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);
57 public void rebuild() { /*vertices.rebuild();*/ }
58 public Vec diagonal() { return vertices.diagonal(); }
59 public Point centroid() { return vertices.centroid(); }
60 public Vertex nearest(Point p) { return vertices.nearest(p); }
62 /** compute the volume of the mesh */
63 public float volume() {
66 double area = t.area();
67 Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
68 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
69 double height = Math.abs(t.norm().dot(origin_to_centroid));
70 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
76 // Vertexices //////////////////////////////////////////////////////////////////////////////
78 /** a vertex in the mesh */
79 public final class Vertex extends HasQuadric implements Visitor {
80 public Point p, goodp;
82 E e; // some edge *leaving* this point
84 private boolean illegal = false;
86 public Point getPoint() { return p; }
87 public float error() { return olderror; }
89 private Vertex(Point p) {
92 if (vertices.get(p) != null) throw new Error();
96 public void reinsert() {
97 vertices.remove(this);
99 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.t.reinsert();
102 public float olderror = 0;
103 public void setError(float nerror) {
109 public float averageTriangleArea() {
112 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
118 public float averageEdgeLength() {
121 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
128 public Matrix _recomputeFundamentalQuadric() {
129 Matrix m = Matrix.ZERO;
131 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
132 m = m.plus(e.t.norm().fundamentalQuadric(e.t.centroid()));
135 return m.times(1/(float)count);
138 public HasQuadric nearest() { return error_against==null ? null : error_against.vertices.nearest(p, this); }
139 public void computeError() {
140 if (error_against==null) return;
142 nearest_in_other_mesh != null
143 ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p)
144 : nearest().fundamentalQuadric().preAndPostMultiply(p);
145 if (quadric_count != 0)
146 nerror = (nerror + quadric.preAndPostMultiply(p))/(quadric_count+1);
148 if (!immutableVertices && quadric_count == 0)
151 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
152 double ang = Math.abs(e.dihedralAngle());
153 if (ang > Math.PI) throw new Error();
154 float minangle = (float)(Math.PI * 0.8);
155 if (ang > minangle) nerror += (ang - minangle);
156 if (e.t.aspect() < 0.2) {
157 nerror += (0.2-e.t.aspect()) * 10;
164 public boolean move(Matrix m, boolean ignoreProblems) {
168 // t2' = t2.getMatrix(t1) * t1'
169 // t2' = t2.getMatrix(t1) * M * t1
170 // t1 = t1.getMatrix(t2) * t2
171 // M * t1 = M * t1.getMatrix(t2) * t2
172 if (bindingGroup!=null && this != bindingGroup.getMaster()) {
173 Matrix v = getBindingMatrix(bindingGroup.getMaster());
174 return ((Vertex)bindingGroup.getMaster()).move(v.inverse().times(m).times(v), ignoreProblems);
177 if (bindingGroup != null) {
179 for(int i=0; i<20 && !m.equals(m2); i++) {
180 m2 = m.times(bindingGroup.krank);
181 //System.out.println(m.minus(m2));
183 if (!m.equals(m2)) return true;
187 Point pt = m.times(this.p);
188 for(Vertex v : (Iterable<Vertex>)getBoundPeers()) {
189 Point pt2 = v.getBindingMatrix(this).times(pt);
191 if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) > 5)
192 throw new Error(v.p+" "+pt2+"\n"+op+" "+pt+"\n"+v.getBindingMatrix(this));
193 if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) < 1/5) throw new Error();
195 good &= v.transform(pt2,
196 ignoreProblems, v.getBindingMatrix(this));
199 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
200 v.recomputeFundamentalQuadricIfNeighborChanged();
204 /** does NOT update bound pairs! */
205 private boolean transform(Point newp, boolean ignoreProblems, Matrix yes) {
207 if (immutableVertices) throw new Error();
209 unApplyQuadricToNeighbor();
213 if (this.p.minus(newp).mag() > 0.1 && !ignoreProblems) {
216 throw new Exception(""+this.p.minus(newp).mag()+" "+ignoreProblems+" "+yes);
217 } catch(Exception e) {
226 applyQuadricToNeighbor();
