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 {
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) {
90 if (vertices.get(p) != null) throw new Error();
94 public void reinsert() {
95 vertices.remove(this);
97 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.t.reinsert();
100 public float olderror = 0;
101 public void setError(float nerror) {
107 public float averageTriangleArea() {
110 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
116 public float averageEdgeLength() {
119 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
126 public Matrix _recomputeFundamentalQuadric() {
127 Matrix m = Matrix.ZERO;
129 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
130 m = m.plus(e.t.norm().fundamentalQuadric(e.t.centroid()));
133 return m.times(1/(float)count);
136 public HasQuadric nearest() { return error_against==null ? null : error_against.vertices.nearest(p, this); }
137 public void computeError() {
138 if (error_against==null) return;
140 nearest_in_other_mesh != null
141 ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p)
142 : nearest().fundamentalQuadric().preAndPostMultiply(p);
143 if (quadric_count != 0)
144 nerror = (/*nerror +*/ quadric.preAndPostMultiply(p))/(quadric_count/*+1*/);
146 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
147 double ang = Math.abs(e.dihedralAngle());
148 if (ang > Math.PI) throw new Error();
149 float minangle = (float)(Math.PI * 0.8);
150 if (ang > minangle) nerror += (ang - minangle);
151 if (e.t.aspect() < 0.2) {
152 nerror += (0.2-e.t.aspect()) * 300;
159 public boolean move(Matrix m, boolean ignoreProblems) {
161 for(Vertex p = this; p != null; p = (p.bound_to==this)?null:p.bound_to)
162 good &= p.transform(m.times(p.p), ignoreProblems);
163 for(Vertex p = this; p != null; p = (p.bound_to==this)?null:p.bound_to)
164 if (good || ignoreProblems) p.reComputeErrorAround();
165 else p.transform(p.oldp, true);
169 /** does NOT update bound pairs! */
170 private boolean transform(Point newp, boolean ignoreProblems) {
172 if (immutableVertices) throw new Error();
174 unApplyQuadricToNeighbor();
177 applyQuadricToNeighbor();
179 if (!ignoreProblems) {
183 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.p2.quadricStale = true;
187 public void checkLegality() {
189 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
190 if (Math.abs(e.dihedralAngle()) > (Math.PI * 0.9) ||
191 Math.abs(e.next.dihedralAngle()) > (Math.PI * 0.9)) illegal = true;
192 if (e.t.aspect() < 0.1) illegal = true;
195 if (!illegal) triangles.range(oldp, this.p, (Visitor<T>)this);
198 public void reComputeErrorAround() {
200 if (nearest_in_other_mesh != null)
201 nearest_in_other_mesh.reComputeError();
202 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
203 e.p2.reComputeError();
206 public boolean visit(Object o) {
207 if (o instanceof Vertex)
208 return ((Vertex)o).e != null && ((Vertex)o).norm().dot(Vertex.this.norm()) >= 0;
210 if (illegal) return false;
211 for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
212 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { illegal = true; }
214 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { illegal = true; }
215 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { illegal = true; }
216 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { illegal = true; }
222 public E getFreeIncident() {
223 E ret = getFreeIncident(e, e);
224 if (ret != null) return ret;
225 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
226 System.out.println(e + " " + e.t);
227 throw new Error("unable to find free incident to " + this);
230 public E getFreeIncident(E start, E before) {
231 for(E e = start; e!=null; e=e.pair.next==before?null:e.pair.next)
232 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null)
237 public E getE(Point p2) {
238 Vertex v = vertices.get(p2);
239 if (v==null) return null;
242 public E getE(Vertex p2) {
243 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
244 if (e.p1 == this && e.p2 == p2) return e;
248 private void glNormal(GL gl) {
250 gl.glNormal3f(norm.x, norm.y, norm.z);
253 Vec norm = new Vec(0, 0, 0);
254 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
256 norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
260 public boolean isBoundTo(Vertex p) {
261 for(Vertex px = p; px!=null; px=(px.bound_to==p?null:px.bound_to))
267 public void unbind() { bound_to = this; binding = Matrix.ONE; }
