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!");
163 System.out.println("count="+count);
166 HashSet<Vertex> verts = new HashSet<Vertex>();
167 for(Vertex v : vertices()) verts.add(v);
168 for (Vertex v : verts)
170 for (Vertex v : verts) {
172 for(E e = v.e; e!=null; e=e.pair.next==v.e?null:e.pair.next) {
180 for(E e = v.e; e!=null; e=e.pair.next==v.e?null:e.pair.next) {
181 for(E e2 = e.p2.e; e2!=null; e2=e2.pair.next==e.p2.e?null:e2.pair.next) {
182 if (e2.p2.original) {
189 for (Vertex v : verts)
191 System.out.println("-------------------------------------------------------------------");
193 for (Vertex v : verts) {
196 for(E e = v.e; e!=null; e=e.pair.next==v.e?null:e.pair.next) {
198 v.wish(e.midpoint());
199 v.wish(e.midpoint());
200 v.wish(e.next.pair.t.centroid());
204 for(int j=0; j<n-3; j++)
205 v.wish(v.getPoint());
208 for (Vertex v : verts)
210 for (Vertex v : verts)
215 // Vertexices //////////////////////////////////////////////////////////////////////////////
217 /** a vertex in the mesh */
218 public final class Vertex extends HasQuadric implements Visitor {
219 public Point p, goodp;
221 E e; // some edge *leaving* this point
223 public boolean original = false;
224 public boolean edge = false;
225 public boolean face = false;
227 private int wishes = 0;
228 private Point wish = Point.ZERO;
229 public void clearWish() { wishes = 0; wish = Point.ZERO; }
230 public void wish(HasPoint hp) {
231 Point p = hp.getPoint();
233 wish = new Point(wish.x+p.x, wish.y+p.y, wish.z+p.z);
235 public void grantWish() {
236 for(Vertex v : (Iterable<Vertex>)getBoundPeers()) {
237 if (v==this) continue;
238 if (v.wishes==0) continue;
239 Point p = this.getBindingMatrix(v).times(v.wish.minus(Point.ZERO).div(v.wishes).plus(Point.ZERO));
240 wish = p.minus(Point.ZERO).times(v.wishes).plus(wish);
244 if (wishes==0) return;
245 Vec d = wish.minus(Point.ZERO).div(wishes).plus(Point.ZERO).minus(getPoint());
249 public void avgWish() {
250 if (wishes==0) return;
251 wish = wish.minus(Point.ZERO).div(wishes).plus(Point.ZERO);
255 private boolean illegal = false;
257 public boolean visible = false;
259 public Point getPoint() { return p; }
260 public float error() { return olderror; }
262 private Vertex(Point p) {
266 if (vertices.get(p) != null) throw new Error();
270 public void reinsert() {
271 vertices.remove(this);
273 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.t.reinsert();
276 // the average of all adjacent points
277 public Point recenter() {
280 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
281 vec = vec.plus(e.getOther(this).getPoint().minus(Point.ZERO));
284 return Point.ZERO.plus(vec.div(count));
287 public float olderror = 0;
288 public void setError(float nerror) {
295 public Vertex hack(GL gl, Point mouse) {
296 double dist = Double.MAX_VALUE;
298 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
299 Vertex v = e.getOther(this);
300 double dist2 = v.getPoint().glProject(gl).distance(mouse);
301 if ((cur==null || dist2 < dist) && v.visible) {
310 public float averageTriangleArea() {
313 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
319 public float averageEdgeLength() {
322 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
329 public Matrix _recomputeFundamentalQuadric() {
330 Matrix m = Matrix.ZERO;
332 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
333 m = m.plus(e.t.norm().fundamentalQuadric(e.t.centroid()));
337 m = m.plus(norm().fundamentalQuadric(this.p).times(count));
340 return m.times(1/(float)count);
