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 boolean visible = false;
89 public Point getPoint() { return p; }
90 public float error() { return olderror; }
92 private Vertex(Point p) {
96 if (vertices.get(p) != null) throw new Error();
100 public void reinsert() {
101 vertices.remove(this);
103 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.t.reinsert();
106 public float olderror = 0;
107 public void setError(float nerror) {
113 public Vertex hack(GL gl, Point mouse) {
114 double dist = Double.MAX_VALUE;
116 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
117 Vertex v = e.getOther(this);
118 double dist2 = v.getPoint().glProject(gl).distance(mouse);
119 if ((cur==null || dist2 < dist) && v.visible) {
127 public float averageTriangleArea() {
130 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
136 public float averageEdgeLength() {
139 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
146 public Matrix _recomputeFundamentalQuadric() {
147 Matrix m = Matrix.ZERO;
149 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
150 m = m.plus(e.t.norm().fundamentalQuadric(e.t.centroid()));
154 m = m.plus(norm().fundamentalQuadric(this.p).times(count));
157 return m.times(1/(float)count);
160 public HasQuadric nearest() { return error_against==null ? null : error_against.vertices.nearest(p, this); }
161 public void computeError() {
162 if (error_against==null) return;
164 nearest_in_other_mesh != null
165 ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p)
166 : nearest().fundamentalQuadric().preAndPostMultiply(p);
167 if (quadric_count != 0)
168 nerror = (nerror + quadric.preAndPostMultiply(p))/(quadric_count+1);
170 if (!immutableVertices && quadric_count == 0) {
171 //nerror = Math.max(nerror, 0.4f);
174 //System.out.println(nerror);
175 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
176 double ang = e.dihedralAngle();
177 if (ang > Math.PI) throw new Error();
178 if (ang < -Math.PI) throw new Error();
179 float minangle = (float)(Math.PI * 0.8);
180 //nerror += ((ang / Math.PI)*(ang/Math.PI)) * e.length() * 0.05;
182 nerror += (1-e.t.quality())*0.0001;
183 if (ang > minangle) nerror += (ang - minangle);
185 //System.out.println(((ang / Math.PI)*(ang/Math.PI)) * 0.000001);
187 if (e.t.aspect() < 0.2) {
188 nerror += (0.2-e.t.aspect()) * 10;
192 if (!immutableVertices) {
193 Vertex n = (Vertex)nearest();
194 float d = norm().dot(n.norm());
195 if (d > 1 || d < -1) throw new Error();
197 nerror *= (2.0f - d);
199 nerror += 0.0003 * (2.0f + d);
200 nerror *= (2.0f + d);
207 public boolean move(Matrix m, boolean ignoreProblems) {
212 // t2' = t2.getMatrix(t1) * t1'
213 // t2' = t2.getMatrix(t1) * M * t1
214 // t1 = t1.getMatrix(t2) * t2
215 // M * t1 = M * t1.getMatrix(t2) * t2
217 if (bindingGroup!=null && this != bindingGroup.getMaster()) {
218 Matrix v = getBindingMatrix(bindingGroup.getMaster());
219 return ((Vertex)bindingGroup.getMaster()).move(v.inverse().times(m).times(v), ignoreProblems);
222 if (bindingGroup != null) {
224 for(int i=0; i<20 && !m.equals(m2); i++) {
225 m2 = m.times(getConstraint());
226 //System.out.println(m.minus(m2));
228 if (!m.equals(m2)) return true;
232 Point pt = m.times(this.p);
233 for(Vertex v : (Iterable<Vertex>)getBoundPeers()) {
234 Point pt2 = v.getBindingMatrix(this).times(pt);
236 if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) > 5)
237 throw new Error(v.p+" "+pt2+"\n"+op+" "+pt+"\n"+v.getBindingMatrix(this));
238 if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) < 1/5) throw new Error();
240 good &= v.transform(pt2, ignoreProblems, v.getBindingMatrix(this));
243 if (!good && !ignoreProblems) {
244 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
245 v.transform(v.oldp, true, null);
248 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
249 v.recomputeFundamentalQuadricIfNeighborChanged();
250 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
251 v.reComputeErrorAround();
255 public boolean ok = true;
257 /** does NOT update bound pairs! */
258 private boolean transform(Point newp, boolean ignoreProblems, Matrix yes) {
260 if (immutableVertices) throw new Error();
262 unApplyQuadricToNeighbor();
265 boolean illegalbefore = illegal;
268 if (this.p.minus(newp).mag() > 0.1 && !ignoreProblems) {
270 throw new Exception(""+this.p.minus(newp).mag()+" "+ignoreProblems+" "+yes);
271 } catch(Exception e) {
280 applyQuadricToNeighbor();
