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 // EDGES RUN COUNTER-CLOCKWISE
16 public class Mesh implements Iterable<Mesh.T> {
18 public static final float EPSILON = (float)0.0001;
19 public static final Random random = new Random();
21 private RTree<T> triangles = new RTree<T>();
22 private PointSet<Vertex> vertices = new PointSet<Vertex>();
24 public boolean option_wireframe = false;
25 public boolean option_errorNormals = false;
26 public boolean option_selectable = true;
28 public void render(GL gl, Matrix m) {
29 if (option_wireframe) {
30 gl.glDisable(GL.GL_LIGHTING);
31 gl.glBegin(GL.GL_LINES);
32 gl.glColor3f(1, 1, 1);
34 m.times(t.e1().p1.goodp).glVertex(gl);
35 m.times(t.e1().p2.goodp).glVertex(gl);
36 m.times(t.e2().p1.goodp).glVertex(gl);
37 m.times(t.e2().p2.goodp).glVertex(gl);
38 m.times(t.e3().p1.goodp).glVertex(gl);
39 m.times(t.e3().p2.goodp).glVertex(gl);
42 gl.glEnable(GL.GL_LIGHTING);
46 gl.glColor4f((float)(0.25+(0.05*t.color)),
47 (float)(0.25+(0.05*t.color)),
48 (float)(0.75+(0.05*t.color)),
52 gl.glColor4f((float)(0.75+(0.05*t.color)),
53 (float)(0.25+(0.05*t.color)),
54 (float)(0.25+(0.05*t.color)),
60 if (option_errorNormals)
62 for(Mesh.Vertex p : new Mesh.Vertex[] { t.v1(), t.v2(), t.v3() }) {
64 gl.glBegin(GL.GL_LINES);
65 gl.glColor3f(1, 1, 1);
67 p.p.plus(p.norm().times((float)p.error()*10)).glVertex(gl);
73 public boolean immutableVertices;
74 public Mesh error_against = null;
75 public double error = 0;
77 public Mesh(boolean immutableVertices) { this.immutableVertices = immutableVertices; }
79 public void makeVerticesImmutable() { this.immutableVertices = true; }
80 public float error() { return (float)error; }
82 public int size() { return vertices.size(); }
83 public Iterable<Vertex> vertices() { return vertices; }
84 public Iterator<T> iterator() { return triangles.iterator(); }
86 public void rebindPoints() {
88 for(Mesh.T t : this) {
93 // ask edges to re-implement their bindings
94 for(Mesh.T t : this) {
99 System.out.println("rebound!");
102 public void transform(Matrix m) {
103 ArrayList<Vertex> set = new ArrayList<Vertex>();
104 for(Vertex v : vertices) set.add(v);
105 for(Vertex v : set) v.transform(m.times(v.p), true, null);
106 for(Vertex v : set) v.goodp = v.p;
109 public void rebuild() { /*vertices.rebuild();*/ }
110 public Vec diagonal() { return vertices.diagonal(); }
111 public Point centroid() { return vertices.centroid(); }
112 public Vertex nearest(Point p) { return vertices.nearest(p); }
114 /** compute the volume of the mesh */
115 public float volume() {
118 double area = t.area();
119 Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
120 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
121 double height = Math.abs(t.norm().dot(origin_to_centroid));
122 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
128 public void subdivide() {
129 for (Vertex v : vertices()) v.original = true;
130 HashSet<E> edges = new HashSet<E>();
131 HashSet<E> flip = new HashSet<E>();
132 HashSet<T> tris = new HashSet<T>();
141 System.out.println("triangles="+count);
144 if (e.destroyed || e.shattered) continue;
145 e.shatter().edge = true;
146 for(E ex : (Iterable<E>)e.getBoundPeers()) {
147 Vertex m = nearest(ex.midpoint());
149 E e3 = ex.p1.getE(m).next;
159 System.out.println("flip!");
164 System.out.println("count="+count);
168 for (T t : this) if (t.v1().edge && t.v2().edge && t.v3().edge) tris.add(t);
174 for(Vertex v : verts) {
