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 Point getPoint() { return p; }
88 public float error() { return olderror; }
90 private Vertex(Point p) {
94 if (vertices.get(p) != null) throw new Error();
98 public void reinsert() {
99 vertices.remove(this);
101 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.t.reinsert();
104 public float olderror = 0;
105 public void setError(float nerror) {
111 public float averageTriangleArea() {
114 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
120 public float averageEdgeLength() {
123 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
130 public Matrix _recomputeFundamentalQuadric() {
131 Matrix m = Matrix.ZERO;
133 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
134 m = m.plus(e.t.norm().fundamentalQuadric(e.t.centroid()));
137 return m.times(1/(float)count);
140 public HasQuadric nearest() { return error_against==null ? null : error_against.vertices.nearest(p, this); }
141 public void computeError() {
142 if (error_against==null) return;
144 nearest_in_other_mesh != null
145 ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p)
146 : nearest().fundamentalQuadric().preAndPostMultiply(p);
147 if (quadric_count != 0)
148 nerror = (nerror + quadric.preAndPostMultiply(p))/(quadric_count+1);
150 if (!immutableVertices && quadric_count == 0)
152 //System.out.println(nerror);
153 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
154 double ang = e.dihedralAngle();
155 if (ang > Math.PI) throw new Error();
156 if (ang < -Math.PI) throw new Error();
157 //float minangle = (float)(Math.PI * 0.8);
158 nerror += ((ang / Math.PI)*(ang/Math.PI)) * e.length() * 0.05;
159 //System.out.println(((ang / Math.PI)*(ang/Math.PI)) * 0.000001);
160 //if (ang > minangle) nerror += (ang - minangle);
162 if (e.t.aspect() < 0.2) {
163 nerror += (0.2-e.t.aspect()) * 10;
171 public boolean move(Matrix m, boolean ignoreProblems) {
175 // t2' = t2.getMatrix(t1) * t1'
176 // t2' = t2.getMatrix(t1) * M * t1
177 // t1 = t1.getMatrix(t2) * t2
178 // M * t1 = M * t1.getMatrix(t2) * t2
180 if (bindingGroup!=null && this != bindingGroup.getMaster()) {
181 Matrix v = getBindingMatrix(bindingGroup.getMaster());
182 return ((Vertex)bindingGroup.getMaster()).move(v.inverse().times(m).times(v), ignoreProblems);
185 if (bindingGroup != null) {
187 for(int i=0; i<20 && !m.equals(m2); i++) {
188 m2 = m.times(getConstraint());
189 //System.out.println(m.minus(m2));
191 if (!m.equals(m2)) return true;
195 Point pt = m.times(this.p);
196 for(Vertex v : (Iterable<Vertex>)getBoundPeers()) {
197 Point pt2 = v.getBindingMatrix(this).times(pt);
199 if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) > 5)
200 throw new Error(v.p+" "+pt2+"\n"+op+" "+pt+"\n"+v.getBindingMatrix(this));
201 if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) < 1/5) throw new Error();
203 good &= v.transform(pt2, ignoreProblems, v.getBindingMatrix(this));
206 if (!good && !ignoreProblems) {
207 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
208 v.transform(v.oldp, true, null);
211 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
212 v.recomputeFundamentalQuadricIfNeighborChanged();
213 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
214 v.reComputeErrorAround();
218 /** does NOT update bound pairs! */
219 private boolean transform(Point newp, boolean ignoreProblems, Matrix yes) {
221 if (immutableVertices) throw new Error();
223 unApplyQuadricToNeighbor();
226 boolean illegalbefore = illegal;
229 if (this.p.minus(newp).mag() > 0.1 && !ignoreProblems) {
231 throw new Exception(""+this.p.minus(newp).mag()+" "+ignoreProblems+" "+yes);
232 } catch(Exception e) {
241 applyQuadricToNeighbor();
243 if (!ignoreProblems) {
246 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
247 e.p2.quadricStale = true;
248 return !illegal || (illegalbefore && illegal);
251 public void checkLegality() {
253 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
254 if (Math.abs(e.dihedralAngle()) > (Math.PI * 0.9) ||
255 Math.abs(e.next.dihedralAngle()) > (Math.PI * 0.9)) illegal = true;