282 if (!ignoreProblems) {
285 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
286 e.p2.quadricStale = true;
287 return !illegal || (illegalbefore && illegal);
290 public void checkLegality() {
292 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
293 if (Math.abs(e.dihedralAngle()) > (Math.PI * 0.9) ||
294 Math.abs(e.next.dihedralAngle()) > (Math.PI * 0.9)) illegal = true;
295 if (e.t.aspect() < 0.2) illegal = true;
298 if (!illegal) triangles.range(oldp, this.p, (Visitor<T>)this);
301 public void reComputeErrorAround() {
303 if (nearest_in_other_mesh != null)
304 nearest_in_other_mesh.reComputeError();
305 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
306 e.p2.reComputeError();
309 public boolean visit(Object o) {
310 if (o instanceof Vertex)
311 return ((Vertex)o).e != null && ((Vertex)o).norm().dot(Vertex.this.norm()) >= 0;
313 if (illegal) return false;
314 for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
315 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { illegal = true; }
317 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { illegal = true; }
318 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { illegal = true; }
319 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { illegal = true; }
325 public E getEdge() { return e; }
326 public E getFreeIncident() {
327 E ret = getFreeIncident(e, e);
328 if (ret != null) return ret;
329 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
330 System.out.println(e + " " + e.t);
331 throw new Error("unable to find free incident to " + this);
334 public E getFreeIncident(E start, E before) {
335 for(E e = start; e!=null; e=e.pair.next==before?null:e.pair.next)
336 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null)
341 public E getE(Point p2) {
342 Vertex v = vertices.get(p2);
343 if (v==null) return null;
346 public E getE(Vertex p2) {
347 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
348 if (e.p1 == this && e.p2 == p2) return e;
352 private void glNormal(GL gl) {
354 gl.glNormal3f(norm.x, norm.y, norm.z);
357 Vec norm = new Vec(0, 0, 0);
358 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
360 norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
364 public void bindTo(Vertex p) { bindTo(Matrix.ONE, p); }
368 /** [UNIQUE] an edge */
369 public final class E extends HasBindingGroup implements Comparable<E> {
371 public final Vertex p1, p2;
372 T t; // triangle to our "left"
373 E prev; // previous half-edge
374 E next; // next half-edge
375 E pair; // partner half-edge
376 boolean shattered = false;
378 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
380 public Segment getSegment() { return new Segment(p1.getPoint(), p2.getPoint()); }
382 public void bindingGroupChanged(edu.berkeley.qfat.geom.BindingGroup newBindingGroup_) {
384 edu.berkeley.qfat.geom.BindingGroup<E> newBindingGroup =
385 (edu.berkeley.qfat.geom.BindingGroup<E>)newBindingGroup_;
386 if (newBindingGroup==null) return;
387 if (this==newBindingGroup.getMaster()) return;
388 HashSet<E> nbg = new HashSet<E>();
389 for(E eother : (Iterable<E>)newBindingGroup) nbg.add(eother);
390 for(E eother : nbg) {
391 if (next==null || prev==null) continue;
392 if (eother.next==null || eother.prev==null) continue;
394 if (next.isBoundTo(eother.pair.prev.pair) && !prev.isBoundTo(eother.pair.next.pair))
395 prev.bindTo(next.getBindingMatrix(eother.pair.prev.pair), eother.pair.next.pair);
396 if (!next.isBoundTo(eother.pair.prev.pair) && prev.isBoundTo(eother.pair.next.pair))
397 next.bindTo(prev.getBindingMatrix(eother.pair.next.pair), eother.pair.prev.pair);
400 if (next.isBoundTo(eother.prev) && !prev.isBoundTo(eother.next))
401 prev.bindTo(next.getBindingMatrix(eother.prev), eother.next);
402 if (!next.isBoundTo(eother.prev) && prev.isBoundTo(eother.next))
403 next.bindTo(prev.getBindingMatrix(eother.next), eother.prev);
405 if (next.isBoundTo(eother.next) && !prev.isBoundTo(eother.prev))
406 prev.bindTo(next.getBindingMatrix(eother.next), eother.prev);
407 if (!next.isBoundTo(eother.next) && prev.isBoundTo(eother.prev))
408 next.bindTo(prev.getBindingMatrix(eother.prev), eother.next);
413 public float stretchRatio() {
414 Vertex nearest = error_against.nearest(midpoint());
415 float nearest_distance = midpoint().distance(nearest.p);
416 float other_distance =
417 (p1.p.distance(error_against.nearest(p1.p).p)+
418 p2.p.distance(error_against.nearest(p2.p).p))/2;
