 private HashSet<T> visited = new HashSet<T>();
637 private LinkedList<T> next = new LinkedList<T>();
638 public FaceIterator() { }
639 public FaceIterator(Vert v) { next.addFirst(v.e.t); }
640 public boolean hasNext() { return next.peek()!=null; }
641 public void remove() { throw new Error(); }
643 T ret = next.removeFirst();
644 if (ret == null) return null;
646 T t1 = ret.e1().pair.t;
647 T t2 = ret.e2().pair.t;
648 T t3 = ret.e3().pair.t;
649 if (t1 != null && !visited.contains(t1)) next.addFirst(t1);
650 if (t2 != null && !visited.contains(t2)) next.addFirst(t2);
651 if (t3 != null && !visited.contains(t3)) next.addFirst(t3);
656 /** [UNIQUE] a triangle (face) */
657 public final class T extends Triangle {
659 public final int color;
661 public void destroy() {
668 if (e1==e2 || e1==e3) throw new Error();
669 if (e3.next!=e1) throw new Error();
670 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
673 e1.next.next.t = this;
675 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
677 int color = Math.abs(random.nextInt());
680 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
681 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
682 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
687 public E e1() { return e1; }
688 public E e2() { return e1.next; }
689 public E e3() { return e1.prev; }
690 public Vert v1() { return e1.p1; }
691 public Vert v2() { return e1.p2; }
692 public Vert v3() { return e1.next.p2; }
693 public Point p1() { return e1.p1.p; }
694 public Point p2() { return e1.p2.p; }
695 public Point p3() { return e1.next.p2.p; }
696 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
697 public boolean has(Vert v) { return v1()==v || v2()==v || v3()==v; }