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.wlu.cs.levy.CG.KDTree;
10 import edu.berkeley.qfat.bind.*;
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 // fixme used to be .goodp
35 m.times(t.e1().v1.p).glVertex(gl);
36 m.times(t.e1().v2.p).glVertex(gl);
37 m.times(t.e2().v1.p).glVertex(gl);
38 m.times(t.e2().v2.p).glVertex(gl);
39 m.times(t.e3().v1.p).glVertex(gl);
40 m.times(t.e3().v2.p).glVertex(gl);
43 gl.glEnable(GL.GL_LIGHTING);
47 gl.glColor4f((float)(0.25+(0.05*t.color)),
48 (float)(0.25+(0.05*t.color)),
49 (float)(0.75+(0.05*t.color)),
53 gl.glColor4f((float)(0.75+(0.05*t.color)),
54 (float)(0.25+(0.05*t.color)),
55 (float)(0.25+(0.05*t.color)),
61 if (option_errorNormals)
63 for(Mesh.Vertex p : new Mesh.Vertex[] { t.v1(), t.v2(), t.v3() }) {
65 gl.glBegin(GL.GL_LINES);
66 gl.glColor3f(1, 1, 1);
68 p.p.plus(p.norm().times((float)p.error()*10)).glVertex(gl);
74 public boolean immutableVertices;
75 public Mesh error_against = null;
76 public double error = 0;
78 public Mesh(boolean immutableVertices) { this.immutableVertices = immutableVertices; }
80 public void makeVerticesImmutable() { this.immutableVertices = true; }
81 public float error() { return (float)error; }
83 public int size() { return vertices.size(); }
84 public Iterable<Vertex> vertices() { return vertices; }
85 public Iterator<T> iterator() { return triangles.iterator(); }
87 public void rebindPoints() {
89 for(Mesh.T t : this) {
94 // ask edges to re-implement their bindings
95 for(Mesh.T t : this) {
100 System.out.println("rebound!");
103 public void transform(Matrix m) {
104 ArrayList<Vertex> set = new ArrayList<Vertex>();
105 for(Vertex v : vertices) set.add(v);
106 for(Vertex v : set) v.transform(m.times(v.p), true, null);
107 for(Vertex v : set) v.goodp = v.p;
110 public void rebuild() { /*vertices.rebuild();*/ }
111 public Vec diagonal() { return vertices.diagonal(); }
112 public Point centroid() { return vertices.centroid(); }
113 public Vertex nearest(Point p) { return vertices.nearest(p); }
115 /** compute the volume of the mesh */
116 public float volume() {
119 double area = t.area();
120 Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
121 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
122 double height = Math.abs(t.norm().dot(origin_to_centroid));
123 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
129 public void subdivide() {
130 for (Vertex v : vertices()) v.original = true;
131 HashSet<E> edges = new HashSet<E>();
132 HashSet<E> flip = new HashSet<E>();
133 HashSet<T> tris = new HashSet<T>();
142 System.out.println("triangles="+count);
145 if (e.destroyed || e.shattered) continue;
146 e.shatter().edge = true;
147 for(E ex : (Iterable<E>)e.getBoundPeers()) {
148 Vertex m = nearest(ex.midpoint());
150 E e3 = ex.v1.getE(m).next;
160 System.out.println("flip!");
164 System.out.println("count="+count);
167 HashSet<Vertex> verts = new HashSet<Vertex>();
168 for(Vertex v : vertices()) verts.add(v);
169 for (Vertex v : verts)
171 for (Vertex v : verts) {
173 for(E e = v.e; e!=null; e=e.pair.next==v.e?null:e.pair.next) {
181 for(E e = v.e; e!=null; e=e.pair.next==v.e?null:e.pair.next) {
182 for(E e2 = e.v2.e; e2!=null; e2=e2.pair.next==e.v2.e?null:e2.pair.next) {
183 if (e2.v2.original) {
190 for (Vertex v : verts)
192 System.out.println("-------------------------------------------------------------------");
194 for (Vertex v : verts) {
197 for(E e = v.e; e!=null; e=e.pair.next==v.e?null:e.pair.next) {