175 if (!v.face) continue;
176 v.move(v.recenter().minus(v.getPoint()), false);
180 Queue<T> q = new LinkedList<T>();
183 if (t.old) { t.shatter(); continue OUTER; }
190 HashSet<Vertex> verts = new HashSet<Vertex>();
191 for(Vertex v : vertices()) verts.add(v);
192 for (Vertex v : verts)
194 for (Vertex v : verts) {
196 for(E e = v.e; e!=null; e=e.pair.next==v.e?null:e.pair.next) {
204 for(E e = v.e; e!=null; e=e.pair.next==v.e?null:e.pair.next) {
205 for(E e2 = e.p2.e; e2!=null; e2=e2.pair.next==e.p2.e?null:e2.pair.next) {
206 if (e2.p2.original) {
213 for (Vertex v : verts)
218 // Vertexices //////////////////////////////////////////////////////////////////////////////
220 /** a vertex in the mesh */
221 public final class Vertex extends HasQuadric implements Visitor {
222 public Point p, goodp;
224 E e; // some edge *leaving* this point
226 public boolean original = false;
227 public boolean edge = false;
228 public boolean face = false;
230 private int wishes = 0;
231 private Point wish = Point.ZERO;
232 public void clearWish() { wishes = 0; wish = Point.ZERO; }
233 public void wish(HasPoint hp) {
234 Point p = hp.getPoint();
236 wish = new Point(wish.x+p.x, wish.y+p.y, wish.z+p.z);
238 public void grantWish() {
239 for(Vertex v : (Iterable<Vertex>)getBoundPeers()) {
240 if (v==this) continue;
241 Point p = this.getBindingMatrix(v).times(v.wish.minus(Point.ZERO).div(v.wishes).plus(Point.ZERO));
242 wish = p.minus(Point.ZERO).times(v.wishes).plus(wish);
246 if (wishes==0) return;
247 Vec d = wish.minus(Point.ZERO).div(wishes).plus(Point.ZERO).minus(getPoint());
252 private boolean illegal = false;
254 public boolean visible = false;
256 public Point getPoint() { return p; }
257 public float error() { return olderror; }
259 private Vertex(Point p) {
263 if (vertices.get(p) != null) throw new Error();
267 public void reinsert() {
268 vertices.remove(this);
270 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.t.reinsert();
273 // the average of all adjacent points
274 public Point recenter() {
277 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
278 vec = vec.plus(e.getOther(this).getPoint().minus(Point.ZERO));
281 return Point.ZERO.plus(vec.div(count));
284 public float olderror = 0;
285 public void setError(float nerror) {
292 public Vertex hack(GL gl, Point mouse) {
293 double dist = Double.MAX_VALUE;
295 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
296 Vertex v = e.getOther(this);
297 double dist2 = v.getPoint().glProject(gl).distance(mouse);
298 if ((cur==null || dist2 < dist) && v.visible) {
307 public float averageTriangleArea() {
310 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
316 public float averageEdgeLength() {
319 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
326 public Matrix _recomputeFundamentalQuadric() {
327 Matrix m = Matrix.ZERO;
329 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
330 m = m.plus(e.t.norm().fundamentalQuadric(e.t.centroid()));
334 m = m.plus(norm().fundamentalQuadric(this.p).times(count));
337 return m.times(1/(float)count);
340 public HasQuadric nearest() { return error_against==null ? null : error_against.vertices.nearest(p, this); }
341 public void computeError() {
342 if (error_against==null) return;
343 if (nearest_in_other_mesh == null && nearest()==null) return;
345 nearest_in_other_mesh != null
346 ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p)
347 : nearest().fundamentalQuadric().preAndPostMultiply(p);