228 if (!ignoreProblems) {
231 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
232 e.p2.quadricStale = true;
236 public void checkLegality() {
237 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
238 if (Math.abs(e.dihedralAngle()) > (Math.PI * 0.9) ||
239 Math.abs(e.next.dihedralAngle()) > (Math.PI * 0.9)) illegal = true;
240 if (e.t.aspect() < 0.2) illegal = true;
242 if (!illegal) triangles.range(oldp, this.p, (Visitor<T>)this);
245 public void reComputeErrorAround() {
247 if (nearest_in_other_mesh != null)
248 nearest_in_other_mesh.reComputeError();
249 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
250 e.p2.reComputeError();
253 public boolean visit(Object o) {
254 if (o instanceof Vertex)
255 return ((Vertex)o).e != null && ((Vertex)o).norm().dot(Vertex.this.norm()) >= 0;
257 if (illegal) return false;
258 for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
259 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { illegal = true; }
261 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { illegal = true; }
262 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { illegal = true; }
263 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { illegal = true; }
269 public E getFreeIncident() {
270 E ret = getFreeIncident(e, e);
271 if (ret != null) return ret;
272 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
273 System.out.println(e + " " + e.t);
274 throw new Error("unable to find free incident to " + this);
277 public E getFreeIncident(E start, E before) {
278 for(E e = start; e!=null; e=e.pair.next==before?null:e.pair.next)
279 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null)
284 public E getE(Point p2) {
285 Vertex v = vertices.get(p2);
286 if (v==null) return null;
289 public E getE(Vertex p2) {
290 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
291 if (e.p1 == this && e.p2 == p2) return e;
295 private void glNormal(GL gl) {
297 gl.glNormal3f(norm.x, norm.y, norm.z);
300 Vec norm = new Vec(0, 0, 0);
301 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
303 norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
307 public void bindTo(Vertex p) { bindTo(Matrix.ONE, p); }
311 /** [UNIQUE] an edge */
312 public final class E extends HasBindingGroup implements Comparable<E> {
314 public final Vertex p1, p2;
315 T t; // triangle to our "left"
316 E prev; // previous half-edge
317 E next; // next half-edge
318 E pair; // partner half-edge
319 boolean shattered = false;
321 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
323 public void bindingGroupChanged(edu.berkeley.qfat.geom.BindingGroup newBindingGroup_) {
325 edu.berkeley.qfat.geom.BindingGroup<E> newBindingGroup =
326 (edu.berkeley.qfat.geom.BindingGroup<E>)newBindingGroup_;
327 if (newBindingGroup==null) return;
328 if (this==newBindingGroup.getMaster()) return;
329 HashSet<E> nbg = new HashSet<E>();
330 for(E eother : (Iterable<E>)newBindingGroup) nbg.add(eother);
331 for(E eother : nbg) {
332 if (next==null || prev==null) continue;
333 if (eother.next==null || eother.prev==null) continue;
334 if (next.isBoundTo(eother.pair.prev.pair) && !prev.isBoundTo(eother.pair.next.pair))
335 prev.bindTo(next.getBindingMatrix(eother.pair.prev.pair), eother.pair.next.pair);
336 if (!next.isBoundTo(eother.pair.prev.pair) && prev.isBoundTo(eother.pair.next.pair))
337 next.bindTo(prev.getBindingMatrix(eother.pair.next.pair), eother.pair.prev.pair);
339 if (next.isBoundTo(eother.next) && !prev.isBoundTo(eother.prev))
340 prev.bindTo(next.getBindingMatrix(eother.next), eother.prev);
341 if (!next.isBoundTo(eother.next) && prev.isBoundTo(eother.prev))
342 next.bindTo(prev.getBindingMatrix(eother.prev), eother.next);
347 public float stretchRatio() {
348 Vertex nearest = error_against.nearest(midpoint());
349 float nearest_distance = midpoint().distance(nearest.p);
350 float other_distance =
351 (p1.p.distance(error_against.nearest(p1.p).p)+
352 p2.p.distance(error_against.nearest(p2.p).p))/2;
353 return nearest_distance/other_distance;
355 public float comparator() {
357 //return t==null?0:(1/t.aspect());