199 v.wish(e.midpoint());
200 v.wish(e.midpoint());
201 v.wish(e.next.pair.t.centroid());
205 for(int j=0; j<n-3; j++)
206 v.wish(v.getPoint());
209 for (Vertex v : verts)
211 for (Vertex v : verts)
216 // Vertexices //////////////////////////////////////////////////////////////////////////////
219 /** a vertex in the mesh */
220 public final class Vertex extends HasQuadric implements Visitor, HasPoint {
221 public void bindTo(Matrix bindingMatrix, HasBindingGroup other) {
222 bindTo(bindingMatrix, other, EPSILON);
224 public float getMaxX() { return getPoint().getMaxX(); }
225 public float getMinX() { return getPoint().getMinX(); }
226 public float getMaxY() { return getPoint().getMaxY(); }
227 public float getMinY() { return getPoint().getMinY(); }
228 public float getMaxZ() { return getPoint().getMaxZ(); }
229 public float getMinZ() { return getPoint().getMinZ(); }
231 public Point p, goodp;
233 E e; // some edge *leaving* this point
235 public boolean original = false;
236 public boolean edge = false;
237 public boolean face = false;
239 private int wishes = 0;
240 private Point wish = Point.ZERO;
241 public void clearWish() { wishes = 0; wish = Point.ZERO; }
242 public void wish(HasPoint hp) {
243 Point p = hp.getPoint();
245 wish = new Point(wish.x+p.x, wish.y+p.y, wish.z+p.z);
247 public void grantWish() {
248 for(Vertex v : (Iterable<Vertex>)getBoundPeers()) {
249 if (v==this) continue;
250 if (v.wishes==0) continue;
251 Point p = this.getBindingMatrix(v).times(v.wish.minus(Point.ZERO).div(v.wishes).plus(Point.ZERO));
252 wish = p.minus(Point.ZERO).times(v.wishes).plus(wish);
256 if (wishes==0) return;
257 Vec d = wish.minus(Point.ZERO).div(wishes).plus(Point.ZERO).minus(getPoint());
261 public void avgWish() {
262 if (wishes==0) return;
263 wish = wish.minus(Point.ZERO).div(wishes).plus(Point.ZERO);
267 private boolean illegal = false;
269 public boolean visible = false;
271 public Point getPoint() { return p; }
272 public float error() { return olderror; }
274 private Vertex(Point p) {
278 if (vertices.get(p) != null) throw new Error();
282 public void reinsert() {
283 vertices.remove(this);
285 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.t.reinsert();
288 // the average of all adjacent points
289 public Point recenter() {
292 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
293 vec = vec.plus(e.getOther(this).getPoint().minus(Point.ZERO));
296 return Point.ZERO.plus(vec.div(count));
299 public float olderror = 0;
300 public void setError(float nerror) {
307 public Vertex hack(GL gl, Point mouse) {
308 double dist = Double.MAX_VALUE;
310 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
311 Vertex v = e.getOther(this);
312 double dist2 = v.getPoint().glProject(gl).distance(mouse);
313 if ((cur==null || dist2 < dist) && v.visible) {
322 public float averageTriangleArea() {
325 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
331 public float averageEdgeLength() {
334 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
341 public Matrix _recomputeFundamentalQuadric() {
342 Matrix m = Matrix.ZERO;
344 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
345 m = m.plus(e.t.norm().fundamentalQuadric(e.t.centroid()));
349 m = m.plus(norm().fundamentalQuadric(this.p).times(count));
352 return m.times(1/(float)count);
355 public HasQuadric nearest() { return error_against==null ? null : error_against.vertices.nearest(p, this); }
356 public void computeError() {
357 if (error_against==null) return;