268 public void bind(Vertex p) { bind(p, Matrix.ONE); }
269 public void bind(Vertex p, Matrix binding) {
270 if (isBoundTo(p)) return;
271 Vertex temp_bound_to = p.bound_to;
272 Matrix temp_binding = p.binding;
273 p.bound_to = this.bound_to;
274 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
275 this.bound_to = temp_bound_to;
276 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
280 public class BindingGroup {
281 private HashSet<E> set = new HashSet<E>();
282 public BindingGroup bind_others;
283 public BindingGroup other() { return bind_others; }
284 public BindingGroup(BindingGroup bind_others) { this.bind_others = bind_others; }
285 public BindingGroup() { this.bind_others = new BindingGroup(this); }
286 public BindingGroup(E e) { this(); set.add(e); }
287 public void add(E e) {
288 if (set.contains(e)) return;
290 BindingGroup e_bind_peers = e.bind_peers;
291 BindingGroup e_bind_to = e.bind_to;
293 e.bind_to = bind_others;
294 for (E epeer : e_bind_peers.set) add(epeer);
295 for (E eother : e_bind_to.set) bind_others.add(eother);
297 for(E eother : bind_others.set) {
298 if (e.next.bind_to.set.contains(eother.prev)) {
299 e.next.next.bindEdge(eother.prev.prev);
301 if (e.prev.bind_to.set.contains(eother.next)) {
302 e.prev.prev.bindEdge(eother.next.next);
307 public void dobind(E e) {
308 for(E ebound : set) {
309 e.p1.bind(ebound.p2);
310 e.p2.bind(ebound.p1);
313 public void shatter(BindingGroup bg1, BindingGroup bg2) {
315 e.shatter(e.midpoint(), bg1, bg2);
320 /** [UNIQUE] an edge */
321 public final class E implements Comparable<E> {
323 public final Vertex p1, p2;
324 T t; // triangle to our "left"
325 E prev; // previous half-edge
326 E next; // next half-edge
327 E pair; // partner half-edge
328 public BindingGroup bind_peers = new BindingGroup(this);
329 public BindingGroup bind_to = bind_peers.other();
330 boolean shattered = false;
332 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
334 public float stretchRatio() {
335 Vertex nearest = error_against.nearest(midpoint());
336 float nearest_distance = midpoint().distance(nearest.p);
337 float other_distance =
338 (p1.p.distance(error_against.nearest(p1.p).p)+
339 p2.p.distance(error_against.nearest(p2.p).p))/2;
340 return nearest_distance/other_distance;
342 public float comparator() {
346 //return t==null?0:(1/t.aspect());
348 public int compareTo(E e) {
349 return e.comparator() > comparator() ? 1 : -1;
351 public void bindEdge(E e) { bind_to.add(e); }
352 public void dobind() { bind_to.dobind(this); }
354 public Point shatter() { return shatter(midpoint(), null, null); }
355 public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
356 if (shattered || destroyed) return mid;
363 int old_colorclass = t==null ? 0 : t.colorclass;
364 if (bg1==null) bg1 = new BindingGroup();
365 if (bg2==null) bg2 = new BindingGroup();
366 BindingGroup old_bind_to = bind_to;
367 bind_peers.shatter(bg1, bg2);
368 old_bind_to.shatter(bg2.other(), bg1.other());
372 newT(r.p, p1.p, mid, null, old_colorclass);
373 newT(r.p, mid, p2.p, null, old_colorclass);
374 bg1.add(p1.getE(mid));
375 bg2.add(p2.getE(mid).pair);
379 public boolean destroyed = false;
380 public void destroy() {
381 if (destroyed) return;
383 pair.destroyed = true;
385 if (t != null) t.destroy();
388 if (pair.t != null) pair.t.destroy();
391 if (next.t != null) next.t.destroy();
392 if (prev.t != null) prev.t.destroy();
396 if (pair.next.t != null) pair.next.t.destroy();
397 if (pair.prev.t != null) pair.next.t.destroy();
403 this.bind_peers = null;
404 pair.bind_peers = null;
405 pair.prev.next = next;
406 next.prev = pair.prev;
407 prev.next = pair.next;
409 if (p1.e == this) p1.e = prev.next;
410 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
413 private void sync() {
414 this.prev.next = this;
415 this.next.prev = this;
416 this.pair.pair = this;
417 bind_peers.add(this);
418 if (this.next.p1 != p2) throw new Error();
419 if (this.prev.p2 != p1) throw new Error();
420 if (this.p1.e == null) this.p1.e = this;
421 if (!added) added = true;
423 private boolean added = false;
425 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
427 public double dihedralAngle() {
428 Vec v1 = t.norm().times(-1);
429 Vec v2 = pair.t.norm().times(-1);
430 return Math.acos(v1.norm().dot(v2.norm()));
433 /** angle between this half-edge and the next */
434 public double angle() {
435 Vec v1 = next.p2.p.minus(p2.p);