343 public HasQuadric nearest() { return error_against==null ? null : error_against.vertices.nearest(p, this); }
344 public void computeError() {
345 if (error_against==null) return;
346 if (nearest_in_other_mesh == null && nearest()==null) return;
348 nearest_in_other_mesh != null
349 ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p)
350 : nearest().fundamentalQuadric().preAndPostMultiply(p);
351 if (quadric_count != 0)
352 nerror = (nerror + quadric.preAndPostMultiply(p))/(quadric_count+1);
354 if (!immutableVertices && quadric_count == 0) {
355 //nerror = Math.max(nerror, 0.4f);
358 //System.out.println(nerror);
359 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
360 double ang = e.dihedralAngle();
361 if (ang > Math.PI) throw new Error();
362 if (ang < -Math.PI) throw new Error();
363 float minangle = (float)(Math.PI * 0.8);
364 //nerror += ((ang / Math.PI)*(ang/Math.PI)) * e.length() * 0.05;
366 nerror += (1-e.t.quality())*0.0001;
367 if (ang > minangle) nerror += (ang - minangle);
369 //System.out.println(((ang / Math.PI)*(ang/Math.PI)) * 0.000001);
371 if (e.t.aspect() < 0.2) {
372 nerror += (0.2-e.t.aspect()) * 10;
376 if (!immutableVertices) {
377 Vertex n = (Vertex)nearest();
378 float d = norm().dot(n.norm());
379 if (d > 1 || d < -1) throw new Error();
381 nerror *= (2.0f - d);
383 nerror += 0.0003 * (2.0f + d);
384 nerror *= (2.0f + d);
391 public boolean move(Vec vv, boolean ignoreProblems) {
396 // t2' = t2.getMatrix(t1) * t1'
397 // t2' = t2.getMatrix(t1) * M * t1
398 // t1 = t1.getMatrix(t2) * t2
399 // M * t1 = M * t1.getMatrix(t2) * t2
401 if (bindingGroup!=null && this != bindingGroup.getMaster()) {
402 Matrix m2 = getBindingMatrix(bindingGroup.getMaster());
403 Vec v2 = m2.times(vv.plus(getPoint())).minus(m2.times(getPoint()));
404 return ((Vertex)bindingGroup.getMaster()).move(v2, ignoreProblems);
408 Point pp = vv.plus(getPoint());
409 if (bindingGroup != null) {
411 for(int i=0; i<20 ; i++) {
412 Point v2 = getConstraint().times(pp);
413 pp = pp.midpoint(v2);
414 //System.out.println(m.minus(m2));
417 //pp = getConstraint().times(pp);
419 //pp = pp.minus(op).norm().times(vv.mag()).plus(op);
422 for(Vertex v : (Iterable<Vertex>)getBoundPeers()) {
423 Point pt2 = v.getBindingMatrix(this).times(pt);
425 if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) > 5)
426 throw new Error(v.p+" "+pt2+"\n"+op+" "+pt+"\n"+v.getBindingMatrix(this));
427 if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) < 1/5) throw new Error();
429 good &= v.transform(pt2, ignoreProblems, v.getBindingMatrix(this));
432 if (!good && !ignoreProblems) {
433 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
434 v.transform(v.oldp, true, null);
437 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
438 v.recomputeFundamentalQuadricIfNeighborChanged();
439 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
440 v.reComputeErrorAround();
444 public boolean ok = true;
446 /** does NOT update bound pairs! */
447 private boolean transform(Point newp, boolean ignoreProblems, Matrix yes) {
449 if (immutableVertices) throw new Error();
451 unApplyQuadricToNeighbor();
453 boolean illegalbefore = illegal;
456 if (this.p.minus(newp).mag() > 0.1 && !ignoreProblems) {
458 throw new Exception(""+this.p.minus(newp).mag()+" "+ignoreProblems+" "+yes);
459 } catch(Exception e) {
468 applyQuadricToNeighbor();
470 if (!ignoreProblems) {
473 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
474 e.p2.quadricStale = true;
