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.berkeley.qfat.geom.HasBindingGroup;
10 import edu.wlu.cs.levy.CG.KDTree;
11 import edu.berkeley.qfat.geom.Point;
12 import com.infomatiq.jsi.IntProcedure;
14 public class Mesh implements Iterable<Mesh.T> {
16 public static final float EPSILON = (float)0.0001;
17 public static final Random random = new Random();
19 private RTree<T> triangles = new RTree<T>();
20 private PointSet<Vertex> vertices = new PointSet<Vertex>();
22 public boolean immutableVertices;
23 public Mesh error_against = null;
24 public double error = 0;
26 public Mesh(boolean immutableVertices) { this.immutableVertices = immutableVertices; }
28 public void makeVerticesImmutable() { this.immutableVertices = true; }
29 public float error() { return (float)error; }
31 public int size() { return vertices.size(); }
32 public Iterable<Vertex> vertices() { return vertices; }
33 public Iterator<T> iterator() { return triangles.iterator(); }
35 public void rebindPoints() {
37 for(Mesh.T t : this) {
42 // ask edges to re-implement their bindings
43 for(Mesh.T t : this) {
48 System.out.println("rebound!");
51 public void transform(Matrix m) {
52 ArrayList<Vertex> set = new ArrayList<Vertex>();
53 for(Vertex v : vertices) set.add(v);
54 for(Vertex v : set) v.transform(m.times(v.p), true, null);
55 for(Vertex v : set) v.goodp = v.p;
58 public void rebuild() { /*vertices.rebuild();*/ }
59 public Vec diagonal() { return vertices.diagonal(); }
60 public Point centroid() { return vertices.centroid(); }
61 public Vertex nearest(Point p) { return vertices.nearest(p); }
63 /** compute the volume of the mesh */
64 public float volume() {
67 double area = t.area();
68 Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
69 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
70 double height = Math.abs(t.norm().dot(origin_to_centroid));
71 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
77 // Vertexices //////////////////////////////////////////////////////////////////////////////
79 /** a vertex in the mesh */
80 public final class Vertex extends HasQuadric implements Visitor {
81 public Point p, goodp;
83 E e; // some edge *leaving* this point
85 private boolean illegal = false;
87 public Point getPoint() { return p; }
88 public float error() { return olderror; }
90 private Vertex(Point p) {
94 if (vertices.get(p) != null) throw new Error();
98 public void reinsert() {
99 vertices.remove(this);
101 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.t.reinsert();
104 public float olderror = 0;
105 public void setError(float nerror) {
111 public float averageTriangleArea() {
114 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
120 public float averageEdgeLength() {
123 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
130 public Matrix _recomputeFundamentalQuadric() {
131 Matrix m = Matrix.ZERO;
133 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
134 m = m.plus(e.t.norm().fundamentalQuadric(e.t.centroid()));
138 m = m.plus(norm().fundamentalQuadric(this.p).times(count));
141 return m.times(1/(float)count);
144 public HasQuadric nearest() { return error_against==null ? null : error_against.vertices.nearest(p, this); }
145 public void computeError() {
146 if (error_against==null) return;
148 nearest_in_other_mesh != null
149 ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p)
150 : nearest().fundamentalQuadric().preAndPostMultiply(p);
151 if (quadric_count != 0)
152 nerror = (nerror + quadric.preAndPostMultiply(p))/(quadric_count+1);
154 if (!immutableVertices && quadric_count == 0) {
155 //nerror = Math.max(nerror, 0.4f);
158 //System.out.println(nerror);
159 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
160 double ang = e.dihedralAngle();
161 if (ang > Math.PI) throw new Error();
162 if (ang < -Math.PI) throw new Error();
