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;
11 import com.infomatiq.jsi.IntProcedure;
13 public class Mesh implements Iterable<Mesh.T> {
15 public static final float EPSILON = (float)0.0001;
16 public static final Random random = new Random();
18 private RTree<T> triangles = new RTree<T>();
19 private PointSet<Vertex> vertices = new PointSet<Vertex>();
21 public boolean immutableVertices;
22 public Mesh error_against = null;
23 public double error = 0;
25 public Mesh(boolean immutableVertices) { this.immutableVertices = immutableVertices; }
27 public void makeVerticesImmutable() { this.immutableVertices = true; }
28 public float error() { return (float)error; }
30 public int size() { return vertices.size(); }
31 public Iterable<Vertex> vertices() { return vertices; }
32 public Iterator<T> iterator() { return triangles.iterator(); }
34 public void rebindPoints() {
36 for(Mesh.T t : this) {
41 // ask edges to re-implement their bindings
42 for(Mesh.T t : this) {
49 public void transform(Matrix m) {
50 ArrayList<Vertex> set = new ArrayList<Vertex>();
51 for(Vertex v : vertices) set.add(v);
52 for(Vertex v : set) v.transform(m.times(v.p), true);
55 public void rebuild() { /*vertices.rebuild();*/ }
56 public Vec diagonal() { return vertices.diagonal(); }
57 public Point centroid() { return vertices.centroid(); }
58 public Vertex nearest(Point p) { return vertices.nearest(p); }
60 /** compute the volume of the mesh */
61 public float volume() {
64 double area = t.area();
65 Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
66 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
67 double height = Math.abs(t.norm().dot(origin_to_centroid));
68 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
74 // Vertexices //////////////////////////////////////////////////////////////////////////////
76 /** a vertex in the mesh */
77 public final class Vertex extends HasQuadric implements Visitor {
78 public Point p, oldp, goodp;
79 E e; // some edge *leaving* this point
81 Matrix binding = Matrix.ONE;
82 Vertex bound_to = this;
83 private boolean illegal = false;
85 public Point getPoint() { return p; }
86 public float error() { return olderror; }
88 private Vertex(Point p) {
91 if (vertices.get(p) != null) throw new Error();
95 public void reinsert() {
96 vertices.remove(this);
98 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.t.reinsert();
101 public float olderror = 0;
102 public void setError(float nerror) {
108 public float averageTriangleArea() {
111 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
117 public float averageEdgeLength() {
120 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
127 public Matrix _recomputeFundamentalQuadric() {
128 Matrix m = Matrix.ZERO;
130 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
131 m = m.plus(e.t.norm().fundamentalQuadric(e.t.centroid()));
134 return m.times(1/(float)count);
137 public HasQuadric nearest() { return error_against==null ? null : error_against.vertices.nearest(p, this); }
138 public void computeError() {
139 if (error_against==null) return;
141 nearest_in_other_mesh != null
142 ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p)
143 : nearest().fundamentalQuadric().preAndPostMultiply(p);
144 if (quadric_count != 0)
145 nerror = (nerror + quadric.preAndPostMultiply(p))/(quadric_count+1);
147 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
148 double ang = Math.abs(e.dihedralAngle());
149 if (ang > Math.PI) throw new Error();
150 float minangle = (float)(Math.PI * 0.8);
151 if (ang > minangle) nerror += (ang - minangle);
153 if (e.t.aspect() < 0.2) {
154 nerror += (0.2-e.t.aspect()) * 10;
162 public boolean move(Matrix m, boolean ignoreProblems) {
164 for(Vertex p = this; p != null; p = (p.bound_to==this)?null:p.bound_to)
165 good &= p.transform(m.times(p.p), ignoreProblems);
166 for(Vertex p = this; p != null; p = (p.bound_to==this)?null:p.bound_to)
167 if (good || ignoreProblems) p.reComputeErrorAround();
168 else p.transform(p.oldp, true);
172 /** does NOT update bound pairs! */
173 private boolean transform(Point newp, boolean ignoreProblems) {
175 if (immutableVertices) throw new Error();
177 unApplyQuadricToNeighbor();
180 applyQuadricToNeighbor();
182 if (!ignoreProblems) {
186 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.p2.quadricStale = true;
190 public void checkLegality() {
192 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
193 if (Math.abs(e.dihedralAngle()) > (Math.PI * 0.9) ||
194 Math.abs(e.next.dihedralAngle()) > (Math.PI * 0.9)) illegal = true;
195 if (e.t.aspect() < 0.1) illegal = true;
198 if (!illegal) triangles.range(oldp, this.p, (Visitor<T>)this);
201 public void reComputeErrorAround() {
203 if (nearest_in_other_mesh != null)
204 nearest_in_other_mesh.reComputeError();
205 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
206 e.p2.reComputeError();
209 public boolean visit(Object o) {
210 if (o instanceof Vertex)
211 return ((Vertex)o).e != null && ((Vertex)o).norm().dot(Vertex.this.norm()) >= 0;
213 if (illegal) return false;