475 return !illegal || (illegalbefore && illegal);
478 public void checkLegality() {
480 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
481 if (Math.abs(e.dihedralAngle()) > (Math.PI * 0.9) ||
482 Math.abs(e.next.dihedralAngle()) > (Math.PI * 0.9)) illegal = true;
483 if (e.t.aspect() < 0.2) illegal = true;
486 if (!illegal) triangles.range(oldp, this.p, (Visitor<T>)this);
489 public void reComputeErrorAround() {
491 if (nearest_in_other_mesh != null)
492 nearest_in_other_mesh.reComputeError();
493 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
494 e.p2.reComputeError();
497 public boolean visit(Object o) {
498 if (o instanceof Vertex)
499 return ((Vertex)o).e != null && ((Vertex)o).norm().dot(Vertex.this.norm()) >= 0;
501 if (illegal) return false;
502 for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
503 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { illegal = true; }
505 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { illegal = true; }
506 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { illegal = true; }
507 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { illegal = true; }
513 public E getEdge() { return e; }
514 public E getFreeIncident() {
515 E ret = getFreeIncident(e, e);
516 if (ret != null) return ret;
517 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
518 System.out.println(e + " " + e.t);
519 throw new Error("unable to find free incident to " + this);
522 public E getFreeIncident(E start, E before) {
523 for(E e = start; e!=null; e=e.pair.next==before?null:e.pair.next)
524 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null)
529 public E getE(Point p2) {
530 Vertex v = vertices.get(p2);
531 if (v==null) return null;
534 public E getE(Vertex p2) {
535 if (this.e!=null && this!=this.e.p1 && this!=this.e.p2) throw new RuntimeException();
537 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
538 if (e.p1 == this && e.p2 == p2) return e;
541 if (e.destroyed) throw new RuntimeException("fark " + i + " " + e.prev + " " + (e.prev.next==e) + " " + e.prev.destroyed);
546 private void glNormal(GL gl) {
548 gl.glNormal3f(norm.x, norm.y, norm.z);
551 Vec norm = new Vec(0, 0, 0);
552 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
554 norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
558 public void bindTo(Vertex p) { bindTo(Matrix.ONE, p); }
562 /** [UNIQUE] an edge */
563 public final class E extends HasBindingGroup implements Comparable<E> {
565 public void sanity() {
566 if (destroyed) return;
567 if (pair!=null && (pair.p1!=p2 || pair.p2!=p1)) throw new RuntimeException();
568 if (next!=null && next.p1!=p2) throw new RuntimeException();
569 if (prev!=null && prev.p2!=p1) throw new RuntimeException();
572 public final Vertex p1, p2;
573 T t; // triangle to our "left"
574 E prev; // previous half-edge
575 E next; // next half-edge
576 E pair; // partner half-edge
577 boolean shattered = false;
579 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
581 public Segment getSegment() { return new Segment(p1.getPoint(), p2.getPoint()); }
584 // FIXME: coplanarity check needed
585 if (destroyed) return;
586 for (E e : (Iterable<E>)getBoundPeers()) {
587 if (!e.pair.isBoundTo(pair)) throw new RuntimeException("cannot flip!");
589 Vertex v1 = t.getOtherVertex(this);
590 Vertex v2 = pair.t.getOtherVertex(pair);
593 T t1 = newT(v1, v2, p2);
594 T t2 = newT(v2, v1, p1);
602 for (E e : (Iterable<E>)getBoundPeers()) {
603 if (e==this) continue;
604 if (e.destroyed) continue;
605 Vertex v1e = e.t.getOtherVertex(e);