358 if (nearest_in_other_mesh == null && nearest()==null) return;
360 nearest_in_other_mesh != null
361 ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p)
362 : nearest().fundamentalQuadric().preAndPostMultiply(p);
363 if (quadric_count != 0)
364 nerror = (nerror + quadric.preAndPostMultiply(p))/(quadric_count+1);
366 if (!immutableVertices && quadric_count == 0) {
367 //nerror = Math.max(nerror, 0.4f);
370 //System.out.println(nerror);
371 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
372 double ang = e.dihedralAngle();
373 if (ang > Math.PI) throw new Error();
374 if (ang < -Math.PI) throw new Error();
375 float minangle = (float)(Math.PI * 0.8);
376 //nerror += ((ang / Math.PI)*(ang/Math.PI)) * e.length() * 0.05;
378 //nerror += (1-e.t.quality())*0.0001;
379 if (ang > minangle) nerror += (ang - minangle);
381 //System.out.println(((ang / Math.PI)*(ang/Math.PI)) * 0.000001);
383 if (e.t.aspect() < 0.2) {
384 nerror += (0.2-e.t.aspect()) * 10;
388 if (!immutableVertices) {
389 Vertex n = (Vertex)nearest();
390 float d = norm().dot(n.norm());
391 if (d > 1 || d < -1) throw new Error();
393 nerror *= (2.0f - d);
395 nerror += 0.0003 * (2.0f + d);
396 nerror *= (2.0f + d);
403 public boolean move(Vec vv, boolean ignoreProblems) {
408 // t2' = t2.getMatrix(t1) * t1'
409 // t2' = t2.getMatrix(t1) * M * t1
410 // t1 = t1.getMatrix(t2) * t2
411 // M * t1 = M * t1.getMatrix(t2) * t2
414 if (bindingGroup!=null && this != bindingGroup.getMaster()) {
415 Matrix m2 = getBindingMatrix(bindingGroup.getMaster());
416 Vec v2 = m2.times(vv.plus(getPoint())).minus(m2.times(getPoint()));
417 return ((Vertex)bindingGroup.getMaster()).move(v2, ignoreProblems);
422 Point pt = vv.plus(getPoint());
424 pt = getBindingConstraint().getProjection(pp);
425 if (pt==null) return false;
426 System.out.println(pt.minus(pp).mag() + " " + getBindingConstraint());
428 for(Vertex v : (Iterable<Vertex>)getBoundPeers()) {
429 Point pt2 = v.getBindingMatrix(this).times(pt);
431 if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) > 5)
432 throw new Error(v.p+" "+pt2+"\n"+op+" "+pt+"\n"+v.getBindingMatrix(this));
433 if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) < 1/5) throw new Error();
435 good &= v.transform(pt2, ignoreProblems, v.getBindingMatrix(this));
438 if (!good && !ignoreProblems) {
439 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
440 v.transform(v.oldp, true, null);
443 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
444 v.recomputeFundamentalQuadricIfNeighborChanged();
445 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
446 v.reComputeErrorAround();
450 public boolean ok = true;
452 /** does NOT update bound pairs! */
453 private boolean transform(Point newp, boolean ignoreProblems, Matrix yes) {
455 if (immutableVertices) throw new Error();
457 unApplyQuadricToNeighbor();
459 boolean illegalbefore = illegal;
462 if (this.p.minus(newp).mag() > 0.1 && !ignoreProblems) {
464 throw new Exception(""+this.p.minus(newp).mag()+" "+ignoreProblems+" "+yes);
465 } catch(Exception e) {
474 applyQuadricToNeighbor();
476 if (!ignoreProblems) {
479 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
480 e.v2.quadricStale = true;
481 return !illegal || (illegalbefore && illegal);
484 public void checkLegality() {
486 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
487 if (Math.abs(e.dihedralAngle()) > (Math.PI * 0.9) ||
488 Math.abs(e.next.dihedralAngle()) > (Math.PI * 0.9)) illegal = true;