419 return nearest_distance/other_distance;
421 public float comparator() {
424 public int compareTo(E e) {
425 return e.comparator() > comparator() ? 1 : -1;
427 public void bindEdge(E e, Matrix m) {
429 pair._bindEdge(e.pair, m);
431 public void _bindEdge(E e, Matrix m) {
434 //assumes edges are identical length at binding time
435 Vec reflectionPlaneNormal = e.p2.p.minus(e.p1.p).norm();
436 float a = reflectionPlaneNormal.x;
437 float b = reflectionPlaneNormal.y;
438 float c = reflectionPlaneNormal.z;
439 Matrix reflectionMatrix =
440 new Matrix( 1-2*a*a, -2*a*b, -2*a*c, 0,
441 -2*a*b, 1-2*b*b, -2*b*c, 0,
442 -2*a*c, -2*b*c, 1-2*c*c, 0,
444 m = m.times(Matrix.translate(e.midpoint().minus(Point.ORIGIN))
445 .times(reflectionMatrix)
446 .times(Matrix.translate(Point.ORIGIN.minus(e.midpoint()))));
447 System.out.println(reflectionPlaneNormal);
448 System.out.println(" " + p1.p + " " + m.times(e.p1.p));
449 System.out.println(" " + p2.p + " " + m.times(e.p2.p));
452 if (m.times(e.p1.p).minus(p1.p).mag() > EPSILON) throw new Error();
453 if (m.times(e.p2.p).minus(p2.p).mag() > EPSILON) throw new Error();
458 public void dobind() {
459 for(E e : (Iterable<E>)getBoundPeers()) {
460 if (e==this) continue;
461 p1.bindTo(getBindingMatrix(e), e.p1);
462 p2.bindTo(getBindingMatrix(e), e.p2);
463 e.p1.setConstraint(getConstraint());
464 e.p2.setConstraint(getConstraint());
468 public Point shatter() {
469 if (shattered || destroyed) return null;
475 for(E e : (Iterable<E>)getBoundPeers()) {
478 E pnext = e.pair.next;
479 E pprev = e.pair.prev;
480 Point mid = e.midpoint();
481 Vertex r = e.next.p2;
482 Vertex l = e.pair.next.p2;
486 newT(r.p, e.p1.p, mid, null, 0);
487 newT(r.p, mid, e.p2.p, null, 0);
488 newT(l.p, mid, e.p1.p, null, 0);
489 newT(l.p, e.p2.p, mid, null, 0);
492 for(E e : (Iterable<E>)getBoundPeers()) {
493 Point mid = e.midpoint();
495 first = e.p1.getE(mid);
498 firstq = e.p2.getE(mid).pair;
501 e.p1.getE(mid). bindTo(e.getBindingMatrix(firste), first);
502 e.p1.getE(mid).pair. bindTo(e.getBindingMatrix(firste), first.pair);
503 e.p2.getE(mid).pair. bindTo(e.getBindingMatrix(firste), firstq);
504 e.p2.getE(mid).pair.pair.bindTo(e.getBindingMatrix(firste), firstq.pair);
507 first.setConstraint(firste.getConstraint());
508 firstq.setConstraint(firste.getConstraint());
513 public boolean destroyed = false;
514 public void destroy() {
515 if (destroyed) return;
517 pair.destroyed = true;
519 if (t != null) t.destroy();
522 if (pair.t != null) pair.t.destroy();
525 if (next.t != null) next.t.destroy();
526 if (prev.t != null) prev.t.destroy();
530 if (pair.next.t != null) pair.next.t.destroy();
531 if (pair.prev.t != null) pair.next.t.destroy();
535 pair.prev.next = next;
536 next.prev = pair.prev;
537 prev.next = pair.next;
539 if (p1.e == this) p1.e = prev.next;
540 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
543 private void sync() {
544 this.prev.next = this;
545 this.next.prev = this;
546 this.pair.pair = this;
547 if (this.next.p1 != p2) throw new Error();
548 if (this.prev.p2 != p1) throw new Error();
549 if (this.p1.e == null) this.p1.e = this;
550 if (!added) added = true;
552 private boolean added = false;
554 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
556 public double dihedralAngle() {
557 Vec v1 = t.norm().times(-1);
558 Vec v2 = pair.t.norm().times(-1);
559 double prod = v1.norm().dot(v2.norm());
560 prod = Math.min(1,prod);
561 prod = Math.max(-1,prod);
562 double ret = Math.acos(prod);
563 if (Double.isNaN(ret)) throw new Error("nan! " + prod);
567 /** angle between this half-edge and the next */
568 public double angle() {
569 Vec v1 = next.p2.p.minus(p2.p);
570 Vec v2 = this.p1.p.minus(p2.p);
571 return Math.acos(v1.norm().dot(v2.norm()));
574 public Vertex getOther(Vertex v) {
575 if (this.p1 == v) return p2;
576 if (this.p2 == v) return p1;
580 public void makeAdjacent(E e) {
581 if (this.next == e) return;
582 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
583 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free ");
585 E freeIncident = p2.getFreeIncident(e, this);
587 e.prev.next = freeIncident.next;
588 freeIncident.next.prev = e.prev;
590 freeIncident.next = this.next;
591 this.next.prev = freeIncident;
600 /** creates an isolated edge out in the middle of space */
601 public E(Point p1, Point p2) {
602 if (vertices.get(p1) != null) throw new Error();
603 if (vertices.get(p2) != null) throw new Error();