606 Vertex v2e = e.pair.t.getOtherVertex(e.pair);
609 if (v1e.getE(v2e)!=null) throw new RuntimeException();
610 newT(v1e, v2e, e.p2).red = true;
611 newT(v2e, v1e, e.p1).red = true;
612 v2e.getE(v1e).bindTo(e.getBindingMatrix(this), v1.getE(v2));
613 v1e.getE(v2e).bindTo(e.pair.getBindingMatrix(this.pair), v2.getE(v1));
618 public void bindingGroupChanged(edu.berkeley.qfat.geom.BindingGroup newBindingGroup_) {
620 edu.berkeley.qfat.geom.BindingGroup<E> newBindingGroup =
621 (edu.berkeley.qfat.geom.BindingGroup<E>)newBindingGroup_;
622 if (newBindingGroup==null) return;
623 if (this==newBindingGroup.getMaster()) return;
624 HashSet<E> nbg = new HashSet<E>();
625 for(E eother : (Iterable<E>)newBindingGroup) nbg.add(eother);
626 for(E eother : nbg) {
627 if (next==null || prev==null) continue;
628 if (eother.next==null || eother.prev==null) continue;
630 if (next.isBoundTo(eother.pair.prev.pair) && !prev.isBoundTo(eother.pair.next.pair))
631 prev.bindTo(next.getBindingMatrix(eother.pair.prev.pair), eother.pair.next.pair);
632 if (!next.isBoundTo(eother.pair.prev.pair) && prev.isBoundTo(eother.pair.next.pair))
633 next.bindTo(prev.getBindingMatrix(eother.pair.next.pair), eother.pair.prev.pair);
636 if (next.isBoundTo(eother.prev) && !prev.isBoundTo(eother.next))
637 prev.bindTo(next.getBindingMatrix(eother.prev), eother.next);
638 if (!next.isBoundTo(eother.prev) && prev.isBoundTo(eother.next))
639 next.bindTo(prev.getBindingMatrix(eother.next), eother.prev);
641 if (next.isBoundTo(eother.next) && !prev.isBoundTo(eother.prev))
642 prev.bindTo(next.getBindingMatrix(eother.next), eother.prev);
643 if (!next.isBoundTo(eother.next) && prev.isBoundTo(eother.prev))
644 next.bindTo(prev.getBindingMatrix(eother.prev), eother.next);
649 public float stretchRatio() {
650 Vertex nearest = error_against.nearest(midpoint());
651 float nearest_distance = midpoint().distance(nearest.p);
652 float other_distance =
653 (p1.p.distance(error_against.nearest(p1.p).p)+
654 p2.p.distance(error_against.nearest(p2.p).p))/2;
655 return nearest_distance/other_distance;
657 public float comparator() {
660 public int compareTo(E e) {
661 return e.comparator() > comparator() ? 1 : -1;
663 public void bindEdge(E e, Matrix m) {
665 pair._bindEdge(e.pair, m);
667 public void _bindEdge(E e, Matrix m) {
670 //assumes edges are identical length at binding time
671 Vec reflectionPlaneNormal = e.p2.p.minus(e.p1.p).norm();
672 float a = reflectionPlaneNormal.x;
673 float b = reflectionPlaneNormal.y;
674 float c = reflectionPlaneNormal.z;
675 Matrix reflectionMatrix =
676 new Matrix( 1-2*a*a, -2*a*b, -2*a*c, 0,
677 -2*a*b, 1-2*b*b, -2*b*c, 0,
678 -2*a*c, -2*b*c, 1-2*c*c, 0,
680 m = m.times(Matrix.translate(e.midpoint().minus(Point.ORIGIN))
681 .times(reflectionMatrix)
682 .times(Matrix.translate(Point.ORIGIN.minus(e.midpoint()))));
683 System.out.println(reflectionPlaneNormal);
684 System.out.println(" " + p1.p + " " + m.times(e.p1.p));
685 System.out.println(" " + p2.p + " " + m.times(e.p2.p));
688 if (m.times(e.p1.p).minus(p1.p).mag() > EPSILON) throw new Error();
689 if (m.times(e.p2.p).minus(p2.p).mag() > EPSILON) throw new Error();
694 public void dobind() {
695 for(E e : (Iterable<E>)getBoundPeers()) {
696 if (e==this) continue;
697 p1.bindTo(getBindingMatrix(e), e.p1);
698 p2.bindTo(getBindingMatrix(e), e.p2);
699 e.p1.setConstraint(getConstraint());
700 e.p2.setConstraint(getConstraint());
704 public Vertex shatter() {
705 if (shattered || destroyed) return nearest(midpoint());
