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 class BindingGroup {
120 public HashSet<E> es = new HashSet<E>();
121 public BindingGroup() { }
122 public BindingGroup(E e) {
125 public void add(E e) {
126 if (e.bg != null) { merge(e.bg); return; }
130 public void merge(BindingGroup bg) {
138 public Vec diagonal() { return pointset.diagonal(); }
139 public Point centroid() { return pointset.centroid(); }
140 public Vert nearest(Point p) { return pointset.nearest(p); }
142 public final class Vert extends HasPoint {
144 E e; // some edge *leaving* this point
146 /** the nearest vertex in the "score_against" mesh */
147 Vert nearest_in_other_mesh;
148 /** the number of vertices in the other mesh for which this is the nearest_in_other_mesh */
150 /** the total error quadric (contributions from all vertices in other mesh for which this is nearest) */
151 Matrix quadric = Matrix.ZERO;
153 Vert bound_to = this;
154 Matrix binding = new Matrix();
157 public Matrix errorQuadric() { return quadric; }
158 public Point getPoint() { return p; }
159 public float score() { return oldscore; }
161 private Matrix fundamentalQuadric = null;
162 public Matrix fundamentalQuadric() {
163 if (fundamentalQuadric == null) recomputeFundamentalQuadric();
164 return fundamentalQuadric;
167 private Vert(Point p) {
169 if (pointset.get(p) != null) throw new Error();
173 public void recomputeFundamentalQuadric() {
174 unApplyQuadricToNeighbor();
175 Matrix m = Matrix.ZERO;
179 m = m.plus(t.norm().fundamentalQuadric(t.centroid()));
181 } while(e != this.e);
182 fundamentalQuadric = m;
183 applyQuadricToNeighbor();
186 public void unApplyQuadricToNeighbor() {
187 if (nearest_in_other_mesh == null) return;
188 if (fundamentalQuadric == null) return;
189 nearest_in_other_mesh.unComputeError();
190 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.minus(fundamentalQuadric);
191 nearest_in_other_mesh.quadric_count--;
192 if (nearest_in_other_mesh.quadric_count==0)
193 nearest_in_other_mesh.quadric = Matrix.ZERO;
194 nearest_in_other_mesh.computeError();
195 nearest_in_other_mesh = null;
198 public void applyQuadricToNeighbor() {
199 if (score_against == null) return;
201 if (nearest_in_other_mesh != null) unApplyQuadricToNeighbor();
202 if (nearest_in_other_mesh == null) {
203 nearest_in_other_mesh = score_against.nearest(p);
205 // don't attract to vertices that face the other way
206 if (nearest_in_other_mesh.e == null || nearest_in_other_mesh.norm().dot(norm()) < 0) {
207 nearest_in_other_mesh = null;
209 nearest_in_other_mesh.unComputeError();
210 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.plus(fundamentalQuadric());
211 nearest_in_other_mesh.quadric_count++;
212 nearest_in_other_mesh.computeError();
218 public void reComputeError() {
222 public void unComputeError() {
226 public void computeError() {
227 oldscore = quadric_count == 0 ? 0 : (quadric.preAndPostMultiply(p) / quadric_count);
231 /** does NOT update bound pairs! */
232 public boolean transform(Matrix m) {
233 unApplyQuadricToNeighbor();
235 if (pointset.get(this.p)==null) throw new Error();
236 pointset.remove(this);
237 float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
238 float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
239 float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
240 this.p = new Point(newx, newy, newz);
242 } catch (Exception e) {
243 throw new RuntimeException(e);
245 applyQuadricToNeighbor();
247 // should recompute fundamental quadrics of all vertices sharing a face, but we defer...
248 // FIXME: intersection test needed?