214 for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
215 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { illegal = true; }
217 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { illegal = true; }
218 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { illegal = true; }
219 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { illegal = true; }
225 public E getFreeIncident() {
226 E ret = getFreeIncident(e, e);
227 if (ret != null) return ret;
228 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
229 System.out.println(e + " " + e.t);
230 throw new Error("unable to find free incident to " + this);
233 public E getFreeIncident(E start, E before) {
234 for(E e = start; e!=null; e=e.pair.next==before?null:e.pair.next)
235 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null)
240 public E getE(Point p2) {
241 Vertex v = vertices.get(p2);
242 if (v==null) return null;
245 public E getE(Vertex p2) {
246 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
247 if (e.p1 == this && e.p2 == p2) return e;
251 private void glNormal(GL gl) {
253 gl.glNormal3f(norm.x, norm.y, norm.z);
256 Vec norm = new Vec(0, 0, 0);
257 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
259 norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
263 public boolean isBoundTo(Vertex p) {
264 for(Vertex px = p; px!=null; px=(px.bound_to==p?null:px.bound_to))
270 public void unbind() { bound_to = this; binding = Matrix.ONE; }
271 public void bind(Vertex p) { bind(p, Matrix.ONE); }
272 public void bind(Vertex p, Matrix binding) {
273 if (isBoundTo(p)) return;
274 Vertex temp_bound_to = p.bound_to;
275 Matrix temp_binding = p.binding;
276 p.bound_to = this.bound_to;
277 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
278 this.bound_to = temp_bound_to;
279 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
283 public class BindingGroup {
284 private HashSet<E> set = new HashSet<E>();
285 public BindingGroup bind_others;
286 public BindingGroup other() { return bind_others; }
287 public BindingGroup(BindingGroup bind_others) { this.bind_others = bind_others; }
288 public BindingGroup() { this.bind_others = new BindingGroup(this); }
289 public BindingGroup(E e) { this(); set.add(e); }
290 public void add(E e) {
291 if (set.contains(e)) return;
293 BindingGroup e_bind_peers = e.bind_peers;
294 BindingGroup e_bind_to = e.bind_to;
296 e.bind_to = bind_others;
297 for (E epeer : e_bind_peers.set) add(epeer);
298 for (E eother : e_bind_to.set) bind_others.add(eother);
300 for(E eother : bind_others.set) {
301 if (e.next.bind_to.set.contains(eother.prev)) {
302 e.next.next.bindEdge(eother.prev.prev);
304 if (e.prev.bind_to.set.contains(eother.next)) {
305 e.prev.prev.bindEdge(eother.next.next);
310 public void dobind(E e) {
311 for(E ebound : set) {
312 e.p1.bind(ebound.p2);
313 e.p2.bind(ebound.p1);
316 public void shatter(BindingGroup bg1, BindingGroup bg2) {
318 e.shatter(e.midpoint(), bg1, bg2);
323 /** [UNIQUE] an edge */
324 public final class E implements Comparable<E> {
326 public final Vertex p1, p2;
327 T t; // triangle to our "left"
328 E prev; // previous half-edge
329 E next; // next half-edge
330 E pair; // partner half-edge
331 public BindingGroup bind_peers = new BindingGroup(this);
332 public BindingGroup bind_to = bind_peers.other();
333 boolean shattered = false;
335 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
337 public float stretchRatio() {
338 Vertex nearest = error_against.nearest(midpoint());
339 float nearest_distance = midpoint().distance(nearest.p);
340 float other_distance =
341 (p1.p.distance(error_against.nearest(p1.p).p)+
342 p2.p.distance(error_against.nearest(p2.p).p))/2;
343 return nearest_distance/other_distance;
345 public float comparator() {
349 //return t==null?0:(1/t.aspect());
351 public int compareTo(E e) {
352 return e.comparator() > comparator() ? 1 : -1;
354 public void bindEdge(E e) { bind_to.add(e); }
355 public void dobind() { bind_to.dobind(this); }
357 public Point shatter() { return shatter(midpoint(), null, null); }
358 public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
359 if (shattered || destroyed) return mid;
366 int old_colorclass = t==null ? 0 : t.colorclass;
367 if (bg1==null) bg1 = new BindingGroup();
368 if (bg2==null) bg2 = new BindingGroup();
369 BindingGroup old_bind_to = bind_to;
370 bind_peers.shatter(bg1, bg2);
371 old_bind_to.shatter(bg2.other(), bg1.other());
375 newT(r.p, p1.p, mid, null, old_colorclass);
376 newT(r.p, mid, p2.p, null, old_colorclass);
377 bg1.add(p1.getE(mid));
378 bg2.add(p2.getE(mid).pair);
382 public boolean destroyed = false;
383 public void destroy() {
384 if (destroyed) return;
386 pair.destroyed = true;
388 if (t != null) t.destroy();
391 if (pair.t != null) pair.t.destroy();
394 if (next.t != null) next.t.destroy();
395 if (prev.t != null) prev.t.destroy();
399 if (pair.next.t != null) pair.next.t.destroy();
400 if (pair.prev.t != null) pair.next.t.destroy();
406 this.bind_peers = null;
407 pair.bind_peers = null;
