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.unsc();
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.resc();
195 nearest_in_other_mesh = null;
202 public void applyQuadricToNeighbor() {
203 if (score_against == null) return;
205 if (nearest_in_other_mesh != null) unApplyQuadricToNeighbor();
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.unsc();
214 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.plus(fundamentalQuadric());
215 nearest_in_other_mesh.quadric_count++;
216 nearest_in_other_mesh.resc();
223 oldscore = quadric_count == 0 ? 0 : (quadric.preAndPostMultiply(p) / quadric_count);
227 /** does NOT update bound pairs! */
228 public boolean transform(Matrix m) {
229 unApplyQuadricToNeighbor();
231 if (pointset.get(this.p)==null) throw new Error();
232 pointset.remove(this);
233 float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
234 float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
235 float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
236 this.p = new Point(newx, newy, newz);
238 } catch (Exception e) {
239 throw new RuntimeException(e);
241 applyQuadricToNeighbor();
243 // should recompute fundamental quadrics of all vertices sharing a face, but we defer...
244 // FIXME: intersection test needed?
248 public boolean move(Vec v) {
249 Matrix m = new Matrix(v);
253 good &= p.transform(m);
259 public E getFreeIncident() {
260 E ret = getFreeIncident(e, e);
261 if (ret != null) return ret;
262 ret = getFreeIncident(e.pair.next, e.pair.next);
263 if (ret == null) throw new Error("unable to find free incident to " + this);
267 public E getFreeIncident(E start, E before) {
270 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null) return e.pair;
272 } while(e != before);
276 public E getE(Point p2) {
277 Vert v = pointset.get(p2);
278 if (v==null) return null;
281 public E getE(Vert p2) {
284 if (e==null) return null;
285 if (e.p1 == this && e.p2 == p2) return e;
292 Vec norm = new Vec(0, 0, 0);
295 if (e.t != null) norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
297 } while(e != this.e);
301 public boolean isBoundTo(Vert p) {
304 if (px==this) return true;
309 public void unbind() { bound_to = this; binding = new Matrix(); }
310 public void bind(Vert p) { bind(p, new Matrix()); }
311 public void bind(Vert p, Matrix binding) {
312 if (isBoundTo(p)) return;
313 Vert temp_bound_to = p.bound_to;
314 Matrix temp_binding = p.binding;
315 p.bound_to = this.bound_to;
316 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
317 this.bound_to = temp_bound_to;
318 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
322 /** [UNIQUE] an edge */
323 public final class E implements Comparable<E> {
325 public final Vert p1, p2;
326 T t; // triangle to our "left"
327 E prev; // previous half-edge
328 E next; // next half-edge
329 E pair; // partner half-edge
330 public BindingGroup bg = new BindingGroup(this);
331 boolean shattered = false;
333 public int compareTo(E e) { return e.length() > length() ? 1 : -1; }
335 public void bind(E e) { bind(e, new Matrix()); }
336 public void bind(E e, Matrix m) { e.bg.add(this); }
338 public void dobind() {
339 if (bg==null) return;
341 if (ex==this) continue;
347 public Point shatter() { return shatter(midpoint(), null, null); }
348 public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
349 if (shattered) return mid;
356 if (bg1==null) bg1 = new BindingGroup();
357 if (bg2==null) bg2 = new BindingGroup();
358 for(E e : bg.es) e.shatter(e.midpoint(), bg1, bg2);
362 newT(r.p, p1.p, mid, null);
363 newT(r.p, mid, p2.p, null);
364 bg1.add(p1.getE(mid));
365 bg2.add(p2.getE(mid).pair);
369 public boolean destroyed = false;
370 public void destroy() {
371 if (destroyed) return;
373 pair.destroyed = true;
374 if (next.t != null) next.t.destroy();
375 if (prev.t != null) prev.t.destroy();
382 pair.prev.next = next;
383 next.prev = pair.prev;
384 prev.next = pair.next;
386 if (p1.e == this) p1.e = prev.next;
387 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
388 avgedge -= this.length();
389 avgedge -= pair.length();
394 private void sync() {
395 this.prev.next = this;
396 this.next.prev = this;
397 this.pair.pair = this;
398 if (this.next.p1 != p2) throw new Error();
399 if (this.prev.p2 != p1) throw new Error();
400 if (this.p1.e == null) this.p1.e = this;
407 private boolean added = false;
409 public T makeT() { return t==null ? (t = new T(this)) : t; }
411 /** angle between this half-edge and the next */
412 public double angle() {
413 Vec v1 = next.p2.p.minus(p2.p);
414 Vec v2 = this.p1.p.minus(p2.p);
415 return Math.acos(v1.norm().dot(v2.norm()));
418 public void makeAdjacent(E e) {
419 if (this.next == e) return;
420 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
421 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
423 E freeIncident = p2.getFreeIncident(e, this);
425 e.prev.next = freeIncident.next;
426 freeIncident.next.prev = e.prev;
428 freeIncident.next = this.next;
429 this.next.prev = freeIncident;
438 /** creates an isolated edge out in the middle of space */
439 public E(Point p1, Point p2) {