711 for(E e : (Iterable<E>)getBoundPeers()) {
714 E pnext = e.pair.next;
715 E pprev = e.pair.prev;
716 Point mid = e.midpoint();
717 Vertex r = e.next.p2;
718 Vertex l = e.pair.next.p2;
722 newT(r.p, e.p1.p, mid, null, 0);
723 newT(r.p, mid, e.p2.p, null, 0);
724 newT(l.p, mid, e.p1.p, null, 0);
725 newT(l.p, e.p2.p, mid, null, 0);
728 for(E e : (Iterable<E>)getBoundPeers()) {
729 Point mid = e.midpoint();
731 first = e.p1.getE(mid);
734 firstq = e.p2.getE(mid).pair;
737 e.p1.getE(mid). bindTo(e.getBindingMatrix(firste), first);
738 e.p1.getE(mid).pair. bindTo(e.getBindingMatrix(firste), first.pair);
739 e.p2.getE(mid).pair. bindTo(e.getBindingMatrix(firste), firstq);
740 e.p2.getE(mid).pair.pair.bindTo(e.getBindingMatrix(firste), firstq.pair);
743 first.setConstraint(firste.getConstraint());
744 firstq.setConstraint(firste.getConstraint());
746 return nearest(midpoint());
749 public boolean destroyed = false;
750 public void destroy() {
751 if (destroyed) return;
753 pair.destroyed = true;
755 if (t != null) t.destroy();
758 if (pair.t != null) pair.t.destroy();
761 if (next.t != null) next.t.destroy();
762 if (prev.t != null) prev.t.destroy();
766 if (pair.next.t != null) pair.next.t.destroy();
767 if (pair.prev.t != null) pair.next.t.destroy();
771 pair.prev.next = next;
772 next.prev = pair.prev;
773 prev.next = pair.next;
774 pair.next.prev = prev;
776 if (p1.e == this) p1.e = pair.next;
777 if (pair.p1.e == pair) pair.p1.e = next;
779 if (p2.e == this) throw new RuntimeException();
780 if (pair.p2.e == pair) throw new RuntimeException();
804 private void sync() {
805 this.prev.next = this;
806 this.next.prev = this;
807 this.pair.pair = this;
808 if (this.next.p1 != p2) throw new Error();
809 if (this.prev.p2 != p1) throw new Error();
810 if (this.p1.e == null) this.p1.e = this;
811 if (!added) added = true;
813 private boolean added = false;
815 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
817 public double dihedralAngle() {
818 Vec v1 = t.norm().times(-1);
819 Vec v2 = pair.t.norm().times(-1);
820 double prod = v1.norm().dot(v2.norm());
821 prod = Math.min(1,prod);
822 prod = Math.max(-1,prod);
823 double ret = Math.acos(prod);
824 if (Double.isNaN(ret)) throw new Error("nan! " + prod);
828 /** angle between this half-edge and the next */
829 public double angle() {
830 Vec v1 = next.p2.p.minus(p2.p);
831 Vec v2 = this.p1.p.minus(p2.p);
832 return Math.acos(v1.norm().dot(v2.norm()));
835 public Vertex getOther(Vertex v) {
836 if (this.p1 == v) return p2;
837 if (this.p2 == v) return p1;
841 public void makeAdjacent(E e) {
842 if (this.next == e) return;
843 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex: " + this + " " + e);
844 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free " + t + " " + e.t);
846 E freeIncident = p2.getFreeIncident(e, this);
848 e.prev.next = freeIncident.next;
849 freeIncident.next.prev = e.prev;
851 freeIncident.next = this.next;
852 this.next.prev = freeIncident;
861 /** creates an isolated edge out in the middle of space */
862 public E(Point p1, Point p2) {
863 if (vertices.get(p1) != null) throw new Error();
864 if (vertices.get(p2) != null) throw new Error();
865 this.p1 = new Vertex(p1);
866 this.p2 = new Vertex(p2);
867 this.prev = this.next = this.pair = new E(this, this, this);
869 this.p2.e = this.pair;
873 /** adds a new half-edge from prev.p2 to p2 */
874 public E(E prev, Point p) {
876 p2 = vertices.get(p);
877 if (p2 == null) p2 = new Vertex(p);
881 if (prev.destroyed) throw new RuntimeException();