252 public boolean move(Vec v) {
253 Matrix m = new Matrix(v);
257 good &= p.transform(m);
263 public E getFreeIncident() {
264 E ret = getFreeIncident(e, e);
265 if (ret != null) return ret;
266 ret = getFreeIncident(e.pair.next, e.pair.next);
267 if (ret == null) throw new Error("unable to find free incident to " + this);
271 public E getFreeIncident(E start, E before) {
274 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null) return e.pair;
276 } while(e != before);
280 public E getE(Point p2) {
281 Vert v = pointset.get(p2);
282 if (v==null) return null;
285 public E getE(Vert p2) {
288 if (e==null) return null;
289 if (e.p1 == this && e.p2 == p2) return e;
296 Vec norm = new Vec(0, 0, 0);
299 if (e.t != null) norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
301 } while(e != this.e);
305 public boolean isBoundTo(Vert p) {
308 if (px==this) return true;
313 public void unbind() { bound_to = this; binding = new Matrix(); }
314 public void bind(Vert p) { bind(p, new Matrix()); }
315 public void bind(Vert p, Matrix binding) {
316 if (isBoundTo(p)) return;
317 Vert temp_bound_to = p.bound_to;
318 Matrix temp_binding = p.binding;
319 p.bound_to = this.bound_to;
320 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
321 this.bound_to = temp_bound_to;
322 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
326 /** [UNIQUE] an edge */
327 public final class E implements Comparable<E> {
329 public final Vert p1, p2;
330 T t; // triangle to our "left"
331 E prev; // previous half-edge
332 E next; // next half-edge
333 E pair; // partner half-edge
334 public BindingGroup bg = new BindingGroup(this);
335 boolean shattered = false;
337 public int compareTo(E e) { return e.length() > length() ? 1 : -1; }
339 public void bind(E e) { bind(e, new Matrix()); }
340 public void bind(E e, Matrix m) { e.bg.add(this); }
342 public void dobind() {
343 if (bg==null) return;
345 if (ex==this) continue;
351 public Point shatter() { return shatter(midpoint(), null, null); }
352 public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
353 if (shattered) return mid;
360 if (bg1==null) bg1 = new BindingGroup();
361 if (bg2==null) bg2 = new BindingGroup();
362 for(E e : bg.es) e.shatter(e.midpoint(), bg1, bg2);
366 newT(r.p, p1.p, mid, null);
367 newT(r.p, mid, p2.p, null);
368 bg1.add(p1.getE(mid));
369 bg2.add(p2.getE(mid).pair);
373 public boolean destroyed = false;
374 public void destroy() {
375 if (destroyed) return;
377 pair.destroyed = true;
378 if (next.t != null) next.t.destroy();
379 if (prev.t != null) prev.t.destroy();
386 pair.prev.next = next;
387 next.prev = pair.prev;
388 prev.next = pair.next;
390 if (p1.e == this) p1.e = prev.next;
391 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
392 avgedge -= this.length();
393 avgedge -= pair.length();
398 private void sync() {
399 this.prev.next = this;
400 this.next.prev = this;
401 this.pair.pair = this;
402 if (this.next.p1 != p2) throw new Error();
403 if (this.prev.p2 != p1) throw new Error();
404 if (this.p1.e == null) this.p1.e = this;
411 private boolean added = false;
413 public T makeT() { return t==null ? (t = new T(this)) : t; }
415 /** angle between this half-edge and the next */
416 public double angle() {
417 Vec v1 = next.p2.p.minus(p2.p);
418 Vec v2 = this.p1.p.minus(p2.p);
419 return Math.acos(v1.norm().dot(v2.norm()));
422 public void makeAdjacent(E e) {
423 if (this.next == e) return;
424 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
425 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
427 E freeIncident = p2.getFreeIncident(e, this);
429 e.prev.next = freeIncident.next;
430 freeIncident.next.prev = e.prev;
432 freeIncident.next = this.next;
433 this.next.prev = freeIncident;
442 /** creates an isolated edge out in the middle of space */
443 public E(Point p1, Point p2) {
444 if (pointset.get(p1) != null) throw new Error();
445 if (pointset.get(p2) != null) throw new Error();
446 this.p1 = new Vert(p1);
447 this.p2 = new Vert(p2);
448 this.prev = this.next = this.pair = new E(this, this, this);
450 this.p2.e = this.pair;
454 /** adds a new half-edge from prev.p2 to p2 */
455 public E(E prev, Point p) {
457 p2 = pointset.get(p);
458 if (p2 == null) p2 = new Vert(p);
462 if (p2.getE(p1) != null) throw new Error();
464 this.next = this.pair = new E(this, this, prev.next);
466 E q = p2.getFreeIncident();
468 this.next.prev = this;
470 this.prev.next = this;
471 this.pair = new E(q, this, z);
473 if (p2.e==null) p2.e = this.pair;