348 if (quadric_count != 0)
349 nerror = (nerror + quadric.preAndPostMultiply(p))/(quadric_count+1);
351 if (!immutableVertices && quadric_count == 0) {
352 //nerror = Math.max(nerror, 0.4f);
355 //System.out.println(nerror);
356 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
357 double ang = e.dihedralAngle();
358 if (ang > Math.PI) throw new Error();
359 if (ang < -Math.PI) throw new Error();
360 float minangle = (float)(Math.PI * 0.8);
361 //nerror += ((ang / Math.PI)*(ang/Math.PI)) * e.length() * 0.05;
363 nerror += (1-e.t.quality())*0.0001;
364 if (ang > minangle) nerror += (ang - minangle);
366 //System.out.println(((ang / Math.PI)*(ang/Math.PI)) * 0.000001);
368 if (e.t.aspect() < 0.2) {
369 nerror += (0.2-e.t.aspect()) * 10;
373 if (!immutableVertices) {
374 Vertex n = (Vertex)nearest();
375 float d = norm().dot(n.norm());
376 if (d > 1 || d < -1) throw new Error();
378 nerror *= (2.0f - d);
380 nerror += 0.0003 * (2.0f + d);
381 nerror *= (2.0f + d);
388 public boolean move(Vec vv, boolean ignoreProblems) {
393 // t2' = t2.getMatrix(t1) * t1'
394 // t2' = t2.getMatrix(t1) * M * t1
395 // t1 = t1.getMatrix(t2) * t2
396 // M * t1 = M * t1.getMatrix(t2) * t2
398 if (bindingGroup!=null && this != bindingGroup.getMaster()) {
399 Matrix m2 = getBindingMatrix(bindingGroup.getMaster());
400 Vec v2 = m2.times(vv.plus(getPoint())).minus(m2.times(getPoint()));
401 return ((Vertex)bindingGroup.getMaster()).move(v2, ignoreProblems);
405 Point pp = vv.plus(getPoint());
406 if (bindingGroup != null) {
408 for(int i=0; i<20 ; i++) {
409 Point p2 = getConstraint().times(pp);
410 pp = pp.midpoint(p2);
411 //System.out.println(m.minus(m2));
414 //pp = getConstraint().times(pp);
416 //pp = pp.minus(op).norm().times(vv.mag()).plus(op);
419 for(Vertex v : (Iterable<Vertex>)getBoundPeers()) {
420 Point pt2 = v.getBindingMatrix(this).times(pt);
422 if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) > 5)
423 throw new Error(v.p+" "+pt2+"\n"+op+" "+pt+"\n"+v.getBindingMatrix(this));
424 if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) < 1/5) throw new Error();
426 good &= v.transform(pt2, ignoreProblems, v.getBindingMatrix(this));
429 if (!good && !ignoreProblems) {
430 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
431 v.transform(v.oldp, true, null);
434 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
435 v.recomputeFundamentalQuadricIfNeighborChanged();
436 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
437 v.reComputeErrorAround();
441 public boolean ok = true;
443 /** does NOT update bound pairs! */
444 private boolean transform(Point newp, boolean ignoreProblems, Matrix yes) {
446 if (immutableVertices) throw new Error();
448 unApplyQuadricToNeighbor();
450 boolean illegalbefore = illegal;
453 if (this.p.minus(newp).mag() > 0.1 && !ignoreProblems) {
455 throw new Exception(""+this.p.minus(newp).mag()+" "+ignoreProblems+" "+yes);
456 } catch(Exception e) {
465 applyQuadricToNeighbor();
467 if (!ignoreProblems) {
470 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
471 e.p2.quadricStale = true;
472 return !illegal || (illegalbefore && illegal);
475 public void checkLegality() {
477 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
478 if (Math.abs(e.dihedralAngle()) > (Math.PI * 0.9) ||
479 Math.abs(e.next.dihedralAngle()) > (Math.PI * 0.9)) illegal = true;
480 if (e.t.aspect() < 0.2) illegal = true;