882 if (p2.getE(p1) != null) throw new Error();
884 this.next = this.pair = new E(this, this, prev.next);
886 E q = p2.getFreeIncident();
888 this.next.prev = this;
890 this.prev.next = this;
891 this.pair = new E(q, this, z);
893 if (p2.e==null) p2.e = this.pair;
897 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
898 public E(E prev, E pair, E next) {
901 if (prev.destroyed) throw new RuntimeException();
907 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); }
908 public boolean has(Vertex v) { return v==p1 || v==p2; }
909 public float length() { return p1.p.minus(p2.p).mag(); }
910 public String toString() { return p1+"->"+p2; }
914 public E makeE(Point p1, Point p2) {
915 Vertex v1 = vertices.get(p1);
916 Vertex v2 = vertices.get(p2);
917 if (v1 != null && v2 != null) {
919 if (e != null) return e;
921 if (e != null) return e;
923 if (v1 != null) return new E(v1.getFreeIncident(), p2);
924 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
925 return new E(p1, p2);
927 public boolean coalesce = false;
928 private static float round(float f) {
929 return Math.round(f*1000)/1000f;
931 public T newT(HasPoint p1, HasPoint p2, HasPoint p3) {
932 return newT(p1.getPoint(), p2.getPoint(), p3.getPoint(), null, 0);
934 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
937 for(Vertex v : vertices) { if (p1.distance(v.p) < EPSILON) { p1 = v.p; break; } }
938 for(Vertex v : vertices) { if (p2.distance(v.p) < EPSILON) { p2 = v.p; break; } }
939 for(Vertex v : vertices) { if (p3.distance(v.p) < EPSILON) { p3 = v.p; break; } }
941 p1 = new Point(round(p1.x), round(p1.y), round(p1.z));
942 p2 = new Point(round(p2.x), round(p2.y), round(p2.z));
943 p3 = new Point(round(p3.x), round(p3.y), round(p3.z));
947 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
948 float dot = norm.dot(norm2);
949 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
950 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
952 E e12 = makeE(p1, p2);
953 E e23 = makeE(p2, p3);
954 E e31 = makeE(p3, p1);
955 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
956 e12.makeAdjacent(e23);
957 e23.makeAdjacent(e31);
958 e31.makeAdjacent(e12);
960 T ret = e12.makeT(colorclass);
961 if (e12.t == null) throw new Error();
962 if (e23.t == null) throw new Error();
963 if (e31.t == null) throw new Error();
967 private int max_serial = 0;
968 /** [UNIQUE] a triangle (face) */
969 public final class T extends Triangle {
971 public final int color;
972 public final int colorclass;
974 public boolean red = false;
975 public boolean old = false;
977 public final int serial = max_serial++;
978 public boolean occluded;
980 public Point shatter() {
981 if (destroyed) return null;
984 HashSet<E> forward = new HashSet<E>();
985 HashSet<E> backward = new HashSet<E>();
986 HashSet<E> both = new HashSet<E>();
988 for(E eb : (Iterable<E>)e.getBoundPeers()) {
990 if (eb.next.isBoundTo(e.next) && eb.prev.isBoundTo(e.prev)) {
994 if (eb.pair.next.pair.isBoundTo(e.prev) && eb.pair.prev.pair.isBoundTo(e.next)) {
995 backward.add(eb.pair);
1000 Vertex v1 = e.t.v1();
1001 Vertex v2 = e.t.v2();
1002 Vertex v3 = e.t.v3();
1003 Point c = e.t.centroid();
1011 // FIXME: forward too
1012 for(E ex : backward) {
1013 Vertex v1x = ex.t.v1();
1014 Vertex v2x = ex.t.v2();
1015 Vertex v3x = ex.t.v3();
1016 Point cx = ex.t.centroid();
1017 E ex_next = ex.next;
1018 E ex_prev = ex.prev;
1024 // FIXME: i have no idea if this is right
1025 e.next.bindTo(e.getBindingMatrix(ex.pair), ex.prev);
