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) {
114 public Vertex hack(GL gl, Point mouse) {
115 double dist = Double.MAX_VALUE;
117 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
118 Vertex v = e.getOther(this);
119 double dist2 = v.getPoint().glProject(gl).distance(mouse);
120 if ((cur==null || dist2 < dist) && v.visible) {
129 public float averageTriangleArea() {
132 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
138 public float averageEdgeLength() {
141 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
148 public Matrix _recomputeFundamentalQuadric() {
149 Matrix m = Matrix.ZERO;
151 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
152 m = m.plus(e.t.norm().fundamentalQuadric(e.t.centroid()));
156 m = m.plus(norm().fundamentalQuadric(this.p).times(count));
159 return m.times(1/(float)count);
162 public HasQuadric nearest() { return error_against==null ? null : error_against.vertices.nearest(p, this); }
163 public void computeError() {
164 if (error_against==null) return;
166 nearest_in_other_mesh != null
167 ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p)
168 : nearest().fundamentalQuadric().preAndPostMultiply(p);
169 if (quadric_count != 0)
170 nerror = (nerror + quadric.preAndPostMultiply(p))/(quadric_count+1);
172 if (!immutableVertices && quadric_count == 0) {
173 //nerror = Math.max(nerror, 0.4f);
176 //System.out.println(nerror);
177 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
178 double ang = e.dihedralAngle();
179 if (ang > Math.PI) throw new Error();
180 if (ang < -Math.PI) throw new Error();
181 float minangle = (float)(Math.PI * 0.8);
182 //nerror += ((ang / Math.PI)*(ang/Math.PI)) * e.length() * 0.05;
184 nerror += (1-e.t.quality())*0.0001;
185 if (ang > minangle) nerror += (ang - minangle);
187 //System.out.println(((ang / Math.PI)*(ang/Math.PI)) * 0.000001);
189 if (e.t.aspect() < 0.2) {
190 nerror += (0.2-e.t.aspect()) * 10;
194 if (!immutableVertices) {
195 Vertex n = (Vertex)nearest();
196 float d = norm().dot(n.norm());
197 if (d > 1 || d < -1) throw new Error();
199 nerror *= (2.0f - d);
201 nerror += 0.0003 * (2.0f + d);
202 nerror *= (2.0f + d);
209 public boolean move(Matrix m, boolean ignoreProblems) {
214 // t2' = t2.getMatrix(t1) * t1'
215 // t2' = t2.getMatrix(t1) * M * t1
216 // t1 = t1.getMatrix(t2) * t2
217 // M * t1 = M * t1.getMatrix(t2) * t2
219 if (bindingGroup!=null && this != bindingGroup.getMaster()) {
220 Matrix v = getBindingMatrix(bindingGroup.getMaster());
221 return ((Vertex)bindingGroup.getMaster()).move(v.inverse().times(m).times(v), ignoreProblems);
224 if (bindingGroup != null) {
226 for(int i=0; i<20 && !m.equals(m2); i++) {
227 m2 = m.times(getConstraint());
228 //System.out.println(m.minus(m2));
230 if (!m.equals(m2)) return true;
234 Point pt = m.times(this.p);
235 for(Vertex v : (Iterable<Vertex>)getBoundPeers()) {
236 Point pt2 = v.getBindingMatrix(this).times(pt);
238 if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) > 5)
239 throw new Error(v.p+" "+pt2+"\n"+op+" "+pt+"\n"+v.getBindingMatrix(this));
240 if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) < 1/5) throw new Error();
242 good &= v.transform(pt2, ignoreProblems, v.getBindingMatrix(this));
245 if (!good && !ignoreProblems) {
246 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
247 v.transform(v.oldp, true, null);
250 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
251 v.recomputeFundamentalQuadricIfNeighborChanged();
252 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
253 v.reComputeErrorAround();
257 public boolean ok = true;
259 /** does NOT update bound pairs! */
260 private boolean transform(Point newp, boolean ignoreProblems, Matrix yes) {
262 if (immutableVertices) throw new Error();
264 unApplyQuadricToNeighbor();
267 boolean illegalbefore = illegal;
270 if (this.p.minus(newp).mag() > 0.1 && !ignoreProblems) {
272 throw new Exception(""+this.p.minus(newp).mag()+" "+ignoreProblems+" "+yes);
273 } catch(Exception e) {
282 applyQuadricToNeighbor();
284 if (!ignoreProblems) {
287 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
288 e.p2.quadricStale = true;
289 return !illegal || (illegalbefore && illegal);
292 public void checkLegality() {
294 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
295 if (Math.abs(e.dihedralAngle()) > (Math.PI * 0.9) ||