483 if (!illegal) triangles.range(oldp, this.p, (Visitor<T>)this);
486 public void reComputeErrorAround() {
488 if (nearest_in_other_mesh != null)
489 nearest_in_other_mesh.reComputeError();
490 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
491 e.p2.reComputeError();
494 public boolean visit(Object o) {
495 if (o instanceof Vertex)
496 return ((Vertex)o).e != null && ((Vertex)o).norm().dot(Vertex.this.norm()) >= 0;
498 if (illegal) return false;
499 for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
500 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { illegal = true; }
502 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { illegal = true; }
503 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { illegal = true; }
504 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { illegal = true; }
510 public E getEdge() { return e; }
511 public E getFreeIncident() {
512 E ret = getFreeIncident(e, e);
513 if (ret != null) return ret;
514 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
515 System.out.println(e + " " + e.t);
516 throw new Error("unable to find free incident to " + this);
519 public E getFreeIncident(E start, E before) {
520 for(E e = start; e!=null; e=e.pair.next==before?null:e.pair.next)
521 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null)
526 public E getE(Point p2) {
527 Vertex v = vertices.get(p2);
528 if (v==null) return null;
531 public E getE(Vertex p2) {
532 if (this.e!=null && this!=this.e.p1 && this!=this.e.p2) throw new RuntimeException();
534 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
535 if (e.p1 == this && e.p2 == p2) return e;
538 if (e.destroyed) throw new RuntimeException("fark " + i + " " + e.prev + " " + (e.prev.next==e) + " " + e.prev.destroyed);
543 private void glNormal(GL gl) {
545 gl.glNormal3f(norm.x, norm.y, norm.z);
548 Vec norm = new Vec(0, 0, 0);
549 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
551 norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
555 public void bindTo(Vertex p) { bindTo(Matrix.ONE, p); }
559 /** [UNIQUE] an edge */
560 public final class E extends HasBindingGroup implements Comparable<E> {
562 public void sanity() {
563 if (destroyed) return;
564 if (pair!=null && (pair.p1!=p2 || pair.p2!=p1)) throw new RuntimeException();
565 if (next!=null && next.p1!=p2) throw new RuntimeException();
566 if (prev!=null && prev.p2!=p1) throw new RuntimeException();
569 public final Vertex p1, p2;
570 T t; // triangle to our "left"
571 E prev; // previous half-edge
572 E next; // next half-edge
573 E pair; // partner half-edge
574 boolean shattered = false;
576 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
578 public Segment getSegment() { return new Segment(p1.getPoint(), p2.getPoint()); }
581 // FIXME: coplanarity check needed
582 if (destroyed) return;
583 for (E e : (Iterable<E>)getBoundPeers()) {
584 if (!e.pair.isBoundTo(pair)) throw new RuntimeException("cannot flip!");
586 Vertex v1 = t.getOtherVertex(this);
587 Vertex v2 = pair.t.getOtherVertex(pair);
590 T t1 = newT(v1, v2, p2);
591 T t2 = newT(v2, v1, p1);
599 for (E e : (Iterable<E>)getBoundPeers()) {
600 if (e==this) continue;
601 if (e.destroyed) continue;
602 Vertex v1e = e.t.getOtherVertex(e);
603 Vertex v2e = e.pair.t.getOtherVertex(e.pair);
606 if (v1e.getE(v2e)!=null) throw new RuntimeException();
607 newT(v1e, v2e, e.p2).red = true;
608 newT(v2e, v1e, e.p1).red = true;
609 v2e.getE(v1e).bindTo(e.getBindingMatrix(this), v1.getE(v2));