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;
416 private void sync() {
417 this.prev.next = this;
418 this.next.prev = this;
419 this.pair.pair = this;
420 bind_peers.add(this);
421 if (this.next.p1 != p2) throw new Error();
422 if (this.prev.p2 != p1) throw new Error();
423 if (this.p1.e == null) this.p1.e = this;
424 if (!added) added = true;
426 private boolean added = false;
428 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
430 public double dihedralAngle() {
431 Vec v1 = t.norm().times(-1);
432 Vec v2 = pair.t.norm().times(-1);
433 return Math.acos(v1.norm().dot(v2.norm()));
436 /** angle between this half-edge and the next */
437 public double angle() {
438 Vec v1 = next.p2.p.minus(p2.p);
439 Vec v2 = this.p1.p.minus(p2.p);
440 return Math.acos(v1.norm().dot(v2.norm()));
443 public void makeAdjacent(E e) {
444 if (this.next == e) return;
445 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
446 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
448 E freeIncident = p2.getFreeIncident(e, this);
450 e.prev.next = freeIncident.next;
451 freeIncident.next.prev = e.prev;
453 freeIncident.next = this.next;
454 this.next.prev = freeIncident;
463 /** creates an isolated edge out in the middle of space */
464 public E(Point p1, Point p2) {
465 if (vertices.get(p1) != null) throw new Error();
466 if (vertices.get(p2) != null) throw new Error();
467 this.p1 = new Vertex(p1);
468 this.p2 = new Vertex(p2);
469 this.prev = this.next = this.pair = new E(this, this, this);
471 this.p2.e = this.pair;
475 /** adds a new half-edge from prev.p2 to p2 */
476 public E(E prev, Point p) {
478 p2 = vertices.get(p);
479 if (p2 == null) p2 = new Vertex(p);
483 if (p2.getE(p1) != null) throw new Error();
485 this.next = this.pair = new E(this, this, prev.next);
487 E q = p2.getFreeIncident();
489 this.next.prev = this;
491 this.prev.next = this;
492 this.pair = new E(q, this, z);
494 if (p2.e==null) p2.e = this.pair;
498 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
499 public E(E prev, E pair, E next) {
507 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); }
508 public boolean has(Vertex v) { return v==p1 || v==p2; }
509 public float length() { return p1.p.minus(p2.p).mag(); }
510 public String toString() { return p1+"->"+p2; }
514 public E makeE(Point p1, Point p2) {
515 Vertex v1 = vertices.get(p1);
516 Vertex v2 = vertices.get(p2);
517 if (v1 != null && v2 != null) {
519 if (e != null) return e;
521 if (e != null) return e;
523 if (v1 != null) return new E(v1.getFreeIncident(), p2);
524 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
525 return new E(p1, p2);
527 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
529 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
530 float dot = norm.dot(norm2);
531 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
532 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
534 E e12 = makeE(p1, p2);
535 E e23 = makeE(p2, p3);
536 E e31 = makeE(p3, p1);
537 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
538 e12.makeAdjacent(e23);
539 e23.makeAdjacent(e31);
540 e31.makeAdjacent(e12);
542 T ret = e12.makeT(colorclass);
543 if (e12.t == null) throw new Error();
544 if (e23.t == null) throw new Error();
545 if (e31.t == null) throw new Error();
549 /** [UNIQUE] a triangle (face) */
550 public final class T extends Triangle {
552 public final int color;
553 public final int colorclass;
555 T(E e1, int colorclass) {
559 if (e1==e2 || e1==e3) throw new Error();
560 if (e3.next!=e1) throw new Error();
561 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
564 e1.next.next.t = this;
566 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
568 int color = Math.abs(random.nextInt());
571 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
572 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
573 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
577 this.colorclass = colorclass;
580 public E e1() { return e1; }
581 public E e2() { return e1.next; }
582 public E e3() { return e1.prev; }
583 public Vertex v1() { return e1.p1; }
584 public Vertex v2() { return e1.p2; }
585 public Vertex v3() { return e1.next.p2; }
586 public Point p1() { return e1.p1.p; }
587 public Point p2() { return e1.p2.p; }
588 public Point p3() { return e1.next.p2.p; }
589 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
590 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
592 public void removeFromRTree() { triangles.remove(this); }
593 public void addToRTree() { triangles.insert(this); }
594 public void destroy() { triangles.remove(this); }
595 public void reinsert() { triangles.remove(this); triangles.add(this); }
597 public boolean shouldBeDrawn() {
598 if (e1().bind_to.set.size() == 0) return false;
599 if (e2().bind_to.set.size() == 0) return false;
600 if (e3().bind_to.set.size() == 0) return false;
604 /** issue gl.glVertex() for each of the triangle's points */
605 public void glVertices(GL gl) {
606 if (!shouldBeDrawn()) return;
608 Point p1 = v1().goodp;
609 Point p2 = v2().goodp;
610 Point p3 = v3().goodp;