436 Vec v2 = this.p1.p.minus(p2.p);
437 return Math.acos(v1.norm().dot(v2.norm()));
440 public void makeAdjacent(E e) {
441 if (this.next == e) return;
442 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
443 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
445 E freeIncident = p2.getFreeIncident(e, this);
447 e.prev.next = freeIncident.next;
448 freeIncident.next.prev = e.prev;
450 freeIncident.next = this.next;
451 this.next.prev = freeIncident;
460 /** creates an isolated edge out in the middle of space */
461 public E(Point p1, Point p2) {
462 if (vertices.get(p1) != null) throw new Error();
463 if (vertices.get(p2) != null) throw new Error();
464 this.p1 = new Vertex(p1);
465 this.p2 = new Vertex(p2);
466 this.prev = this.next = this.pair = new E(this, this, this);
468 this.p2.e = this.pair;
472 /** adds a new half-edge from prev.p2 to p2 */
473 public E(E prev, Point p) {
475 p2 = vertices.get(p);
476 if (p2 == null) p2 = new Vertex(p);
480 if (p2.getE(p1) != null) throw new Error();
482 this.next = this.pair = new E(this, this, prev.next);
484 E q = p2.getFreeIncident();
486 this.next.prev = this;
488 this.prev.next = this;
489 this.pair = new E(q, this, z);
491 if (p2.e==null) p2.e = this.pair;
495 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
496 public E(E prev, E pair, E next) {
504 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); }
505 public boolean has(Vertex v) { return v==p1 || v==p2; }
506 public float length() { return p1.p.minus(p2.p).mag(); }
507 public String toString() { return p1+"->"+p2; }
511 public E makeE(Point p1, Point p2) {
512 Vertex v1 = vertices.get(p1);
513 Vertex v2 = vertices.get(p2);
514 if (v1 != null && v2 != null) {
516 if (e != null) return e;
518 if (e != null) return e;
520 if (v1 != null) return new E(v1.getFreeIncident(), p2);
521 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
522 return new E(p1, p2);
524 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
526 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
527 float dot = norm.dot(norm2);
528 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
529 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
531 E e12 = makeE(p1, p2);
532 E e23 = makeE(p2, p3);
533 E e31 = makeE(p3, p1);
534 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
535 e12.makeAdjacent(e23);
536 e23.makeAdjacent(e31);
537 e31.makeAdjacent(e12);
539 T ret = e12.makeT(colorclass);
540 if (e12.t == null) throw new Error();
541 if (e23.t == null) throw new Error();
542 if (e31.t == null) throw new Error();
546 /** [UNIQUE] a triangle (face) */
547 public final class T extends Triangle {
549 public final int color;
550 public final int colorclass;
552 T(E e1, int colorclass) {
556 if (e1==e2 || e1==e3) throw new Error();
557 if (e3.next!=e1) throw new Error();
558 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
561 e1.next.next.t = this;
563 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
565 int color = Math.abs(random.nextInt());
568 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
569 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
570 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
574 this.colorclass = colorclass;
577 public E e1() { return e1; }
578 public E e2() { return e1.next; }
579 public E e3() { return e1.prev; }
580 public Vertex v1() { return e1.p1; }
581 public Vertex v2() { return e1.p2; }
582 public Vertex v3() { return e1.next.p2; }
583 public Point p1() { return e1.p1.p; }
584 public Point p2() { return e1.p2.p; }
585 public Point p3() { return e1.next.p2.p; }
586 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
587 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
589 public void removeFromRTree() { triangles.remove(this); }
590 public void addToRTree() { triangles.insert(this); }
591 public void destroy() { triangles.remove(this); }
592 public void reinsert() { triangles.remove(this); triangles.add(this); }
594 public boolean shouldBeDrawn() {
595 if (e1().bind_to.set.size() == 0) return false;
596 if (e2().bind_to.set.size() == 0) return false;
597 if (e3().bind_to.set.size() == 0) return false;
601 /** issue gl.glVertex() for each of the triangle's points */
602 public void glVertices(GL gl) {
603 if (!shouldBeDrawn()) return;
605 Point p1 = v1().oldp;
606 Point p2 = v2().oldp;
607 Point p3 = v3().oldp;
608 if (p1==null || p2==null || p3==null) return;