610 v1e.getE(v2e).bindTo(e.pair.getBindingMatrix(this.pair), v2.getE(v1));
615 public void bindingGroupChanged(edu.berkeley.qfat.geom.BindingGroup newBindingGroup_) {
617 edu.berkeley.qfat.geom.BindingGroup<E> newBindingGroup =
618 (edu.berkeley.qfat.geom.BindingGroup<E>)newBindingGroup_;
619 if (newBindingGroup==null) return;
620 if (this==newBindingGroup.getMaster()) return;
621 HashSet<E> nbg = new HashSet<E>();
622 for(E eother : (Iterable<E>)newBindingGroup) nbg.add(eother);
623 for(E eother : nbg) {
624 if (next==null || prev==null) continue;
625 if (eother.next==null || eother.prev==null) continue;
627 if (next.isBoundTo(eother.pair.prev.pair) && !prev.isBoundTo(eother.pair.next.pair))
628 prev.bindTo(next.getBindingMatrix(eother.pair.prev.pair), eother.pair.next.pair);
629 if (!next.isBoundTo(eother.pair.prev.pair) && prev.isBoundTo(eother.pair.next.pair))
630 next.bindTo(prev.getBindingMatrix(eother.pair.next.pair), eother.pair.prev.pair);
633 if (next.isBoundTo(eother.prev) && !prev.isBoundTo(eother.next))
634 prev.bindTo(next.getBindingMatrix(eother.prev), eother.next);
635 if (!next.isBoundTo(eother.prev) && prev.isBoundTo(eother.next))
636 next.bindTo(prev.getBindingMatrix(eother.next), eother.prev);
638 if (next.isBoundTo(eother.next) && !prev.isBoundTo(eother.prev))
639 prev.bindTo(next.getBindingMatrix(eother.next), eother.prev);
640 if (!next.isBoundTo(eother.next) && prev.isBoundTo(eother.prev))
641 next.bindTo(prev.getBindingMatrix(eother.prev), eother.next);
646 public float stretchRatio() {
647 Vertex nearest = error_against.nearest(midpoint());
648 float nearest_distance = midpoint().distance(nearest.p);
649 float other_distance =
650 (p1.p.distance(error_against.nearest(p1.p).p)+
651 p2.p.distance(error_against.nearest(p2.p).p))/2;
652 return nearest_distance/other_distance;
654 public float comparator() {
657 public int compareTo(E e) {
658 return e.comparator() > comparator() ? 1 : -1;
660 public void bindEdge(E e, Matrix m) {
662 pair._bindEdge(e.pair, m);
664 public void _bindEdge(E e, Matrix m) {
667 //assumes edges are identical length at binding time
668 Vec reflectionPlaneNormal = e.p2.p.minus(e.p1.p).norm();
669 float a = reflectionPlaneNormal.x;
670 float b = reflectionPlaneNormal.y;
671 float c = reflectionPlaneNormal.z;
672 Matrix reflectionMatrix =
673 new Matrix( 1-2*a*a, -2*a*b, -2*a*c, 0,
674 -2*a*b, 1-2*b*b, -2*b*c, 0,
675 -2*a*c, -2*b*c, 1-2*c*c, 0,
677 m = m.times(Matrix.translate(e.midpoint().minus(Point.ORIGIN))
678 .times(reflectionMatrix)
679 .times(Matrix.translate(Point.ORIGIN.minus(e.midpoint()))));
680 System.out.println(reflectionPlaneNormal);
681 System.out.println(" " + p1.p + " " + m.times(e.p1.p));
682 System.out.println(" " + p2.p + " " + m.times(e.p2.p));
685 if (m.times(e.p1.p).minus(p1.p).mag() > EPSILON) throw new Error();
686 if (m.times(e.p2.p).minus(p2.p).mag() > EPSILON) throw new Error();
691 public void dobind() {
692 for(E e : (Iterable<E>)getBoundPeers()) {
693 if (e==this) continue;
694 p1.bindTo(getBindingMatrix(e), e.p1);
695 p2.bindTo(getBindingMatrix(e), e.p2);
696 e.p1.setConstraint(getConstraint());
697 e.p2.setConstraint(getConstraint());
701 public Vertex shatter() {
702 if (shattered || destroyed) return nearest(midpoint());
708 for(E e : (Iterable<E>)getBoundPeers()) {
711 E pnext = e.pair.next;
712 E pprev = e.pair.prev;
713 Point mid = e.midpoint();
714 Vertex r = e.next.p2;
715 Vertex l = e.pair.next.p2;