440 if (pointset.get(p1) != null) throw new Error();
441 if (pointset.get(p2) != null) throw new Error();
442 this.p1 = new Vert(p1);
443 this.p2 = new Vert(p2);
444 this.prev = this.next = this.pair = new E(this, this, this);
446 this.p2.e = this.pair;
450 /** adds a new half-edge from prev.p2 to p2 */
451 public E(E prev, Point p) {
453 p2 = pointset.get(p);
454 if (p2 == null) p2 = new Vert(p);
458 if (p2.getE(p1) != null) throw new Error();
460 this.next = this.pair = new E(this, this, prev.next);
462 E q = p2.getFreeIncident();
464 this.next.prev = this;
466 this.prev.next = this;
467 this.pair = new E(q, this, z);
469 if (p2.e==null) p2.e = this.pair;
473 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
474 public E(E prev, E pair, E next) {
482 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); }
483 public boolean has(Vert v) { return v==p1 || v==p2; }
484 public float length() { return p1.p.minus(p2.p).mag(); }
485 public String toString() { return p1+"->"+p2; }
487 public boolean intersects(T t) {
488 double A0=t.v1().p.x, A1=t.v1().p.y, A2=t.v1().p.z;
489 double B0=t.v2().p.x, B1=t.v2().p.y, B2=t.v2().p.z;
490 double C0=t.v3().p.x, C1=t.v3().p.y, C2=t.v3().p.z;
491 double j0=p1.p.x, j1=p1.p.y, j2=p1.p.z;
492 double k0=p2.p.x, k1=p2.p.y, k2=p2.p.z;
500 double R00, R01, R02, R03,
514 /* c = a × b */
515 c0 = a1 * b2 - a2 * b1;
516 c1 = a2 * b0 - a0 * b2;
517 c2 = a0 * b1 - a1 * b0;
519 /* M^(-1) = (1/det(M)) * adj(M) */
520 in_det = 1 / (c0 * c0 + c1 * c1 + c2 * c2);
521 R00 = (b1 * c2 - b2 * c1) * in_det;
522 R01 = (b2 * c0 - b0 * c2) * in_det;
523 R02 = (b0 * c1 - b1 * c0) * in_det;
524 R10 = (c1 * a2 - c2 * a1) * in_det;
525 R11 = (c2 * a0 - c0 * a2) * in_det;
526 R12 = (c0 * a1 - c1 * a0) * in_det;
532 R03 = -(R00 * A0 + R01 * A1 + R02 * A2);
533 R13 = -(R10 * A0 + R11 * A1 + R12 * A2);
534 R23 = -(R20 * A0 + R21 * A1 + R22 * A2);
536 /* fill in last row of 4x4 matrix */
540 J2 = R20 * j0 + R21 * j1 + R22 * j2 + R23;
541 K2 = R20 * k0 + R21 * k1 + R22 * k2 + R23;
542 if (J2 * K2 >= 0) return false;
544 J0 = R00 * j0 + R01 * j1 + R02 * j2 + R03;
545 K0 = R00 * k0 + R01 * k1 + R02 * k2 + R03;
546 i0 = J0 + J2 * ((K0 - J0) / (J2 - K2));
547 if (i0 < 0 || i0 > 1) return false;
549 J1 = R10 * j0 + R11 * j1 + R12 * j2 + R13;
550 K1 = R10 * k0 + R11 * k1 + R12 * k2 + R13;
551 i1 = J1 + J2 * ((K1 - J1) / (J2 - K2));
552 if (i1 < 0 || i1 > 1 || i0 + i1 > 1) return false;
558 public E makeE(Point p1, Point p2) {
559 Vert v1 = pointset.get(p1);
560 Vert v2 = pointset.get(p2);
561 if (v1 != null && v2 != null) {
563 if (e != null) return e;
565 if (e != null) return e;
567 if (v1 != null) return new E(v1.getFreeIncident(), p2);
568 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
569 return new E(p1, p2);
571 public T newT(Point p1, Point p2, Point p3, Vec norm) {
573 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
574 float dot = norm.dot(norm2);
575 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
576 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
578 E e12 = makeE(p1, p2);
579 E e23 = makeE(p2, p3);
580 E e31 = makeE(p3, p1);
581 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
582 e12.makeAdjacent(e23);
583 e23.makeAdjacent(e31);
584 e31.makeAdjacent(e12);
587 if (e12.t == null) throw new Error();
588 if (e23.t == null) throw new Error();
589 if (e31.t == null) throw new Error();
594 public class FaceIterator implements Iterator<T> {
595 private HashSet<T> visited = new HashSet<T>();
596 private LinkedList<T> next = new LinkedList<T>();
597 public FaceIterator() { }
598 public FaceIterator(Vert v) { next.addFirst(v.e.t); }
599 public boolean hasNext() { return next.peek()!=null; }
600 public void remove() { throw new Error(); }
602 T ret = next.removeFirst();
603 if (ret == null) return null;
605 T t1 = ret.e1().pair.t;
606 T t2 = ret.e2().pair.t;
607 T t3 = ret.e3().pair.t;
608 if (t1 != null && !visited.contains(t1)) next.addFirst(t1);
609 if (t2 != null && !visited.contains(t2)) next.addFirst(t2);
610 if (t3 != null && !visited.contains(t3)) next.addFirst(t3);
615 /** [UNIQUE] a triangle (face) */
616 public final class T extends Triangle {
618 public final int color;
620 public void destroy() {
627 if (e1==e2 || e1==e3) throw new Error();
628 if (e3.next!=e1) throw new Error();
629 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
632 e1.next.next.t = this;
634 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
636 int color = Math.abs(random.nextInt());
639 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
640 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
641 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
646 public E e1() { return e1; }
647 public E e2() { return e1.next; }
648 public E e3() { return e1.prev; }
649 public Vert v1() { return e1.p1; }
650 public Vert v2() { return e1.p2; }
651 public Vert v3() { return e1.next.p2; }
652 public Point p1() { return e1.p1.p; }
653 public Point p2() { return e1.p2.p; }
654 public Point p3() { return e1.next.p2.p; }
655 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
656 public boolean has(Vert v) { return v1()==v || v2()==v || v3()==v; }