256 if (e.t.aspect() < 0.2) illegal = true;
259 if (!illegal) triangles.range(oldp, this.p, (Visitor<T>)this);
262 public void reComputeErrorAround() {
264 if (nearest_in_other_mesh != null)
265 nearest_in_other_mesh.reComputeError();
266 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
267 e.p2.reComputeError();
270 public boolean visit(Object o) {
271 if (o instanceof Vertex)
272 return ((Vertex)o).e != null && ((Vertex)o).norm().dot(Vertex.this.norm()) >= 0;
274 if (illegal) return false;
275 for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
276 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { illegal = true; }
278 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { illegal = true; }
279 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { illegal = true; }
280 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { illegal = true; }
286 public E getFreeIncident() {
287 E ret = getFreeIncident(e, e);
288 if (ret != null) return ret;
289 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
290 System.out.println(e + " " + e.t);
291 throw new Error("unable to find free incident to " + this);
294 public E getFreeIncident(E start, E before) {
295 for(E e = start; e!=null; e=e.pair.next==before?null:e.pair.next)
296 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null)
301 public E getE(Point p2) {
302 Vertex v = vertices.get(p2);
303 if (v==null) return null;
306 public E getE(Vertex p2) {
307 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
308 if (e.p1 == this && e.p2 == p2) return e;
312 private void glNormal(GL gl) {
314 gl.glNormal3f(norm.x, norm.y, norm.z);
317 Vec norm = new Vec(0, 0, 0);
318 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
320 norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
324 public void bindTo(Vertex p) { bindTo(Matrix.ONE, p); }
328 /** [UNIQUE] an edge */
329 public final class E extends HasBindingGroup implements Comparable<E> {
331 public final Vertex p1, p2;
332 T t; // triangle to our "left"
333 E prev; // previous half-edge
334 E next; // next half-edge
335 E pair; // partner half-edge
336 boolean shattered = false;
338 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
340 public void bindingGroupChanged(edu.berkeley.qfat.geom.BindingGroup newBindingGroup_) {
342 edu.berkeley.qfat.geom.BindingGroup<E> newBindingGroup =
343 (edu.berkeley.qfat.geom.BindingGroup<E>)newBindingGroup_;
344 if (newBindingGroup==null) return;
345 if (this==newBindingGroup.getMaster()) return;
346 HashSet<E> nbg = new HashSet<E>();
347 for(E eother : (Iterable<E>)newBindingGroup) nbg.add(eother);
348 for(E eother : nbg) {
349 if (next==null || prev==null) continue;
350 if (eother.next==null || eother.prev==null) continue;
352 if (next.isBoundTo(eother.pair.prev.pair) && !prev.isBoundTo(eother.pair.next.pair))
353 prev.bindTo(next.getBindingMatrix(eother.pair.prev.pair), eother.pair.next.pair);
354 if (!next.isBoundTo(eother.pair.prev.pair) && prev.isBoundTo(eother.pair.next.pair))
355 next.bindTo(prev.getBindingMatrix(eother.pair.next.pair), eother.pair.prev.pair);
357 if (next.isBoundTo(eother.next) && !prev.isBoundTo(eother.prev))
358 prev.bindTo(next.getBindingMatrix(eother.next), eother.prev);
359 if (!next.isBoundTo(eother.next) && prev.isBoundTo(eother.prev))
360 next.bindTo(prev.getBindingMatrix(eother.prev), eother.next);
365 public float stretchRatio() {
366 Vertex nearest = error_against.nearest(midpoint());
367 float nearest_distance = midpoint().distance(nearest.p);
368 float other_distance =
369 (p1.p.distance(error_against.nearest(p1.p).p)+
370 p2.p.distance(error_against.nearest(p2.p).p))/2;
371 return nearest_distance/other_distance;
373 public float comparator() {
375 //return t==null?0:(1/t.aspect());
377 public int compareTo(E e) {
378 return e.comparator() > comparator() ? 1 : -1;
380 public void bindEdge(E e, Matrix m) {
382 pair._bindEdge(e.pair, m);
384 public void _bindEdge(E e, Matrix m) {
387 //assumes edges are identical length at binding time
388 Vec reflectionPlaneNormal = e.p2.p.minus(e.p1.p).norm();
389 float a = reflectionPlaneNormal.x;