163 float minangle = (float)(Math.PI * 0.8);
164 //nerror += ((ang / Math.PI)*(ang/Math.PI)) * e.length() * 0.05;
166 nerror += (1-e.t.quality())*0.0001;
167 if (ang > minangle) nerror += (ang - minangle);
169 //System.out.println(((ang / Math.PI)*(ang/Math.PI)) * 0.000001);
171 if (e.t.aspect() < 0.2) {
172 nerror += (0.2-e.t.aspect()) * 10;
176 if (!immutableVertices) {
177 Vertex n = (Vertex)nearest();
178 float d = norm().dot(n.norm());
179 if (d > 1 || d < -1) throw new Error();
181 nerror *= (2.0f - d);
183 nerror += 0.0003 * (2.0f + d);
184 nerror *= (2.0f + d);
191 public boolean move(Matrix m, boolean ignoreProblems) {
196 // t2' = t2.getMatrix(t1) * t1'
197 // t2' = t2.getMatrix(t1) * M * t1
198 // t1 = t1.getMatrix(t2) * t2
199 // M * t1 = M * t1.getMatrix(t2) * t2
201 if (bindingGroup!=null && this != bindingGroup.getMaster()) {
202 Matrix v = getBindingMatrix(bindingGroup.getMaster());
203 return ((Vertex)bindingGroup.getMaster()).move(v.inverse().times(m).times(v), ignoreProblems);
206 if (bindingGroup != null) {
208 for(int i=0; i<20 && !m.equals(m2); i++) {
209 m2 = m.times(getConstraint());
210 //System.out.println(m.minus(m2));
212 if (!m.equals(m2)) return true;
216 Point pt = m.times(this.p);
217 for(Vertex v : (Iterable<Vertex>)getBoundPeers()) {
218 Point pt2 = v.getBindingMatrix(this).times(pt);
220 if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) > 5)
221 throw new Error(v.p+" "+pt2+"\n"+op+" "+pt+"\n"+v.getBindingMatrix(this));
222 if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) < 1/5) throw new Error();
224 good &= v.transform(pt2, ignoreProblems, v.getBindingMatrix(this));
227 if (!good && !ignoreProblems) {
228 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
229 v.transform(v.oldp, true, null);
232 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
233 v.recomputeFundamentalQuadricIfNeighborChanged();
234 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
235 v.reComputeErrorAround();
239 public boolean ok = true;
241 /** does NOT update bound pairs! */
242 private boolean transform(Point newp, boolean ignoreProblems, Matrix yes) {
244 if (immutableVertices) throw new Error();
246 unApplyQuadricToNeighbor();
249 boolean illegalbefore = illegal;
252 if (this.p.minus(newp).mag() > 0.1 && !ignoreProblems) {
254 throw new Exception(""+this.p.minus(newp).mag()+" "+ignoreProblems+" "+yes);
255 } catch(Exception e) {
264 applyQuadricToNeighbor();
266 if (!ignoreProblems) {
269 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
270 e.p2.quadricStale = true;
271 return !illegal || (illegalbefore && illegal);
274 public void checkLegality() {
276 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
277 if (Math.abs(e.dihedralAngle()) > (Math.PI * 0.9) ||
278 Math.abs(e.next.dihedralAngle()) > (Math.PI * 0.9)) illegal = true;
279 if (e.t.aspect() < 0.2) illegal = true;
282 if (!illegal) triangles.range(oldp, this.p, (Visitor<T>)this);
285 public void reComputeErrorAround() {
287 if (nearest_in_other_mesh != null)
288 nearest_in_other_mesh.reComputeError();
289 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
290 e.p2.reComputeError();
293 public boolean visit(Object o) {
294 if (o instanceof Vertex)
295 return ((Vertex)o).e != null && ((Vertex)o).norm().dot(Vertex.this.norm()) >= 0;
297 if (illegal) return false;
298 for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
299 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { illegal = true; }
301 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { illegal = true; }
302 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { illegal = true; }
303 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { illegal = true; }
309 public E getFreeIncident() {
310 E ret = getFreeIncident(e, e);
311 if (ret != null) return ret;