296 Math.abs(e.next.dihedralAngle()) > (Math.PI * 0.9)) illegal = true;
297 if (e.t.aspect() < 0.2) illegal = true;
300 if (!illegal) triangles.range(oldp, this.p, (Visitor<T>)this);
303 public void reComputeErrorAround() {
305 if (nearest_in_other_mesh != null)
306 nearest_in_other_mesh.reComputeError();
307 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
308 e.p2.reComputeError();
311 public boolean visit(Object o) {
312 if (o instanceof Vertex)
313 return ((Vertex)o).e != null && ((Vertex)o).norm().dot(Vertex.this.norm()) >= 0;
315 if (illegal) return false;
316 for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
317 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { illegal = true; }
319 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { illegal = true; }
320 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { illegal = true; }
321 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { illegal = true; }
327 public E getEdge() { return e; }
328 public E getFreeIncident() {
329 E ret = getFreeIncident(e, e);
330 if (ret != null) return ret;
331 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
332 System.out.println(e + " " + e.t);
333 throw new Error("unable to find free incident to " + this);
336 public E getFreeIncident(E start, E before) {
337 for(E e = start; e!=null; e=e.pair.next==before?null:e.pair.next)
338 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null)
343 public E getE(Point p2) {
344 Vertex v = vertices.get(p2);
345 if (v==null) return null;
348 public E getE(Vertex p2) {
349 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
350 if (e.p1 == this && e.p2 == p2) return e;
354 private void glNormal(GL gl) {
356 gl.glNormal3f(norm.x, norm.y, norm.z);
359 Vec norm = new Vec(0, 0, 0);
360 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
362 norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
366 public void bindTo(Vertex p) { bindTo(Matrix.ONE, p); }
370 /** [UNIQUE] an edge */
371 public final class E extends HasBindingGroup implements Comparable<E> {
373 public final Vertex p1, p2;
374 T t; // triangle to our "left"
375 E prev; // previous half-edge
376 E next; // next half-edge
377 E pair; // partner half-edge
378 boolean shattered = false;
380 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
382 public Segment getSegment() { return new Segment(p1.getPoint(), p2.getPoint()); }
384 public void bindingGroupChanged(edu.berkeley.qfat.geom.BindingGroup newBindingGroup_) {
386 edu.berkeley.qfat.geom.BindingGroup<E> newBindingGroup =
387 (edu.berkeley.qfat.geom.BindingGroup<E>)newBindingGroup_;
388 if (newBindingGroup==null) return;
389 if (this==newBindingGroup.getMaster()) return;
390 HashSet<E> nbg = new HashSet<E>();
391 for(E eother : (Iterable<E>)newBindingGroup) nbg.add(eother);
392 for(E eother : nbg) {
393 if (next==null || prev==null) continue;
394 if (eother.next==null || eother.prev==null) continue;
396 if (next.isBoundTo(eother.pair.prev.pair) && !prev.isBoundTo(eother.pair.next.pair))
397 prev.bindTo(next.getBindingMatrix(eother.pair.prev.pair), eother.pair.next.pair);
398 if (!next.isBoundTo(eother.pair.prev.pair) && prev.isBoundTo(eother.pair.next.pair))
399 next.bindTo(prev.getBindingMatrix(eother.pair.next.pair), eother.pair.prev.pair);
402 if (next.isBoundTo(eother.prev) && !prev.isBoundTo(eother.next))
403 prev.bindTo(next.getBindingMatrix(eother.prev), eother.next);
404 if (!next.isBoundTo(eother.prev) && prev.isBoundTo(eother.next))
405 next.bindTo(prev.getBindingMatrix(eother.next), eother.prev);
407 if (next.isBoundTo(eother.next) && !prev.isBoundTo(eother.prev))
408 prev.bindTo(next.getBindingMatrix(eother.next), eother.prev);
409 if (!next.isBoundTo(eother.next) && prev.isBoundTo(eother.prev))
410 next.bindTo(prev.getBindingMatrix(eother.prev), eother.next);
415 public float stretchRatio() {
416 Vertex nearest = error_against.nearest(midpoint());
417 float nearest_distance = midpoint().distance(nearest.p);
418 float other_distance =
419 (p1.p.distance(error_against.nearest(p1.p).p)+
420 p2.p.distance(error_against.nearest(p2.p).p))/2;
421 return nearest_distance/other_distance;
423 public float comparator() {
426 public int compareTo(E e) {
427 return e.comparator() > comparator() ? 1 : -1;
429 public void bindEdge(E e, Matrix m) {