719 newT(r.p, e.p1.p, mid, null, 0);
720 newT(r.p, mid, e.p2.p, null, 0);
721 newT(l.p, mid, e.p1.p, null, 0);
722 newT(l.p, e.p2.p, mid, null, 0);
725 for(E e : (Iterable<E>)getBoundPeers()) {
726 Point mid = e.midpoint();
728 first = e.p1.getE(mid);
731 firstq = e.p2.getE(mid).pair;
734 e.p1.getE(mid). bindTo(e.getBindingMatrix(firste), first);
735 e.p1.getE(mid).pair. bindTo(e.getBindingMatrix(firste), first.pair);
736 e.p2.getE(mid).pair. bindTo(e.getBindingMatrix(firste), firstq);
737 e.p2.getE(mid).pair.pair.bindTo(e.getBindingMatrix(firste), firstq.pair);
740 first.setConstraint(firste.getConstraint());
741 firstq.setConstraint(firste.getConstraint());
743 return nearest(midpoint());
746 public boolean destroyed = false;
747 public void destroy() {
748 if (destroyed) return;
750 pair.destroyed = true;
752 if (t != null) t.destroy();
755 if (pair.t != null) pair.t.destroy();
758 if (next.t != null) next.t.destroy();
759 if (prev.t != null) prev.t.destroy();
763 if (pair.next.t != null) pair.next.t.destroy();
764 if (pair.prev.t != null) pair.next.t.destroy();
768 pair.prev.next = next;
769 next.prev = pair.prev;
770 prev.next = pair.next;
771 pair.next.prev = prev;
773 if (p1.e == this) p1.e = pair.next;
774 if (pair.p1.e == pair) pair.p1.e = next;
776 if (p2.e == this) throw new RuntimeException();
777 if (pair.p2.e == pair) throw new RuntimeException();
801 private void sync() {
802 this.prev.next = this;
803 this.next.prev = this;
804 this.pair.pair = this;
805 if (this.next.p1 != p2) throw new Error();
806 if (this.prev.p2 != p1) throw new Error();
807 if (this.p1.e == null) this.p1.e = this;
808 if (!added) added = true;
810 private boolean added = false;
812 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
814 public double dihedralAngle() {
815 Vec v1 = t.norm().times(-1);
816 Vec v2 = pair.t.norm().times(-1);
817 double prod = v1.norm().dot(v2.norm());
818 prod = Math.min(1,prod);
819 prod = Math.max(-1,prod);
820 double ret = Math.acos(prod);
821 if (Double.isNaN(ret)) throw new Error("nan! " + prod);
825 /** angle between this half-edge and the next */
826 public double angle() {
827 Vec v1 = next.p2.p.minus(p2.p);
828 Vec v2 = this.p1.p.minus(p2.p);
829 return Math.acos(v1.norm().dot(v2.norm()));
832 public Vertex getOther(Vertex v) {
833 if (this.p1 == v) return p2;
834 if (this.p2 == v) return p1;
838 public void makeAdjacent(E e) {
839 if (this.next == e) return;
840 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex: " + this + " " + e);
841 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free " + t + " " + e.t);
843 E freeIncident = p2.getFreeIncident(e, this);
845 e.prev.next = freeIncident.next;
846 freeIncident.next.prev = e.prev;
848 freeIncident.next = this.next;
849 this.next.prev = freeIncident;
858 /** creates an isolated edge out in the middle of space */
859 public E(Point p1, Point p2) {
860 if (vertices.get(p1) != null) throw new Error();
861 if (vertices.get(p2) != null) throw new Error();
862 this.p1 = new Vertex(p1);
863 this.p2 = new Vertex(p2);
864 this.prev = this.next = this.pair = new E(this, this, this);
866 this.p2.e = this.pair;
870 /** adds a new half-edge from prev.p2 to p2 */
871 public E(E prev, Point p) {
873 p2 = vertices.get(p);
874 if (p2 == null) p2 = new Vertex(p);
878 if (prev.destroyed) throw new RuntimeException();
879 if (p2.getE(p1) != null) throw new Error();
881 this.next = this.pair = new E(this, this, prev.next);