489 if (e.t.aspect() < 0.2) illegal = true;
492 if (!illegal) triangles.range(oldp, this.p, (Visitor<T>)this);
495 public void reComputeErrorAround() {
497 if (nearest_in_other_mesh != null)
498 nearest_in_other_mesh.reComputeError();
499 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
500 e.v2.reComputeError();
503 public boolean visit(Object o) {
504 if (o instanceof Vertex)
505 return ((Vertex)o).e != null && ((Vertex)o).norm().dot(Vertex.this.norm()) >= 0;
507 if (illegal) return false;
508 for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
509 if (!t.has(e.v1) && !t.has(e.v2) && e.intersects(t)) { illegal = true; }
511 if (!e.t.has(t.e1().v1) && !e.t.has(t.e1().v2) && t.e1().intersects(e.t)) { illegal = true; }
512 if (!e.t.has(t.e2().v1) && !e.t.has(t.e2().v2) && t.e2().intersects(e.t)) { illegal = true; }
513 if (!e.t.has(t.e3().v1) && !e.t.has(t.e3().v2) && t.e3().intersects(e.t)) { illegal = true; }
519 public E getEdge() { return e; }
520 public E getFreeIncident() {
521 E ret = getFreeIncident(e, e);
522 if (ret != null) return ret;
523 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
524 System.out.println(e + " " + e.t);
525 throw new Error("unable to find free incident to " + this);
528 public E getFreeIncident(E start, E before) {
529 for(E e = start; e!=null; e=e.pair.next==before?null:e.pair.next)
530 if (e.pair.v2 == this && e.pair.t == null && e.pair.next.t == null)
535 public E getE(Point v2) {
536 Vertex v = vertices.get(v2);
537 if (v==null) return null;
540 public E getE(Vertex v2) {
541 if (this.e!=null && this!=this.e.v1 && this!=this.e.v2) throw new RuntimeException();
543 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
544 if (e.v1 == this && e.v2 == v2) return e;
547 if (e.destroyed) throw new RuntimeException("fark " + i + " " + e.prev + " " + (e.prev.next==e) + " " + e.prev.destroyed);
552 private void glNormal(GL gl) {
554 gl.glNormal3f(norm.x, norm.y, norm.z);
557 Vec norm = new Vec(0, 0, 0);
558 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
560 norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
564 public void bindTo(Vertex p) { bindTo(Matrix.ONE, p); }
568 /** [UNIQUE] an edge */
569 public final class E extends HasBindingGroup implements Comparable<E> {
571 public void bindTo(Matrix bindingMatrix, HasBindingGroup other) {
572 bindTo(bindingMatrix, other, EPSILON);
575 public void sanity() {
576 if (destroyed) return;
577 if (pair!=null && (pair.v1!=v2 || pair.v2!=v1)) throw new RuntimeException();
578 if (next!=null && next.v1!=v2) throw new RuntimeException();
579 if (prev!=null && prev.v2!=v1) throw new RuntimeException();
582 public final Vertex v1, v2;
583 T t; // triangle to our "left"
584 E prev; // previous half-edge
585 E next; // next half-edge
586 E pair; // partner half-edge
587 boolean shattered = false;
589 public boolean intersects(T t) { return t.intersects(v1.p, v2.p); }
591 public Segment getSegment() { return new Segment(v1.getPoint(), v2.getPoint()); }
594 // FIXME: coplanarity check needed
595 if (destroyed) return;
596 for (E e : (Iterable<E>)getBoundPeers()) {
597 if (!e.pair.isBoundTo(pair)) throw new RuntimeException("cannot flip!");
599 Vertex v1 = t.getOtherVertex(this);
600 Vertex v2 = pair.t.getOtherVertex(pair);
603 T t1 = newT(v1, v2, this.v2);
604 T t2 = newT(v2, v1, this.v1);
612 for (E e : (Iterable<E>)getBoundPeers()) {
613 if (e==this) continue;
614 if (e.destroyed) continue;
615 Vertex v1e = e.t.getOtherVertex(e);