390 float b = reflectionPlaneNormal.y;
391 float c = reflectionPlaneNormal.z;
392 Matrix reflectionMatrix =
393 new Matrix( 1-2*a*a, -2*a*b, -2*a*c, 0,
394 -2*a*b, 1-2*b*b, -2*b*c, 0,
395 -2*a*c, -2*b*c, 1-2*c*c, 0,
397 m = m.times(Matrix.translate(e.midpoint().minus(Point.ORIGIN))
398 .times(reflectionMatrix)
399 .times(Matrix.translate(Point.ORIGIN.minus(e.midpoint()))));
400 System.out.println(reflectionPlaneNormal);
401 System.out.println(" " + p1.p + " " + m.times(e.p1.p));
402 System.out.println(" " + p2.p + " " + m.times(e.p2.p));
404 if (m.times(e.p1.p).minus(p1.p).mag() > EPSILON) throw new Error();
405 if (m.times(e.p2.p).minus(p2.p).mag() > EPSILON) throw new Error();
409 public void dobind() {
410 for(E e : (Iterable<E>)getBoundPeers()) {
411 if (e==this) continue;
412 p1.bindTo(getBindingMatrix(e), e.p1);
413 p2.bindTo(getBindingMatrix(e), e.p2);
414 e.p1.setConstraint(getConstraint());
415 e.p2.setConstraint(getConstraint());
419 public Point shatter() {
420 if (shattered || destroyed) return null;
426 for(E e : (Iterable<E>)getBoundPeers()) {
429 E pnext = e.pair.next;
430 E pprev = e.pair.prev;
431 Point mid = e.midpoint();
432 Vertex r = e.next.p2;
433 Vertex l = e.pair.next.p2;
437 newT(r.p, e.p1.p, mid, null, 0);
438 newT(r.p, mid, e.p2.p, null, 0);
439 newT(l.p, mid, e.p1.p, null, 0);
440 newT(l.p, e.p2.p, mid, null, 0);
443 for(E e : (Iterable<E>)getBoundPeers()) {
444 Point mid = e.midpoint();
446 first = e.p1.getE(mid);
449 firstq = e.p2.getE(mid).pair;
452 e.p1.getE(mid). bindTo(e.getBindingMatrix(firste), first);
453 e.p1.getE(mid).pair. bindTo(e.getBindingMatrix(firste), first.pair);
454 e.p2.getE(mid).pair. bindTo(e.getBindingMatrix(firste), firstq);
455 e.p2.getE(mid).pair.pair.bindTo(e.getBindingMatrix(firste), firstq.pair);
458 first.setConstraint(firste.getConstraint());
459 firstq.setConstraint(firste.getConstraint());
464 public boolean destroyed = false;
465 public void destroy() {
466 if (destroyed) return;
468 pair.destroyed = true;
470 if (t != null) t.destroy();
473 if (pair.t != null) pair.t.destroy();
476 if (next.t != null) next.t.destroy();
477 if (prev.t != null) prev.t.destroy();
481 if (pair.next.t != null) pair.next.t.destroy();
482 if (pair.prev.t != null) pair.next.t.destroy();
486 pair.prev.next = next;
487 next.prev = pair.prev;
488 prev.next = pair.next;
490 if (p1.e == this) p1.e = prev.next;
491 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
494 private void sync() {
495 this.prev.next = this;
496 this.next.prev = this;
497 this.pair.pair = this;
498 if (this.next.p1 != p2) throw new Error();
499 if (this.prev.p2 != p1) throw new Error();
500 if (this.p1.e == null) this.p1.e = this;
501 if (!added) added = true;
503 private boolean added = false;
505 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
507 public double dihedralAngle() {
508 Vec v1 = t.norm().times(-1);
509 Vec v2 = pair.t.norm().times(-1);
510 double prod = v1.norm().dot(v2.norm());
511 prod = Math.min(1,prod);
512 prod = Math.max(-1,prod);
513 double ret = Math.acos(prod);
514 if (Double.isNaN(ret)) throw new Error("nan! " + prod);
518 /** angle between this half-edge and the next */
519 public double angle() {
520 Vec v1 = next.p2.p.minus(p2.p);
521 Vec v2 = this.p1.p.minus(p2.p);
522 return Math.acos(v1.norm().dot(v2.norm()));
525 public void makeAdjacent(E e) {
526 if (this.next == e) return;
527 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
528 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free ");
530 E freeIncident = p2.getFreeIncident(e, this);
532 e.prev.next = freeIncident.next;
533 freeIncident.next.prev = e.prev;
535 freeIncident.next = this.next;
536 this.next.prev = freeIncident;
545 /** creates an isolated edge out in the middle of space */
546 public E(Point p1, Point p2) {
547 if (vertices.get(p1) != null) throw new Error();
548 if (vertices.get(p2) != null) throw new Error();
549 this.p1 = new Vertex(p1);
550 this.p2 = new Vertex(p2);
551 this.prev = this.next = this.pair = new E(this, this, this);
553 this.p2.e = this.pair;