312 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
313 System.out.println(e + " " + e.t);
314 throw new Error("unable to find free incident to " + this);
317 public E getFreeIncident(E start, E before) {
318 for(E e = start; e!=null; e=e.pair.next==before?null:e.pair.next)
319 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null)
324 public E getE(Point p2) {
325 Vertex v = vertices.get(p2);
326 if (v==null) return null;
329 public E getE(Vertex p2) {
330 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
331 if (e.p1 == this && e.p2 == p2) return e;
335 private void glNormal(GL gl) {
337 gl.glNormal3f(norm.x, norm.y, norm.z);
340 Vec norm = new Vec(0, 0, 0);
341 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
343 norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
347 public void bindTo(Vertex p) { bindTo(Matrix.ONE, p); }
351 /** [UNIQUE] an edge */
352 public final class E extends HasBindingGroup implements Comparable<E> {
354 public final Vertex p1, p2;
355 T t; // triangle to our "left"
356 E prev; // previous half-edge
357 E next; // next half-edge
358 E pair; // partner half-edge
359 boolean shattered = false;
361 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
363 public void bindingGroupChanged(edu.berkeley.qfat.geom.BindingGroup newBindingGroup_) {
365 edu.berkeley.qfat.geom.BindingGroup<E> newBindingGroup =
366 (edu.berkeley.qfat.geom.BindingGroup<E>)newBindingGroup_;
367 if (newBindingGroup==null) return;
368 if (this==newBindingGroup.getMaster()) return;
369 HashSet<E> nbg = new HashSet<E>();
370 for(E eother : (Iterable<E>)newBindingGroup) nbg.add(eother);
371 for(E eother : nbg) {
372 if (next==null || prev==null) continue;
373 if (eother.next==null || eother.prev==null) continue;
375 if (next.isBoundTo(eother.pair.prev.pair) && !prev.isBoundTo(eother.pair.next.pair))
376 prev.bindTo(next.getBindingMatrix(eother.pair.prev.pair), eother.pair.next.pair);
377 if (!next.isBoundTo(eother.pair.prev.pair) && prev.isBoundTo(eother.pair.next.pair))
378 next.bindTo(prev.getBindingMatrix(eother.pair.next.pair), eother.pair.prev.pair);
381 if (next.isBoundTo(eother.prev) && !prev.isBoundTo(eother.next))
382 prev.bindTo(next.getBindingMatrix(eother.prev), eother.next);
383 if (!next.isBoundTo(eother.prev) && prev.isBoundTo(eother.next))
384 next.bindTo(prev.getBindingMatrix(eother.next), eother.prev);
386 if (next.isBoundTo(eother.next) && !prev.isBoundTo(eother.prev))
387 prev.bindTo(next.getBindingMatrix(eother.next), eother.prev);
388 if (!next.isBoundTo(eother.next) && prev.isBoundTo(eother.prev))
389 next.bindTo(prev.getBindingMatrix(eother.prev), eother.next);
394 public float stretchRatio() {
395 Vertex nearest = error_against.nearest(midpoint());
396 float nearest_distance = midpoint().distance(nearest.p);
397 float other_distance =
398 (p1.p.distance(error_against.nearest(p1.p).p)+
399 p2.p.distance(error_against.nearest(p2.p).p))/2;
400 return nearest_distance/other_distance;
402 public float comparator() {
405 public int compareTo(E e) {
406 return e.comparator() > comparator() ? 1 : -1;
408 public void bindEdge(E e, Matrix m) {
410 pair._bindEdge(e.pair, m);
412 public void _bindEdge(E e, Matrix m) {
415 //assumes edges are identical length at binding time
416 Vec reflectionPlaneNormal = e.p2.p.minus(e.p1.p).norm();
417 float a = reflectionPlaneNormal.x;
418 float b = reflectionPlaneNormal.y;
419 float c = reflectionPlaneNormal.z;
420 Matrix reflectionMatrix =
421 new Matrix( 1-2*a*a, -2*a*b, -2*a*c, 0,
422 -2*a*b, 1-2*b*b, -2*b*c, 0,
423 -2*a*c, -2*b*c, 1-2*c*c, 0,
425 m = m.times(Matrix.translate(e.midpoint().minus(Point.ORIGIN))
426 .times(reflectionMatrix)
427 .times(Matrix.translate(Point.ORIGIN.minus(e.midpoint()))));
428 System.out.println(reflectionPlaneNormal);
429 System.out.println(" " + p1.p + " " + m.times(e.p1.p));