1026 e.prev.bindTo(e.getBindingMatrix(ex.pair), ex.next);
1027 e.next.pair.bindTo(e.getBindingMatrix(ex.pair), ex.prev.pair);
1028 e.prev.pair.bindTo(e.getBindingMatrix(ex.pair), ex.next.pair);
1030 e_next.next.bindTo(e_next.getBindingMatrix(ex_prev.pair), ex_prev.prev.pair);
1031 e_next.prev.bindTo(e_next.getBindingMatrix(ex_prev.pair), ex_prev.next.pair);
1033 e_prev.next.bindTo(e_prev.getBindingMatrix(ex_next.pair), ex_next.prev.pair);
1034 e_prev.prev.bindTo(e_prev.getBindingMatrix(ex_next.pair), ex_next.next.pair);
1043 for(E e : (Iterable<E>)getBoundPeers()) {
1046 E pnext = e.pair.next;
1047 E pprev = e.pair.prev;
1048 Point mid = e.midpoint();
1049 Vertex r = e.next.p2;
1050 Vertex l = e.pair.next.p2;
1054 newT(r.p, e.p1.p, mid, null, 0);
1055 newT(r.p, mid, e.p2.p, null, 0);
1056 newT(l.p, mid, e.p1.p, null, 0);
1057 newT(l.p, e.p2.p, mid, null, 0);
1060 for(E e : (Iterable<E>)getBoundPeers()) {
1061 Point mid = e.midpoint();
1063 first = e.p1.getE(mid);
1066 firstq = e.p2.getE(mid).pair;
1069 e.p1.getE(mid). bindTo(e.getBindingMatrix(firste), first);
1070 e.p1.getE(mid).pair. bindTo(e.getBindingMatrix(firste), first.pair);
1071 e.p2.getE(mid).pair. bindTo(e.getBindingMatrix(firste), firstq);
1072 e.p2.getE(mid).pair.pair.bindTo(e.getBindingMatrix(firste), firstq.pair);
1076 first.setConstraint(firste.getConstraint());
1077 firstq.setConstraint(firste.getConstraint());
1083 T(E e1, int colorclass) {
1087 if (e1==e2 || e1==e3) throw new Error();
1088 if (e3.next!=e1) throw new Error();
1089 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
1092 e1.next.next.t = this;
1094 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
1096 int color = Math.abs(random.nextInt());
1099 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
1100 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
1101 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
1105 this.colorclass = colorclass;
1106 triangles.add(this);
1108 public E e1() { return e1; }
1109 public E e2() { return e1.next; }
1110 public E e3() { return e1.prev; }
1111 public Vertex v1() { return e1.p1; }
1112 public Vertex v2() { return e1.p2; }
1113 public Vertex v3() { return e1.next.p2; }
1114 public Point p1() { return e1.p1.p; }
1115 public Point p2() { return e1.p2.p; }
1116 public Point p3() { return e1.next.p2.p; }
1117 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
1118 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
1120 public Vertex getOtherVertex(E e) {
1121 if (!hasE(e)) throw new RuntimeException();
1122 if (!e.has(v1())) return v1();
1123 if (!e.has(v2())) return v2();
1124 if (!e.has(v3())) return v3();
1125 throw new RuntimeException();
1128 public void removeFromRTree() { triangles.remove(this); }
1129 public void addToRTree() { triangles.insert(this); }
1130 public void destroy() {
1136 triangles.remove(this);
1139 public void reinsert() { triangles.remove(this); triangles.add(this); }
1141 private boolean destroyed = false;
1142 public boolean destroyed() { return destroyed; }
1144 public boolean shouldBeDrawn() {
1146 if (e1().bindingGroupSize() <= 1) return false;
1147 if (e2().bindingGroupSize() <= 1) return false;
1148 if (e3().bindingGroupSize() <= 1) return false;
1153 public void glTriangle(GL gl, Matrix m) {
1154 gl.glPushName(serial);
1155 gl.glBegin(GL.GL_TRIANGLES);
1161 /** issue gl.glVertex() for each of the triangle's points */
1162 public void glVertices(GL gl, Matrix m) {
1163 if (!shouldBeDrawn()) return;
1164 super.glVertices(gl, m);