604 this.p1 = new Vertex(p1);
605 this.p2 = new Vertex(p2);
606 this.prev = this.next = this.pair = new E(this, this, this);
608 this.p2.e = this.pair;
612 /** adds a new half-edge from prev.p2 to p2 */
613 public E(E prev, Point p) {
615 p2 = vertices.get(p);
616 if (p2 == null) p2 = new Vertex(p);
620 if (p2.getE(p1) != null) throw new Error();
622 this.next = this.pair = new E(this, this, prev.next);
624 E q = p2.getFreeIncident();
626 this.next.prev = this;
628 this.prev.next = this;
629 this.pair = new E(q, this, z);
631 if (p2.e==null) p2.e = this.pair;
635 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
636 public E(E prev, E pair, E next) {
644 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); }
645 public boolean has(Vertex v) { return v==p1 || v==p2; }
646 public float length() { return p1.p.minus(p2.p).mag(); }
647 public String toString() { return p1+"->"+p2; }
651 public E makeE(Point p1, Point p2) {
652 Vertex v1 = vertices.get(p1);
653 Vertex v2 = vertices.get(p2);
654 if (v1 != null && v2 != null) {
656 if (e != null) return e;
658 if (e != null) return e;
660 if (v1 != null) return new E(v1.getFreeIncident(), p2);
661 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
662 return new E(p1, p2);
664 public boolean coalesce = false;
665 private static float round(float f) {
666 return Math.round(f*1000)/1000f;
668 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
671 for(Vertex v : vertices) { if (p1.distance(v.p) < EPSILON) { p1 = v.p; break; } }
672 for(Vertex v : vertices) { if (p2.distance(v.p) < EPSILON) { p2 = v.p; break; } }
673 for(Vertex v : vertices) { if (p3.distance(v.p) < EPSILON) { p3 = v.p; break; } }
675 p1 = new Point(round(p1.x), round(p1.y), round(p1.z));
676 p2 = new Point(round(p2.x), round(p2.y), round(p2.z));
677 p3 = new Point(round(p3.x), round(p3.y), round(p3.z));
681 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
682 float dot = norm.dot(norm2);
683 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
684 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
686 E e12 = makeE(p1, p2);
687 E e23 = makeE(p2, p3);
688 E e31 = makeE(p3, p1);
689 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
690 e12.makeAdjacent(e23);
691 e23.makeAdjacent(e31);
692 e31.makeAdjacent(e12);
694 T ret = e12.makeT(colorclass);
695 if (e12.t == null) throw new Error();
696 if (e23.t == null) throw new Error();
697 if (e31.t == null) throw new Error();
701 private int max_serial = 0;
702 /** [UNIQUE] a triangle (face) */
703 public final class T extends Triangle {
705 public final int color;
706 public final int colorclass;
708 public final int serial = max_serial++;
709 public boolean occluded;
711 T(E e1, int colorclass) {
715 if (e1==e2 || e1==e3) throw new Error();
716 if (e3.next!=e1) throw new Error();
717 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
720 e1.next.next.t = this;
722 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
724 int color = Math.abs(random.nextInt());
727 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
728 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
729 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
733 this.colorclass = colorclass;
736 public E e1() { return e1; }
737 public E e2() { return e1.next; }
738 public E e3() { return e1.prev; }
739 public Vertex v1() { return e1.p1; }
740 public Vertex v2() { return e1.p2; }
741 public Vertex v3() { return e1.next.p2; }
742 public Point p1() { return e1.p1.p; }
743 public Point p2() { return e1.p2.p; }
744 public Point p3() { return e1.next.p2.p; }
745 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
746 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
748 public void removeFromRTree() { triangles.remove(this); }
749 public void addToRTree() { triangles.insert(this); }
750 public void destroy() { triangles.remove(this); }
751 public void reinsert() { triangles.remove(this); triangles.add(this); }
753 public boolean shouldBeDrawn() {
755 if (e1().bindingGroupSize() <= 1) return false;
756 if (e2().bindingGroupSize() <= 1) return false;
757 if (e3().bindingGroupSize() <= 1) return false;
762 public void glTriangle(GL gl, Matrix m) {
763 gl.glPushName(serial);
764 gl.glBegin(GL.GL_TRIANGLES);
770 /** issue gl.glVertex() for each of the triangle's points */
771 public void glVertices(GL gl, Matrix m) {
772 if (!shouldBeDrawn()) return;
773 super.glVertices(gl, m);