430 System.out.println(" " + p2.p + " " + m.times(e.p2.p));
433 if (m.times(e.p1.p).minus(p1.p).mag() > EPSILON) throw new Error();
434 if (m.times(e.p2.p).minus(p2.p).mag() > EPSILON) throw new Error();
439 public void dobind() {
440 for(E e : (Iterable<E>)getBoundPeers()) {
441 if (e==this) continue;
442 p1.bindTo(getBindingMatrix(e), e.p1);
443 p2.bindTo(getBindingMatrix(e), e.p2);
444 e.p1.setConstraint(getConstraint());
445 e.p2.setConstraint(getConstraint());
449 public Point shatter() {
450 if (shattered || destroyed) return null;
456 for(E e : (Iterable<E>)getBoundPeers()) {
459 E pnext = e.pair.next;
460 E pprev = e.pair.prev;
461 Point mid = e.midpoint();
462 Vertex r = e.next.p2;
463 Vertex l = e.pair.next.p2;
467 newT(r.p, e.p1.p, mid, null, 0);
468 newT(r.p, mid, e.p2.p, null, 0);
469 newT(l.p, mid, e.p1.p, null, 0);
470 newT(l.p, e.p2.p, mid, null, 0);
473 for(E e : (Iterable<E>)getBoundPeers()) {
474 Point mid = e.midpoint();
476 first = e.p1.getE(mid);
479 firstq = e.p2.getE(mid).pair;
482 e.p1.getE(mid). bindTo(e.getBindingMatrix(firste), first);
483 e.p1.getE(mid).pair. bindTo(e.getBindingMatrix(firste), first.pair);
484 e.p2.getE(mid).pair. bindTo(e.getBindingMatrix(firste), firstq);
485 e.p2.getE(mid).pair.pair.bindTo(e.getBindingMatrix(firste), firstq.pair);
488 first.setConstraint(firste.getConstraint());
489 firstq.setConstraint(firste.getConstraint());
494 public boolean destroyed = false;
495 public void destroy() {
496 if (destroyed) return;
498 pair.destroyed = true;
500 if (t != null) t.destroy();
503 if (pair.t != null) pair.t.destroy();
506 if (next.t != null) next.t.destroy();
507 if (prev.t != null) prev.t.destroy();
511 if (pair.next.t != null) pair.next.t.destroy();
512 if (pair.prev.t != null) pair.next.t.destroy();
516 pair.prev.next = next;
517 next.prev = pair.prev;
518 prev.next = pair.next;
520 if (p1.e == this) p1.e = prev.next;
521 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
524 private void sync() {
525 this.prev.next = this;
526 this.next.prev = this;
527 this.pair.pair = this;
528 if (this.next.p1 != p2) throw new Error();
529 if (this.prev.p2 != p1) throw new Error();
530 if (this.p1.e == null) this.p1.e = this;
531 if (!added) added = true;
533 private boolean added = false;
535 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
537 public double dihedralAngle() {
538 Vec v1 = t.norm().times(-1);
539 Vec v2 = pair.t.norm().times(-1);
540 double prod = v1.norm().dot(v2.norm());
541 prod = Math.min(1,prod);
542 prod = Math.max(-1,prod);
543 double ret = Math.acos(prod);
544 if (Double.isNaN(ret)) throw new Error("nan! " + prod);
548 /** angle between this half-edge and the next */
549 public double angle() {
550 Vec v1 = next.p2.p.minus(p2.p);
551 Vec v2 = this.p1.p.minus(p2.p);
552 return Math.acos(v1.norm().dot(v2.norm()));
555 public void makeAdjacent(E e) {
556 if (this.next == e) return;
557 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
558 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free ");
560 E freeIncident = p2.getFreeIncident(e, this);
562 e.prev.next = freeIncident.next;
563 freeIncident.next.prev = e.prev;
565 freeIncident.next = this.next;
566 this.next.prev = freeIncident;
575 /** creates an isolated edge out in the middle of space */
576 public E(Point p1, Point p2) {
577 if (vertices.get(p1) != null) throw new Error();
578 if (vertices.get(p2) != null) throw new Error();
579 this.p1 = new Vertex(p1);
580 this.p2 = new Vertex(p2);
581 this.prev = this.next = this.pair = new E(this, this, this);
583 this.p2.e = this.pair;
587 /** adds a new half-edge from prev.p2 to p2 */
588 public E(E prev, Point p) {
590 p2 = vertices.get(p);
591 if (p2 == null) p2 = new Vertex(p);
595 if (p2.getE(p1) != null) throw new Error();
597 this.next = this.pair = new E(this, this, prev.next);