477 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
478 public E(E prev, E pair, E next) {
486 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); }
487 public boolean has(Vert v) { return v==p1 || v==p2; }
488 public float length() { return p1.p.minus(p2.p).mag(); }
489 public String toString() { return p1+"->"+p2; }
491 public boolean intersects(T t) {
492 double A0=t.v1().p.x, A1=t.v1().p.y, A2=t.v1().p.z;
493 double B0=t.v2().p.x, B1=t.v2().p.y, B2=t.v2().p.z;
494 double C0=t.v3().p.x, C1=t.v3().p.y, C2=t.v3().p.z;
495 double j0=p1.p.x, j1=p1.p.y, j2=p1.p.z;
496 double k0=p2.p.x, k1=p2.p.y, k2=p2.p.z;
504 double R00, R01, R02, R03,
518 /* c = a × b */
519 c0 = a1 * b2 - a2 * b1;
520 c1 = a2 * b0 - a0 * b2;
521 c2 = a0 * b1 - a1 * b0;
523 /* M^(-1) = (1/det(M)) * adj(M) */
524 in_det = 1 / (c0 * c0 + c1 * c1 + c2 * c2);
525 R00 = (b1 * c2 - b2 * c1) * in_det;
526 R01 = (b2 * c0 - b0 * c2) * in_det;
527 R02 = (b0 * c1 - b1 * c0) * in_det;
528 R10 = (c1 * a2 - c2 * a1) * in_det;
529 R11 = (c2 * a0 - c0 * a2) * in_det;
530 R12 = (c0 * a1 - c1 * a0) * in_det;
536 R03 = -(R00 * A0 + R01 * A1 + R02 * A2);
537 R13 = -(R10 * A0 + R11 * A1 + R12 * A2);
538 R23 = -(R20 * A0 + R21 * A1 + R22 * A2);
540 /* fill in last row of 4x4 matrix */
544 J2 = R20 * j0 + R21 * j1 + R22 * j2 + R23;
545 K2 = R20 * k0 + R21 * k1 + R22 * k2 + R23;
546 if (J2 * K2 >= 0) return false;
548 J0 = R00 * j0 + R01 * j1 + R02 * j2 + R03;
549 K0 = R00 * k0 + R01 * k1 + R02 * k2 + R03;
550 i0 = J0 + J2 * ((K0 - J0) / (J2 - K2));
551 if (i0 < 0 || i0 > 1) return false;
553 J1 = R10 * j0 + R11 * j1 + R12 * j2 + R13;
554 K1 = R10 * k0 + R11 * k1 + R12 * k2 + R13;
555 i1 = J1 + J2 * ((K1 - J1) / (J2 - K2));
556 if (i1 < 0 || i1 > 1 || i0 + i1 > 1) return false;
562 public E makeE(Point p1, Point p2) {
563 Vert v1 = pointset.get(p1);
564 Vert v2 = pointset.get(p2);
565 if (v1 != null && v2 != null) {
567 if (e != null) return e;
569 if (e != null) return e;
571 if (v1 != null) return new E(v1.getFreeIncident(), p2);
572 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
573 return new E(p1, p2);
575 public T newT(Point p1, Point p2, Point p3, Vec norm) {
577 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
578 float dot = norm.dot(norm2);
579 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
580 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
582 E e12 = makeE(p1, p2);
583 E e23 = makeE(p2, p3);
584 E e31 = makeE(p3, p1);
585 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
586 e12.makeAdjacent(e23);
587 e23.makeAdjacent(e31);
588 e31.makeAdjacent(e12);
591 if (e12.t == null) throw new Error();
592 if (e23.t == null) throw new Error();
593 if (e31.t == null) throw new Error();
598 public class FaceIterator implements Iterator<T> {
599 private HashSet<T> visited = new HashSet<T>();
600 private LinkedList<T> next = new LinkedList<T>();
601 public FaceIterator() { }
602 public FaceIterator(Vert v) { next.addFirst(v.e.t); }
603 public boolean hasNext() { return next.peek()!=null; }
604 public void remove() { throw new Error(); }
606 T ret = next.removeFirst();
607 if (ret == null) return null;
609 T t1 = ret.e1().pair.t;
610 T t2 = ret.e2().pair.t;
611 T t3 = ret.e3().pair.t;
612 if (t1 != null && !visited.contains(t1)) next.addFirst(t1);
613 if (t2 != null && !visited.contains(t2)) next.addFirst(t2);
614 if (t3 != null && !visited.contains(t3)) next.addFirst(t3);
619 /** [UNIQUE] a triangle (face) */
620 public final class T extends Triangle {
622 public final int color;
624 public void destroy() {
631 if (e1==e2 || e1==e3) throw new Error();
632 if (e3.next!=e1) throw new Error();
633 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
636 e1.next.next.t = this;
638 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
640 int color = Math.abs(random.nextInt());
643 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
644 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
645 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
650 public E e1() { return e1; }
651 public E e2() { return e1.next; }
652 public E e3() { return e1.prev; }
653 public Vert v1() { return e1.p1; }
654 public Vert v2() { return e1.p2; }
655 public Vert v3() { return e1.next.p2; }
656 public Point p1() { return e1.p1.p; }
657 public Point p2() { return e1.p2.p; }
658 public Point p3() { return e1.next.p2.p; }
659 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
660 public boolean has(Vert v) { return v1()==v || v2()==v || v3()==v; }