883 E q = p2.getFreeIncident();
885 this.next.prev = this;
887 this.prev.next = this;
888 this.pair = new E(q, this, z);
890 if (p2.e==null) p2.e = this.pair;
894 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
895 public E(E prev, E pair, E next) {
898 if (prev.destroyed) throw new RuntimeException();
904 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); }
905 public boolean has(Vertex v) { return v==p1 || v==p2; }
906 public float length() { return p1.p.minus(p2.p).mag(); }
907 public String toString() { return p1+"->"+p2; }
911 public E makeE(Point p1, Point p2) {
912 Vertex v1 = vertices.get(p1);
913 Vertex v2 = vertices.get(p2);
914 if (v1 != null && v2 != null) {
916 if (e != null) return e;
918 if (e != null) return e;
920 if (v1 != null) return new E(v1.getFreeIncident(), p2);
921 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
922 return new E(p1, p2);
924 public boolean coalesce = false;
925 private static float round(float f) {
926 return Math.round(f*1000)/1000f;
928 public T newT(HasPoint p1, HasPoint p2, HasPoint p3) {
929 return newT(p1.getPoint(), p2.getPoint(), p3.getPoint(), null, 0);
931 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
934 for(Vertex v : vertices) { if (p1.distance(v.p) < EPSILON) { p1 = v.p; break; } }
935 for(Vertex v : vertices) { if (p2.distance(v.p) < EPSILON) { p2 = v.p; break; } }
936 for(Vertex v : vertices) { if (p3.distance(v.p) < EPSILON) { p3 = v.p; break; } }
938 p1 = new Point(round(p1.x), round(p1.y), round(p1.z));
939 p2 = new Point(round(p2.x), round(p2.y), round(p2.z));
940 p3 = new Point(round(p3.x), round(p3.y), round(p3.z));
944 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
945 float dot = norm.dot(norm2);
946 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
947 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
949 E e12 = makeE(p1, p2);
950 E e23 = makeE(p2, p3);
951 E e31 = makeE(p3, p1);
952 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
953 e12.makeAdjacent(e23);
954 e23.makeAdjacent(e31);
955 e31.makeAdjacent(e12);
957 T ret = e12.makeT(colorclass);
958 if (e12.t == null) throw new Error();
959 if (e23.t == null) throw new Error();
960 if (e31.t == null) throw new Error();
964 private int max_serial = 0;
965 /** [UNIQUE] a triangle (face) */
966 public final class T extends Triangle {
968 public final int color;
969 public final int colorclass;
971 public boolean red = false;
972 public boolean old = false;
974 public final int serial = max_serial++;
975 public boolean occluded;
977 public Point shatter() {
978 if (destroyed) return null;
981 HashSet<E> forward = new HashSet<E>();
982 HashSet<E> backward = new HashSet<E>();
983 HashSet<E> both = new HashSet<E>();
985 for(E eb : (Iterable<E>)e.getBoundPeers()) {
987 if (eb.next.isBoundTo(e.next) && eb.prev.isBoundTo(e.prev)) {
991 if (eb.pair.next.pair.isBoundTo(e.prev) && eb.pair.prev.pair.isBoundTo(e.next)) {
992 backward.add(eb.pair);
997 Vertex v1 = e.t.v1();
998 Vertex v2 = e.t.v2();
999 Vertex v3 = e.t.v3();
1000 Point c = e.t.centroid();
1008 // FIXME: forward too
1009 for(E ex : backward) {
1010 Vertex v1x = ex.t.v1();
1011 Vertex v2x = ex.t.v2();
1012 Vertex v3x = ex.t.v3();
1013 Point cx = ex.t.centroid();
1014 E ex_next = ex.next;
1015 E ex_prev = ex.prev;
1021 // FIXME: i have no idea if this is right
1022 e.next.bindTo(e.getBindingMatrix(ex.pair), ex.prev);
1023 e.prev.bindTo(e.getBindingMatrix(ex.pair), ex.next);