599 E q = p2.getFreeIncident();
601 this.next.prev = this;
603 this.prev.next = this;
604 this.pair = new E(q, this, z);
606 if (p2.e==null) p2.e = this.pair;
610 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
611 public E(E prev, E pair, E next) {
619 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); }
620 public boolean has(Vertex v) { return v==p1 || v==p2; }
621 public float length() { return p1.p.minus(p2.p).mag(); }
622 public String toString() { return p1+"->"+p2; }
626 public E makeE(Point p1, Point p2) {
627 Vertex v1 = vertices.get(p1);
628 Vertex v2 = vertices.get(p2);
629 if (v1 != null && v2 != null) {
631 if (e != null) return e;
633 if (e != null) return e;
635 if (v1 != null) return new E(v1.getFreeIncident(), p2);
636 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
637 return new E(p1, p2);
639 public boolean coalesce = false;
640 private static float round(float f) {
641 return Math.round(f*1000)/1000f;
643 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
646 for(Vertex v : vertices) { if (p1.distance(v.p) < EPSILON) { p1 = v.p; break; } }
647 for(Vertex v : vertices) { if (p2.distance(v.p) < EPSILON) { p2 = v.p; break; } }
648 for(Vertex v : vertices) { if (p3.distance(v.p) < EPSILON) { p3 = v.p; break; } }
650 p1 = new Point(round(p1.x), round(p1.y), round(p1.z));
651 p2 = new Point(round(p2.x), round(p2.y), round(p2.z));
652 p3 = new Point(round(p3.x), round(p3.y), round(p3.z));
656 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
657 float dot = norm.dot(norm2);
658 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
659 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
661 E e12 = makeE(p1, p2);
662 E e23 = makeE(p2, p3);
663 E e31 = makeE(p3, p1);
664 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
665 e12.makeAdjacent(e23);
666 e23.makeAdjacent(e31);
667 e31.makeAdjacent(e12);
669 T ret = e12.makeT(colorclass);
670 if (e12.t == null) throw new Error();
671 if (e23.t == null) throw new Error();
672 if (e31.t == null) throw new Error();
676 /** [UNIQUE] a triangle (face) */
677 public final class T extends Triangle {
679 public final int color;
680 public final int colorclass;
682 T(E e1, int colorclass) {
686 if (e1==e2 || e1==e3) throw new Error();
687 if (e3.next!=e1) throw new Error();
688 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
691 e1.next.next.t = this;
693 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
695 int color = Math.abs(random.nextInt());
698 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
699 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
700 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
704 this.colorclass = colorclass;
707 public E e1() { return e1; }
708 public E e2() { return e1.next; }
709 public E e3() { return e1.prev; }
710 public Vertex v1() { return e1.p1; }
711 public Vertex v2() { return e1.p2; }
712 public Vertex v3() { return e1.next.p2; }
713 public Point p1() { return e1.p1.p; }
714 public Point p2() { return e1.p2.p; }
715 public Point p3() { return e1.next.p2.p; }
716 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
717 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
719 public void removeFromRTree() { triangles.remove(this); }
720 public void addToRTree() { triangles.insert(this); }
721 public void destroy() { triangles.remove(this); }
722 public void reinsert() { triangles.remove(this); triangles.add(this); }
724 public boolean shouldBeDrawn() {
726 if (e1().bindingGroupSize() <= 1) return false;
727 if (e2().bindingGroupSize() <= 1) return false;
728 if (e3().bindingGroupSize() <= 1) return false;
733 /** issue gl.glVertex() for each of the triangle's points */
734 public void glVertices(GL gl) {
735 if (!shouldBeDrawn()) return;
737 Point p1 = v1().goodp;
738 Point p2 = v2().goodp;
739 Point p3 = v3().goodp;