616 Vertex v2e = e.pair.t.getOtherVertex(e.pair);
619 if (v1e.getE(v2e)!=null) throw new RuntimeException();
620 newT(v1e, v2e, e.v2).red = true;
621 newT(v2e, v1e, e.v1).red = true;
622 v2e.getE(v1e).bindTo(e.getBindingMatrix(this), v1.getE(v2));
623 v1e.getE(v2e).bindTo(e.pair.getBindingMatrix(this.pair), v2.getE(v1));
628 public void bindingGroupChanged() {
629 HashSet<E> nbg = new HashSet<E>();
630 for(E eother : (Iterable<E>)getBoundPeers()) nbg.add(eother);
631 for(E eother : nbg) {
632 if (next==null || prev==null) continue;
633 if (eother.next==null || eother.prev==null) continue;
635 if (next.isBoundTo(eother.pair.prev.pair) && !prev.isBoundTo(eother.pair.next.pair))
636 prev.bindTo(next.getBindingMatrix(eother.pair.prev.pair), eother.pair.next.pair);
637 if (!next.isBoundTo(eother.pair.prev.pair) && prev.isBoundTo(eother.pair.next.pair))
638 next.bindTo(prev.getBindingMatrix(eother.pair.next.pair), eother.pair.prev.pair);
641 if (next.isBoundTo(eother.prev) && !prev.isBoundTo(eother.next))
642 prev.bindTo(next.getBindingMatrix(eother.prev), eother.next);
643 if (!next.isBoundTo(eother.prev) && prev.isBoundTo(eother.next))
644 next.bindTo(prev.getBindingMatrix(eother.next), eother.prev);
646 if (next.isBoundTo(eother.next) && !prev.isBoundTo(eother.prev))
647 prev.bindTo(next.getBindingMatrix(eother.next), eother.prev);
648 if (!next.isBoundTo(eother.next) && prev.isBoundTo(eother.prev))
649 next.bindTo(prev.getBindingMatrix(eother.prev), eother.next);
654 public float stretchRatio() {
655 Vertex nearest = error_against.nearest(midpoint());
656 float nearest_distance = midpoint().distance(nearest.p);
657 float other_distance =
658 (v1.p.distance(error_against.nearest(v1.p).p)+
659 v2.p.distance(error_against.nearest(v2.p).p))/2;
660 return nearest_distance/other_distance;
662 public float comparator() {
665 public int compareTo(E e) {
666 return e.comparator() > comparator() ? 1 : -1;
668 public void bindEdge(E e, Matrix m) {
670 pair._bindEdge(e.pair, m);
672 public void _bindEdge(E e, Matrix m) {
675 //assumes edges are identical length at binding time
676 Vec reflectionPlaneNormal = e.v2.p.minus(e.v1.p).norm();
677 float a = reflectionPlaneNormal.x;
678 float b = reflectionPlaneNormal.y;
679 float c = reflectionPlaneNormal.z;
680 Matrix reflectionMatrix =
681 new Matrix( 1-2*a*a, -2*a*b, -2*a*c, 0,
682 -2*a*b, 1-2*b*b, -2*b*c, 0,
683 -2*a*c, -2*b*c, 1-2*c*c, 0,
685 m = m.times(Matrix.translate(e.midpoint().minus(Point.ORIGIN))
686 .times(reflectionMatrix)
687 .times(Matrix.translate(Point.ORIGIN.minus(e.midpoint()))));
688 System.out.println(reflectionPlaneNormal);
689 System.out.println(" " + v1.p + " " + m.times(e.v1.p));
690 System.out.println(" " + v2.p + " " + m.times(e.v2.p));
693 if (m.times(e.v1.p).minus(v1.p).mag() > EPSILON) throw new Error();
694 if (m.times(e.v2.p).minus(v2.p).mag() > EPSILON) throw new Error();
699 public void dobind() {
700 for(E e : (Iterable<E>)getBoundPeers()) {
701 if (e==this) continue;
702 v1.bindTo(getBindingMatrix(e), e.v1);
703 v2.bindTo(getBindingMatrix(e), e.v2);
705 e.v1.setConstraint(getAffineConstraint());
706 e.v2.setConstraint(getAffineConstraint());
711 public Vertex shatter() {
712 if (shattered || destroyed) return nearest(midpoint());
718 for(E e : (Iterable<E>)getBoundPeers()) {
721 E pnext = e.pair.next;
722 E pprev = e.pair.prev;
723 Point mid = e.midpoint();
724 Vertex r = e.next.v2;
725 Vertex l = e.pair.next.v2;
729 newT(r.p, e.v1.p, mid, null, 0);