1024 e.next.pair.bindTo(e.getBindingMatrix(ex.pair), ex.prev.pair);
1025 e.prev.pair.bindTo(e.getBindingMatrix(ex.pair), ex.next.pair);
1027 e_next.next.bindTo(e_next.getBindingMatrix(ex_prev.pair), ex_prev.prev.pair);
1028 e_next.prev.bindTo(e_next.getBindingMatrix(ex_prev.pair), ex_prev.next.pair);
1030 e_prev.next.bindTo(e_prev.getBindingMatrix(ex_next.pair), ex_next.prev.pair);
1031 e_prev.prev.bindTo(e_prev.getBindingMatrix(ex_next.pair), ex_next.next.pair);
1040 for(E e : (Iterable<E>)getBoundPeers()) {
1043 E pnext = e.pair.next;
1044 E pprev = e.pair.prev;
1045 Point mid = e.midpoint();
1046 Vertex r = e.next.p2;
1047 Vertex l = e.pair.next.p2;
1051 newT(r.p, e.p1.p, mid, null, 0);
1052 newT(r.p, mid, e.p2.p, null, 0);
1053 newT(l.p, mid, e.p1.p, null, 0);
1054 newT(l.p, e.p2.p, mid, null, 0);
1057 for(E e : (Iterable<E>)getBoundPeers()) {
1058 Point mid = e.midpoint();
1060 first = e.p1.getE(mid);
1063 firstq = e.p2.getE(mid).pair;
1066 e.p1.getE(mid). bindTo(e.getBindingMatrix(firste), first);
1067 e.p1.getE(mid).pair. bindTo(e.getBindingMatrix(firste), first.pair);
1068 e.p2.getE(mid).pair. bindTo(e.getBindingMatrix(firste), firstq);
1069 e.p2.getE(mid).pair.pair.bindTo(e.getBindingMatrix(firste), firstq.pair);
1073 first.setConstraint(firste.getConstraint());
1074 firstq.setConstraint(firste.getConstraint());
1080 T(E e1, int colorclass) {
1084 if (e1==e2 || e1==e3) throw new Error();
1085 if (e3.next!=e1) throw new Error();
1086 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
1089 e1.next.next.t = this;
1091 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
1093 int color = Math.abs(random.nextInt());
1096 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
1097 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
1098 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
1102 this.colorclass = colorclass;
1103 triangles.add(this);
1105 public E e1() { return e1; }
1106 public E e2() { return e1.next; }
1107 public E e3() { return e1.prev; }
1108 public Vertex v1() { return e1.p1; }
1109 public Vertex v2() { return e1.p2; }
1110 public Vertex v3() { return e1.next.p2; }
1111 public Point p1() { return e1.p1.p; }
1112 public Point p2() { return e1.p2.p; }
1113 public Point p3() { return e1.next.p2.p; }
1114 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
1115 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
1117 public Vertex getOtherVertex(E e) {
1118 if (!hasE(e)) throw new RuntimeException();
1119 if (!e.has(v1())) return v1();
1120 if (!e.has(v2())) return v2();
1121 if (!e.has(v3())) return v3();
1122 throw new RuntimeException();
1125 public void removeFromRTree() { triangles.remove(this); }
1126 public void addToRTree() { triangles.insert(this); }
1127 public void destroy() {
1133 triangles.remove(this);
1136 public void reinsert() { triangles.remove(this); triangles.add(this); }
1138 private boolean destroyed = false;
1139 public boolean destroyed() { return destroyed; }
1141 public boolean shouldBeDrawn() {
1143 if (e1().bindingGroupSize() <= 1) return false;
1144 if (e2().bindingGroupSize() <= 1) return false;
1145 if (e3().bindingGroupSize() <= 1) return false;
1150 public void glTriangle(GL gl, Matrix m) {
1151 gl.glPushName(serial);
1152 gl.glBegin(GL.GL_TRIANGLES);
1158 /** issue gl.glVertex() for each of the triangle's points */
1159 public void glVertices(GL gl, Matrix m) {
1160 if (!shouldBeDrawn()) return;
1161 super.glVertices(gl, m);