359 public int compareTo(E e) {
360 return e.comparator() > comparator() ? 1 : -1;
362 public void bindEdge(E e, Matrix m) {
364 pair._bindEdge(e.pair, m);
366 public void _bindEdge(E e, Matrix m) {
369 //assumes edges are identical length at binding time
370 Vec reflectionPlaneNormal = e.p2.p.minus(e.p1.p).norm();
371 float a = reflectionPlaneNormal.x;
372 float b = reflectionPlaneNormal.y;
373 float c = reflectionPlaneNormal.z;
374 Matrix reflectionMatrix =
375 new Matrix( 1-2*a*a, -2*a*b, -2*a*c, 0,
376 -2*a*b, 1-2*b*b, -2*b*c, 0,
377 -2*a*c, -2*b*c, 1-2*c*c, 0,
379 m = m.times(Matrix.translate(e.midpoint().minus(Point.ORIGIN))
380 .times(reflectionMatrix)
381 .times(Matrix.translate(Point.ORIGIN.minus(e.midpoint()))));
382 System.out.println(reflectionPlaneNormal);
383 System.out.println(" " + p1.p + " " + m.times(e.p1.p));
384 System.out.println(" " + p2.p + " " + m.times(e.p2.p));
386 if (m.times(e.p1.p).minus(p1.p).mag() > EPSILON) throw new Error();
387 if (m.times(e.p2.p).minus(p2.p).mag() > EPSILON) throw new Error();
391 public void dobind() {
392 for(E e : (Iterable<E>)getBoundPeers()) {
393 if (e==this) continue;
394 p1.bindTo(getBindingMatrix(e), e.p1);
395 p2.bindTo(getBindingMatrix(e), e.p2);
399 public Point shatter() {
400 if (shattered || destroyed) return null;
406 for(E e : (Iterable<E>)getBoundPeers()) {
409 E pnext = e.pair.next;
410 E pprev = e.pair.prev;
411 Point mid = e.midpoint();
412 Vertex r = e.next.p2;
413 Vertex l = e.pair.next.p2;
416 newT(r.p, e.p1.p, mid, null, 0);
417 newT(r.p, mid, e.p2.p, null, 0);
418 newT(l.p, mid, e.p1.p, null, 0);
419 newT(l.p, e.p2.p, mid, null, 0);
421 for(E e : (Iterable<E>)getBoundPeers()) {
422 Point mid = e.midpoint();
424 first = e.p1.getE(mid);
427 firstq = e.p2.getE(mid).pair;
430 e.p1.getE(mid). bindTo(e.getBindingMatrix(firste), first);
431 e.p1.getE(mid).pair. bindTo(e.getBindingMatrix(firste), first.pair);
432 e.p2.getE(mid).pair. bindTo(e.getBindingMatrix(firste), firstq);
433 e.p2.getE(mid).pair.pair.bindTo(e.getBindingMatrix(firste), firstq.pair);
438 public boolean destroyed = false;
439 public void destroy() {
440 if (destroyed) return;
442 pair.destroyed = true;
444 if (t != null) t.destroy();
447 if (pair.t != null) pair.t.destroy();
450 if (next.t != null) next.t.destroy();
451 if (prev.t != null) prev.t.destroy();
455 if (pair.next.t != null) pair.next.t.destroy();
456 if (pair.prev.t != null) pair.next.t.destroy();
460 pair.prev.next = next;
461 next.prev = pair.prev;
462 prev.next = pair.next;
464 if (p1.e == this) p1.e = prev.next;
465 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
468 private void sync() {
469 this.prev.next = this;
470 this.next.prev = this;
471 this.pair.pair = this;
472 if (this.next.p1 != p2) throw new Error();
473 if (this.prev.p2 != p1) throw new Error();
474 if (this.p1.e == null) this.p1.e = this;
475 if (!added) added = true;
477 private boolean added = false;
479 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
481 public double dihedralAngle() {
482 Vec v1 = t.norm().times(-1);
483 Vec v2 = pair.t.norm().times(-1);
484 return Math.acos(v1.norm().dot(v2.norm()));
487 /** angle between this half-edge and the next */
488 public double angle() {
489 Vec v1 = next.p2.p.minus(p2.p);
490 Vec v2 = this.p1.p.minus(p2.p);
491 return Math.acos(v1.norm().dot(v2.norm()));
494 public void makeAdjacent(E e) {
495 if (this.next == e) return;
496 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
497 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free ");
499 E freeIncident = p2.getFreeIncident(e, this);
501 e.prev.next = freeIncident.next;
502 freeIncident.next.prev = e.prev;
504 freeIncident.next = this.next;
505 this.next.prev = freeIncident;
514 /** creates an isolated edge out in the middle of space */
515 public E(Point p1, Point p2) {
516 if (vertices.get(p1) != null) throw new Error();
517 if (vertices.get(p2) != null) throw new Error();
518 this.p1 = new Vertex(p1);
519 this.p2 = new Vertex(p2);
520 this.prev = this.next = this.pair = new E(this, this, this);
522 this.p2.e = this.pair;