557 /** adds a new half-edge from prev.p2 to p2 */
558 public E(E prev, Point p) {
560 p2 = vertices.get(p);
561 if (p2 == null) p2 = new Vertex(p);
565 if (p2.getE(p1) != null) throw new Error();
567 this.next = this.pair = new E(this, this, prev.next);
569 E q = p2.getFreeIncident();
571 this.next.prev = this;
573 this.prev.next = this;
574 this.pair = new E(q, this, z);
576 if (p2.e==null) p2.e = this.pair;
580 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
581 public E(E prev, E pair, E next) {
589 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); }
590 public boolean has(Vertex v) { return v==p1 || v==p2; }
591 public float length() { return p1.p.minus(p2.p).mag(); }
592 public String toString() { return p1+"->"+p2; }
596 public E makeE(Point p1, Point p2) {
597 Vertex v1 = vertices.get(p1);
598 Vertex v2 = vertices.get(p2);
599 if (v1 != null && v2 != null) {
601 if (e != null) return e;
603 if (e != null) return e;
605 if (v1 != null) return new E(v1.getFreeIncident(), p2);
606 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
607 return new E(p1, p2);
609 public boolean coalesce = false;
610 private static float round(float f) {
611 return Math.round(f*1000)/1000f;
613 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
616 for(Vertex v : vertices) { if (p1.distance(v.p) < EPSILON) { p1 = v.p; break; } }
617 for(Vertex v : vertices) { if (p2.distance(v.p) < EPSILON) { p2 = v.p; break; } }
618 for(Vertex v : vertices) { if (p3.distance(v.p) < EPSILON) { p3 = v.p; break; } }
620 p1 = new Point(round(p1.x), round(p1.y), round(p1.z));
621 p2 = new Point(round(p2.x), round(p2.y), round(p2.z));
622 p3 = new Point(round(p3.x), round(p3.y), round(p3.z));
626 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
627 float dot = norm.dot(norm2);
628 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
629 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
631 E e12 = makeE(p1, p2);
632 E e23 = makeE(p2, p3);
633 E e31 = makeE(p3, p1);
634 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
635 e12.makeAdjacent(e23);
636 e23.makeAdjacent(e31);
637 e31.makeAdjacent(e12);
639 T ret = e12.makeT(colorclass);
640 if (e12.t == null) throw new Error();
641 if (e23.t == null) throw new Error();
642 if (e31.t == null) throw new Error();
646 /** [UNIQUE] a triangle (face) */
647 public final class T extends Triangle {
649 public final int color;
650 public final int colorclass;
652 T(E e1, int colorclass) {
656 if (e1==e2 || e1==e3) throw new Error();
657 if (e3.next!=e1) throw new Error();
658 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
661 e1.next.next.t = this;
663 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
665 int color = Math.abs(random.nextInt());
668 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
669 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
670 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
674 this.colorclass = colorclass;
677 public E e1() { return e1; }
678 public E e2() { return e1.next; }
679 public E e3() { return e1.prev; }
680 public Vertex v1() { return e1.p1; }
681 public Vertex v2() { return e1.p2; }
682 public Vertex v3() { return e1.next.p2; }
683 public Point p1() { return e1.p1.p; }
684 public Point p2() { return e1.p2.p; }
685 public Point p3() { return e1.next.p2.p; }
686 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
687 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
689 public void removeFromRTree() { triangles.remove(this); }
690 public void addToRTree() { triangles.insert(this); }
691 public void destroy() { triangles.remove(this); }
692 public void reinsert() { triangles.remove(this); triangles.add(this); }
694 public boolean shouldBeDrawn() {
696 if (e1().bindingGroupSize() <= 1) return false;
697 if (e2().bindingGroupSize() <= 1) return false;
698 if (e3().bindingGroupSize() <= 1) return false;
703 /** issue gl.glVertex() for each of the triangle's points */
704 public void glVertices(GL gl) {
705 if (!shouldBeDrawn()) return;
707 Point p1 = v1().goodp;
708 Point p2 = v2().goodp;
709 Point p3 = v3().goodp;