431 pair._bindEdge(e.pair, m);
433 public void _bindEdge(E e, Matrix m) {
436 //assumes edges are identical length at binding time
437 Vec reflectionPlaneNormal = e.p2.p.minus(e.p1.p).norm();
438 float a = reflectionPlaneNormal.x;
439 float b = reflectionPlaneNormal.y;
440 float c = reflectionPlaneNormal.z;
441 Matrix reflectionMatrix =
442 new Matrix( 1-2*a*a, -2*a*b, -2*a*c, 0,
443 -2*a*b, 1-2*b*b, -2*b*c, 0,
444 -2*a*c, -2*b*c, 1-2*c*c, 0,
446 m = m.times(Matrix.translate(e.midpoint().minus(Point.ORIGIN))
447 .times(reflectionMatrix)
448 .times(Matrix.translate(Point.ORIGIN.minus(e.midpoint()))));
449 System.out.println(reflectionPlaneNormal);
450 System.out.println(" " + p1.p + " " + m.times(e.p1.p));
451 System.out.println(" " + p2.p + " " + m.times(e.p2.p));
454 if (m.times(e.p1.p).minus(p1.p).mag() > EPSILON) throw new Error();
455 if (m.times(e.p2.p).minus(p2.p).mag() > EPSILON) throw new Error();
460 public void dobind() {
461 for(E e : (Iterable<E>)getBoundPeers()) {
462 if (e==this) continue;
463 p1.bindTo(getBindingMatrix(e), e.p1);
464 p2.bindTo(getBindingMatrix(e), e.p2);
465 e.p1.setConstraint(getConstraint());
466 e.p2.setConstraint(getConstraint());
470 public Point shatter() {
471 if (shattered || destroyed) return null;
477 for(E e : (Iterable<E>)getBoundPeers()) {
480 E pnext = e.pair.next;
481 E pprev = e.pair.prev;
482 Point mid = e.midpoint();
483 Vertex r = e.next.p2;
484 Vertex l = e.pair.next.p2;
488 newT(r.p, e.p1.p, mid, null, 0);
489 newT(r.p, mid, e.p2.p, null, 0);
490 newT(l.p, mid, e.p1.p, null, 0);
491 newT(l.p, e.p2.p, mid, null, 0);
494 for(E e : (Iterable<E>)getBoundPeers()) {
495 Point mid = e.midpoint();
497 first = e.p1.getE(mid);
500 firstq = e.p2.getE(mid).pair;
503 e.p1.getE(mid). bindTo(e.getBindingMatrix(firste), first);
504 e.p1.getE(mid).pair. bindTo(e.getBindingMatrix(firste), first.pair);
505 e.p2.getE(mid).pair. bindTo(e.getBindingMatrix(firste), firstq);
506 e.p2.getE(mid).pair.pair.bindTo(e.getBindingMatrix(firste), firstq.pair);
509 first.setConstraint(firste.getConstraint());
510 firstq.setConstraint(firste.getConstraint());
515 public boolean destroyed = false;
516 public void destroy() {
517 if (destroyed) return;
519 pair.destroyed = true;
521 if (t != null) t.destroy();
524 if (pair.t != null) pair.t.destroy();
527 if (next.t != null) next.t.destroy();
528 if (prev.t != null) prev.t.destroy();
532 if (pair.next.t != null) pair.next.t.destroy();
533 if (pair.prev.t != null) pair.next.t.destroy();
537 pair.prev.next = next;
538 next.prev = pair.prev;
539 prev.next = pair.next;
541 if (p1.e == this) p1.e = prev.next;
542 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
545 private void sync() {
546 this.prev.next = this;
547 this.next.prev = this;
548 this.pair.pair = this;
549 if (this.next.p1 != p2) throw new Error();
550 if (this.prev.p2 != p1) throw new Error();
551 if (this.p1.e == null) this.p1.e = this;
552 if (!added) added = true;
554 private boolean added = false;
556 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
558 public double dihedralAngle() {
559 Vec v1 = t.norm().times(-1);
560 Vec v2 = pair.t.norm().times(-1);
561 double prod = v1.norm().dot(v2.norm());
562 prod = Math.min(1,prod);
563 prod = Math.max(-1,prod);
564 double ret = Math.acos(prod);
565 if (Double.isNaN(ret)) throw new Error("nan! " + prod);
569 /** angle between this half-edge and the next */
570 public double angle() {
571 Vec v1 = next.p2.p.minus(p2.p);
572 Vec v2 = this.p1.p.minus(p2.p);
573 return Math.acos(v1.norm().dot(v2.norm()));
576 public Vertex getOther(Vertex v) {
577 if (this.p1 == v) return p2;
578 if (this.p2 == v) return p1;
582 public void makeAdjacent(E e) {
583 if (this.next == e) return;
584 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
585 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free ");
587 E freeIncident = p2.getFreeIncident(e, this);
589 e.prev.next = freeIncident.next;
590 freeIncident.next.prev = e.prev;
592 freeIncident.next = this.next;
593 this.next.prev = freeIncident;
602 /** creates an isolated edge out in the middle of space */
603 public E(Point p1, Point p2) {
604 if (vertices.get(p1) != null) throw new Error();
605 if (vertices.get(p2) != null) throw new Error();
606 this.p1 = new Vertex(p1);
607 this.p2 = new Vertex(p2);