526 /** adds a new half-edge from prev.p2 to p2 */
527 public E(E prev, Point p) {
529 p2 = vertices.get(p);
530 if (p2 == null) p2 = new Vertex(p);
534 if (p2.getE(p1) != null) throw new Error();
536 this.next = this.pair = new E(this, this, prev.next);
538 E q = p2.getFreeIncident();
540 this.next.prev = this;
542 this.prev.next = this;
543 this.pair = new E(q, this, z);
545 if (p2.e==null) p2.e = this.pair;
549 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
550 public E(E prev, E pair, E next) {
558 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); }
559 public boolean has(Vertex v) { return v==p1 || v==p2; }
560 public float length() { return p1.p.minus(p2.p).mag(); }
561 public String toString() { return p1+"->"+p2; }
565 public E makeE(Point p1, Point p2) {
566 Vertex v1 = vertices.get(p1);
567 Vertex v2 = vertices.get(p2);
568 if (v1 != null && v2 != null) {
570 if (e != null) return e;
572 if (e != null) return e;
574 if (v1 != null) return new E(v1.getFreeIncident(), p2);
575 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
576 return new E(p1, p2);
578 public boolean coalesce = false;
579 private static float round(float f) {
580 return Math.round(f*1000)/1000f;
582 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
585 for(Vertex v : vertices) { if (p1.distance(v.p) < EPSILON) { p1 = v.p; break; } }
586 for(Vertex v : vertices) { if (p2.distance(v.p) < EPSILON) { p2 = v.p; break; } }
587 for(Vertex v : vertices) { if (p3.distance(v.p) < EPSILON) { p3 = v.p; break; } }
589 p1 = new Point(round(p1.x), round(p1.y), round(p1.z));
590 p2 = new Point(round(p2.x), round(p2.y), round(p2.z));
591 p3 = new Point(round(p3.x), round(p3.y), round(p3.z));
595 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
596 float dot = norm.dot(norm2);
597 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
598 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
600 E e12 = makeE(p1, p2);
601 E e23 = makeE(p2, p3);
602 E e31 = makeE(p3, p1);
603 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
604 e12.makeAdjacent(e23);
605 e23.makeAdjacent(e31);
606 e31.makeAdjacent(e12);
608 T ret = e12.makeT(colorclass);
609 if (e12.t == null) throw new Error();
610 if (e23.t == null) throw new Error();
611 if (e31.t == null) throw new Error();
615 /** [UNIQUE] a triangle (face) */
616 public final class T extends Triangle {
618 public final int color;
619 public final int colorclass;
621 T(E e1, int colorclass) {
625 if (e1==e2 || e1==e3) throw new Error();
626 if (e3.next!=e1) throw new Error();
627 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
630 e1.next.next.t = this;
632 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
634 int color = Math.abs(random.nextInt());
637 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
638 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
639 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
643 this.colorclass = colorclass;
646 public E e1() { return e1; }
647 public E e2() { return e1.next; }
648 public E e3() { return e1.prev; }
649 public Vertex v1() { return e1.p1; }
650 public Vertex v2() { return e1.p2; }
651 public Vertex v3() { return e1.next.p2; }
652 public Point p1() { return e1.p1.p; }
653 public Point p2() { return e1.p2.p; }
654 public Point p3() { return e1.next.p2.p; }
655 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
656 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
658 public void removeFromRTree() { triangles.remove(this); }
659 public void addToRTree() { triangles.insert(this); }
660 public void destroy() { triangles.remove(this); }
661 public void reinsert() { triangles.remove(this); triangles.add(this); }
663 public boolean shouldBeDrawn() {
665 if (e1().bindingGroupSize() <= 1) return false;
666 if (e2().bindingGroupSize() <= 1) return false;
667 if (e3().bindingGroupSize() <= 1) return false;
672 /** issue gl.glVertex() for each of the triangle's points */
673 public void glVertices(GL gl) {
674 if (!shouldBeDrawn()) return;
676 Point p1 = v1().goodp;
677 Point p2 = v2().goodp;
678 Point p3 = v3().goodp;