730 newT(r.p, mid, e.v2.p, null, 0);
731 newT(l.p, mid, e.v1.p, null, 0);
732 newT(l.p, e.v2.p, mid, null, 0);
735 for(E e : (Iterable<E>)getBoundPeers()) {
736 Point mid = e.midpoint();
738 first = e.v1.getE(mid);
741 firstq = e.v2.getE(mid).pair;
744 e.v1.getE(mid). bindTo(e.getBindingMatrix(firste), first);
745 e.v1.getE(mid).pair. bindTo(e.getBindingMatrix(firste), first.pair);
746 e.v2.getE(mid).pair. bindTo(e.getBindingMatrix(firste), firstq);
747 e.v2.getE(mid).pair.pair.bindTo(e.getBindingMatrix(firste), firstq.pair);
750 first.setConstraint(firste.getAffineConstraint());
751 firstq.setConstraint(firste.getAffineConstraint());
753 return nearest(midpoint());
756 public boolean destroyed = false;
757 public void destroy() {
758 if (destroyed) return;
760 pair.destroyed = true;
762 if (t != null) t.destroy();
765 if (pair.t != null) pair.t.destroy();
768 if (next.t != null) next.t.destroy();
769 if (prev.t != null) prev.t.destroy();
773 if (pair.next.t != null) pair.next.t.destroy();
774 if (pair.prev.t != null) pair.next.t.destroy();
778 pair.prev.next = next;
779 next.prev = pair.prev;
780 prev.next = pair.next;
781 pair.next.prev = prev;
783 if (v1.e == this) v1.e = pair.next;
784 if (pair.v1.e == pair) pair.v1.e = next;
786 if (v2.e == this) throw new RuntimeException();
787 if (pair.v2.e == pair) throw new RuntimeException();
811 private void sync() {
812 this.prev.next = this;
813 this.next.prev = this;
814 this.pair.pair = this;
815 if (this.next.v1 != v2) throw new Error();
816 if (this.prev.v2 != v1) throw new Error();
817 if (this.v1.e == null) this.v1.e = this;
818 if (!added) added = true;
820 private boolean added = false;
822 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
824 public double dihedralAngle() {
825 Vec v1 = t.norm().times(-1);
826 Vec v2 = pair.t.norm().times(-1);
827 double prod = v1.norm().dot(v2.norm());
828 prod = Math.min(1,prod);
829 prod = Math.max(-1,prod);
830 double ret = Math.acos(prod);
831 if (Double.isNaN(ret)) throw new Error("nan! " + prod);
835 /** angle between this half-edge and the next */
836 public double angle() {
837 Vec v1 = next.v2.p.minus(this.v2.p);
838 Vec v2 = this.v1.p.minus(this.v2.p);
839 return Math.acos(v1.norm().dot(v2.norm()));
842 public Vertex getOther(Vertex v) {
843 if (this.v1 == v) return v2;
844 if (this.v2 == v) return v1;
848 public void makeAdjacent(E e) {
849 if (this.next == e) return;
850 if (v2 != e.v1) throw new Error("cannot make adjacent -- no shared vertex: " + this + " " + e);
851 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free " + t + " " + e.t);
853 E freeIncident = v2.getFreeIncident(e, this);
855 e.prev.next = freeIncident.next;
856 freeIncident.next.prev = e.prev;
858 freeIncident.next = this.next;
859 this.next.prev = freeIncident;
868 /** creates an isolated edge out in the middle of space */
869 public E(Point v1, Point v2) {
870 if (vertices.get(v1) != null) throw new Error();
871 if (vertices.get(v2) != null) throw new Error();
872 this.v1 = new Vertex(v1);
873 this.v2 = new Vertex(v2);
874 this.prev = this.next = this.pair = new E(this, this, this);
876 this.v2.e = this.pair;
880 /** adds a new half-edge from prev.v2 to v2 */
881 public E(E prev, Point p) {
883 v2 = vertices.get(p);
884 if (v2 == null) v2 = new Vertex(p);
888 if (prev.destroyed) throw new RuntimeException();
889 if (v2.getE(v1) != null) throw new Error();
891 this.next = this.pair = new E(this, this, prev.next);