608 this.prev = this.next = this.pair = new E(this, this, this);
610 this.p2.e = this.pair;
614 /** adds a new half-edge from prev.p2 to p2 */
615 public E(E prev, Point p) {
617 p2 = vertices.get(p);
618 if (p2 == null) p2 = new Vertex(p);
622 if (p2.getE(p1) != null) throw new Error();
624 this.next = this.pair = new E(this, this, prev.next);
626 E q = p2.getFreeIncident();
628 this.next.prev = this;
630 this.prev.next = this;
631 this.pair = new E(q, this, z);
633 if (p2.e==null) p2.e = this.pair;
637 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
638 public E(E prev, E pair, E next) {
646 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); }
647 public boolean has(Vertex v) { return v==p1 || v==p2; }
648 public float length() { return p1.p.minus(p2.p).mag(); }
649 public String toString() { return p1+"->"+p2; }
653 public E makeE(Point p1, Point p2) {
654 Vertex v1 = vertices.get(p1);
655 Vertex v2 = vertices.get(p2);
656 if (v1 != null && v2 != null) {
658 if (e != null) return e;
660 if (e != null) return e;
662 if (v1 != null) return new E(v1.getFreeIncident(), p2);
663 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
664 return new E(p1, p2);
666 public boolean coalesce = false;
667 private static float round(float f) {
668 return Math.round(f*1000)/1000f;
670 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
673 for(Vertex v : vertices) { if (p1.distance(v.p) < EPSILON) { p1 = v.p; break; } }
674 for(Vertex v : vertices) { if (p2.distance(v.p) < EPSILON) { p2 = v.p; break; } }
675 for(Vertex v : vertices) { if (p3.distance(v.p) < EPSILON) { p3 = v.p; break; } }
677 p1 = new Point(round(p1.x), round(p1.y), round(p1.z));
678 p2 = new Point(round(p2.x), round(p2.y), round(p2.z));
679 p3 = new Point(round(p3.x), round(p3.y), round(p3.z));
683 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
684 float dot = norm.dot(norm2);
685 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
686 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
688 E e12 = makeE(p1, p2);
689 E e23 = makeE(p2, p3);
690 E e31 = makeE(p3, p1);
691 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
692 e12.makeAdjacent(e23);
693 e23.makeAdjacent(e31);
694 e31.makeAdjacent(e12);
696 T ret = e12.makeT(colorclass);
697 if (e12.t == null) throw new Error();
698 if (e23.t == null) throw new Error();
699 if (e31.t == null) throw new Error();
703 private int max_serial = 0;
704 /** [UNIQUE] a triangle (face) */
705 public final class T extends Triangle {
707 public final int color;
708 public final int colorclass;
710 public final int serial = max_serial++;
711 public boolean occluded;
713 T(E e1, int colorclass) {
717 if (e1==e2 || e1==e3) throw new Error();
718 if (e3.next!=e1) throw new Error();
719 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
722 e1.next.next.t = this;
724 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
726 int color = Math.abs(random.nextInt());
729 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
730 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
731 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
735 this.colorclass = colorclass;
738 public E e1() { return e1; }
739 public E e2() { return e1.next; }
740 public E e3() { return e1.prev; }
741 public Vertex v1() { return e1.p1; }
742 public Vertex v2() { return e1.p2; }
743 public Vertex v3() { return e1.next.p2; }
744 public Point p1() { return e1.p1.p; }
745 public Point p2() { return e1.p2.p; }
746 public Point p3() { return e1.next.p2.p; }
747 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
748 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
750 public void removeFromRTree() { triangles.remove(this); }
751 public void addToRTree() { triangles.insert(this); }
752 public void destroy() { triangles.remove(this); }
753 public void reinsert() { triangles.remove(this); triangles.add(this); }
755 public boolean shouldBeDrawn() {
757 if (e1().bindingGroupSize() <= 1) return false;
758 if (e2().bindingGroupSize() <= 1) return false;
759 if (e3().bindingGroupSize() <= 1) return false;
764 public void glTriangle(GL gl, Matrix m) {
765 gl.glPushName(serial);
766 gl.glBegin(GL.GL_TRIANGLES);
772 /** issue gl.glVertex() for each of the triangle's points */
773 public void glVertices(GL gl, Matrix m) {
774 if (!shouldBeDrawn()) return;
775 super.glVertices(gl, m);