893 E q = v2.getFreeIncident();
895 this.next.prev = this;
897 this.prev.next = this;
898 this.pair = new E(q, this, z);
900 if (v2.e==null) v2.e = this.pair;
904 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
905 public E(E prev, E pair, E next) {
908 if (prev.destroyed) throw new RuntimeException();
914 public Point midpoint() { return new Point((v1.p.x+v2.p.x)/2, (v1.p.y+v2.p.y)/2, (v1.p.z+v2.p.z)/2); }
915 public boolean has(Vertex v) { return v==v1 || v==v2; }
916 public float length() { return v1.p.minus(v2.p).mag(); }
917 public String toString() { return v1+"->"+v2; }
921 public E makeE(Point p1, Point p2) {
922 Vertex v1 = vertices.get(p1);
923 Vertex v2 = vertices.get(p2);
924 if (v1 != null && v2 != null) {
926 if (e != null) return e;
928 if (e != null) return e;
930 if (v1 != null) return new E(v1.getFreeIncident(), p2);
931 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
932 return new E(p1, p2);
934 public boolean coalesce = false;
935 private static float round(float f) {
936 return Math.round(f*1000)/1000f;
938 public T newT(HasPoint v1, HasPoint v2, HasPoint v3) {
939 return newT(v1.getPoint(), v2.getPoint(), v3.getPoint(), null, 0);
941 public T newT(Point v1, Point v2, Point v3, Vec norm, int colorclass) {
944 for(Vertex v : vertices) { if (v1.distance(v.p) < EPSILON) { v1 = v.p; break; } }
945 for(Vertex v : vertices) { if (v2.distance(v.p) < EPSILON) { v2 = v.p; break; } }
946 for(Vertex v : vertices) { if (v3.distance(v.p) < EPSILON) { v3 = v.p; break; } }
948 v1 = new Point(round(v1.x), round(v1.y), round(v1.z));
949 v2 = new Point(round(v2.x), round(v2.y), round(v2.z));
950 v3 = new Point(round(v3.x), round(v3.y), round(v3.z));
954 Vec norm2 = v3.minus(v1).cross(v2.minus(v1));
955 float dot = norm.dot(norm2);
956 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
957 if (dot < 0) { Point p = v1; v1=v2; v2 = p; }
959 E e12 = makeE(v1, v2);
960 E e23 = makeE(v2, v3);
961 E e31 = makeE(v3, v1);
962 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
963 e12.makeAdjacent(e23);
964 e23.makeAdjacent(e31);
965 e31.makeAdjacent(e12);
967 T ret = e12.makeT(colorclass);
968 if (e12.t == null) throw new Error();
969 if (e23.t == null) throw new Error();
970 if (e31.t == null) throw new Error();
974 private int max_serial = 0;
975 /** [UNIQUE] a triangle (face) */
976 public final class T extends Triangle {
978 public final int color;
979 public final int colorclass;
981 public boolean red = false;
982 public boolean old = false;
984 public final int serial = max_serial++;
985 public boolean occluded;
987 public Point shatter() {
988 if (destroyed) return null;
991 HashSet<E> forward = new HashSet<E>();
992 HashSet<E> backward = new HashSet<E>();
993 HashSet<E> both = new HashSet<E>();
995 for(E eb : (Iterable<E>)e.getBoundPeers()) {
997 if (eb.next.isBoundTo(e.next) && eb.prev.isBoundTo(e.prev)) {
1001 if (eb.pair.next.pair.isBoundTo(e.prev) && eb.pair.prev.pair.isBoundTo(e.next)) {
1002 backward.add(eb.pair);
1007 Vertex v1 = e.t.v1();
1008 Vertex v2 = e.t.v2();
1009 Vertex v3 = e.t.v3();
1010 Point c = e.t.centroid();
1018 // FIXME: forward too
1019 for(E ex : backward) {
1020 Vertex v1x = ex.t.v1();
1021 Vertex v2x = ex.t.v2();
1022 Vertex v3x = ex.t.v3();
1023 Point cx = ex.t.centroid();
1024 E ex_next = ex.next;
1025 E ex_prev = ex.prev;
1031 // FIXME: i have no idea if this is right
1032 e.next.bindTo(e.getBindingMatrix(ex.pair), ex.prev);
1033 e.prev.bindTo(e.getBindingMatrix(ex.pair), ex.next);
1034 e.next.pair.bindTo(e.getBindingMatrix(ex.pair), ex.prev.pair);
1035 e.prev.pair.bindTo(e.getBindingMatrix(ex.pair), ex.next.pair);
1037 e_next.next.bindTo(e_next.getBindingMatrix(ex_prev.pair), ex_prev.prev.pair);
1038 e_next.prev.bindTo(e_next.getBindingMatrix(ex_prev.pair), ex_prev.next.pair);
1040 e_prev.next.bindTo(e_prev.getBindingMatrix(ex_next.pair), ex_next.prev.pair);
1041 e_prev.prev.bindTo(e_prev.getBindingMatrix(ex_next.pair), ex_next.next.pair);
1050 for(E e : (Iterable<E>)getBoundPeers()) {
1053 E pnext = e.pair.next;
1054 E pprev = e.pair.prev;
1055 Point mid = e.midpoint();
1056 Vertex r = e.next.v2;
1057 Vertex l = e.pair.next.v2;
1061 newT(r.p, e.v1.p, mid, null, 0);
1062 newT(r.p, mid, e.v2.p, null, 0);
1063 newT(l.p, mid, e.v1.p, null, 0);
1064 newT(l.p, e.v2.p, mid, null, 0);
1067 for(E e : (Iterable<E>)getBoundPeers()) {
1068 Point mid = e.midpoint();
1070 first = e.v1.getE(mid);
1073 firstq = e.v2.getE(mid).pair;
1076 e.v1.getE(mid). bindTo(e.getBindingMatrix(firste), first);
1077 e.v1.getE(mid).pair. bindTo(e.getBindingMatrix(firste), first.pair);
1078 e.v2.getE(mid).pair. bindTo(e.getBindingMatrix(firste), firstq);
1079 e.v2.getE(mid).pair.pair.bindTo(e.getBindingMatrix(firste), firstq.pair);
1083 first.setConstraint(firste.getAffineConstraint());
1084 firstq.setConstraint(firste.getAffineConstraint());
1090 T(E e1, int colorclass) {
1094 if (e1==e2 || e1==e3) throw new Error();
1095 if (e3.next!=e1) throw new Error();
1096 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
1099 e1.next.next.t = this;
1101 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
1103 int color = Math.abs(random.nextInt());
1106 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
1107 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
1108 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
1112 this.colorclass = colorclass;
1113 triangles.add(this);
1115 public E e1() { return e1; }
1116 public E e2() { return e1.next; }
1117 public E e3() { return e1.prev; }
1118 public Vertex v1() { return e1.v1; }
1119 public Vertex v2() { return e1.v2; }
1120 public Vertex v3() { return e1.next.v2; }
1121 public Point p1() { return e1.v1.p; }
1122 public Point p2() { return e1.v2.p; }
1123 public Point p3() { return e1.next.v2.p; }
1124 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
1125 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
1127 public Vertex getOtherVertex(E e) {
1128 if (!hasE(e)) throw new RuntimeException();
1129 if (!e.has(v1())) return v1();
1130 if (!e.has(v2())) return v2();
1131 if (!e.has(v3())) return v3();
1132 throw new RuntimeException();
1135 public void removeFromRTree() { triangles.remove(this); }
1136 public void addToRTree() { triangles.insert(this); }
1137 public void destroy() {
1143 triangles.remove(this);
1146 public void reinsert() { triangles.remove(this); triangles.add(this); }
1148 private boolean destroyed = false;
1149 public boolean destroyed() { return destroyed; }
1151 public boolean shouldBeDrawn() {
1153 if (e1().bindingGroupSize() <= 1) return false;
1154 if (e2().bindingGroupSize() <= 1) return false;
1155 if (e3().bindingGroupSize() <= 1) return false;
1160 public void glTriangle(GL gl, Matrix m) {
1161 gl.glPushName(serial);
1162 gl.glBegin(GL.GL_TRIANGLES);
1168 /** issue gl.glVertex() for each of the triangle's points */
1169 public void glVertices(GL gl, Matrix m) {
1170 if (!shouldBeDrawn()) return;
1171 super.glVertices(gl, m);