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, ignoreProblems, v.getBindingMatrix(this));
199 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
200 v.transform(v.oldp, true, null);
203 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
204 v.recomputeFundamentalQuadricIfNeighborChanged();
205 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
206 v.reComputeErrorAround();
210 /** does NOT update bound pairs! */
211 private boolean transform(Point newp, boolean ignoreProblems, Matrix yes) {
213 if (immutableVertices) throw new Error();
215 unApplyQuadricToNeighbor();
219 if (this.p.minus(newp).mag() > 0.1 && !ignoreProblems) {
222 throw new Exception(""+this.p.minus(newp).mag()+" "+ignoreProblems+" "+yes);
223 } catch(Exception e) {
232 applyQuadricToNeighbor();
234 if (!ignoreProblems) {
237 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
238 e.p2.quadricStale = true;
242 public void checkLegality() {
243 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
244 if (Math.abs(e.dihedralAngle()) > (Math.PI * 0.9) ||
245 Math.abs(e.next.dihedralAngle()) > (Math.PI * 0.9)) illegal = true;
246 if (e.t.aspect() < 0.2) illegal = true;
248 if (!illegal) triangles.range(oldp, this.p, (Visitor<T>)this);
251 public void reComputeErrorAround() {
253 if (nearest_in_other_mesh != null)
254 nearest_in_other_mesh.reComputeError();
255 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
256 e.p2.reComputeError();
259 public boolean visit(Object o) {
260 if (o instanceof Vertex)
261 return ((Vertex)o).e != null && ((Vertex)o).norm().dot(Vertex.this.norm()) >= 0;
263 if (illegal) return false;
264 for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
265 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { illegal = true; }
267 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { illegal = true; }
268 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { illegal = true; }
269 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { illegal = true; }
275 public E getFreeIncident() {
276 E ret = getFreeIncident(e, e);
277 if (ret != null) return ret;
278 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
279 System.out.println(e + " " + e.t);
280 throw new Error("unable to find free incident to " + this);
283 public E getFreeIncident(E start, E before) {
284 for(E e = start; e!=null; e=e.pair.next==before?null:e.pair.next)
285 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null)
290 public E getE(Point p2) {
291 Vertex v = vertices.get(p2);
292 if (v==null) return null;
295 public E getE(Vertex p2) {
296 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
297 if (e.p1 == this && e.p2 == p2) return e;
301 private void glNormal(GL gl) {
303 gl.glNormal3f(norm.x, norm.y, norm.z);
306 Vec norm = new Vec(0, 0, 0);
307 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
309 norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
313 public void bindTo(Vertex p) { bindTo(Matrix.ONE, p); }
317 /** [UNIQUE] an edge */
318 public final class E extends HasBindingGroup implements Comparable<E> {
320 public final Vertex p1, p2;
321 T t; // triangle to our "left"
322 E prev; // previous half-edge
323 E next; // next half-edge
324 E pair; // partner half-edge
325 boolean shattered = false;
327 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
329 public void bindingGroupChanged(edu.berkeley.qfat.geom.BindingGroup newBindingGroup_) {
331 edu.berkeley.qfat.geom.BindingGroup<E> newBindingGroup =
332 (edu.berkeley.qfat.geom.BindingGroup<E>)newBindingGroup_;
333 if (newBindingGroup==null) return;
334 if (this==newBindingGroup.getMaster()) return;
335 HashSet<E> nbg = new HashSet<E>();
336 for(E eother : (Iterable<E>)newBindingGroup) nbg.add(eother);
337 for(E eother : nbg) {
338 if (next==null || prev==null) continue;
339 if (eother.next==null || eother.prev==null) continue;
340 if (next.isBoundTo(eother.pair.prev.pair) && !prev.isBoundTo(eother.pair.next.pair))
341 prev.bindTo(next.getBindingMatrix(eother.pair.prev.pair), eother.pair.next.pair);
342 if (!next.isBoundTo(eother.pair.prev.pair) && prev.isBoundTo(eother.pair.next.pair))
343 next.bindTo(prev.getBindingMatrix(eother.pair.next.pair), eother.pair.prev.pair);
345 if (next.isBoundTo(eother.next) && !prev.isBoundTo(eother.prev))
346 prev.bindTo(next.getBindingMatrix(eother.next), eother.prev);
347 if (!next.isBoundTo(eother.next) && prev.isBoundTo(eother.prev))
348 next.bindTo(prev.getBindingMatrix(eother.prev), eother.next);
353 public float stretchRatio() {
354 Vertex nearest = error_against.nearest(midpoint());
355 float nearest_distance = midpoint().distance(nearest.p);
356 float other_distance =
357 (p1.p.distance(error_against.nearest(p1.p).p)+
358 p2.p.distance(error_against.nearest(p2.p).p))/2;
359 return nearest_distance/other_distance;
361 public float comparator() {
363 //return t==null?0:(1/t.aspect());
365 public int compareTo(E e) {
366 return e.comparator() > comparator() ? 1 : -1;
368 public void bindEdge(E e, Matrix m) {
370 pair._bindEdge(e.pair, m);
372 public void _bindEdge(E e, Matrix m) {
375 //assumes edges are identical length at binding time
376 Vec reflectionPlaneNormal = e.p2.p.minus(e.p1.p).norm();
377 float a = reflectionPlaneNormal.x;
378 float b = reflectionPlaneNormal.y;
379 float c = reflectionPlaneNormal.z;
380 Matrix reflectionMatrix =
381 new Matrix( 1-2*a*a, -2*a*b, -2*a*c, 0,
382 -2*a*b, 1-2*b*b, -2*b*c, 0,
383 -2*a*c, -2*b*c, 1-2*c*c, 0,
385 m = m.times(Matrix.translate(e.midpoint().minus(Point.ORIGIN))
386 .times(reflectionMatrix)
387 .times(Matrix.translate(Point.ORIGIN.minus(e.midpoint()))));
388 System.out.println(reflectionPlaneNormal);
389 System.out.println(" " + p1.p + " " + m.times(e.p1.p));
390 System.out.println(" " + p2.p + " " + m.times(e.p2.p));
392 if (m.times(e.p1.p).minus(p1.p).mag() > EPSILON) throw new Error();
393 if (m.times(e.p2.p).minus(p2.p).mag() > EPSILON) throw new Error();
397 public void dobind() {
398 for(E e : (Iterable<E>)getBoundPeers()) {
399 if (e==this) continue;
400 p1.bindTo(getBindingMatrix(e), e.p1);
401 p2.bindTo(getBindingMatrix(e), e.p2);
405 public Point shatter() {
406 if (shattered || destroyed) return null;
412 for(E e : (Iterable<E>)getBoundPeers()) {
415 E pnext = e.pair.next;
416 E pprev = e.pair.prev;
417 Point mid = e.midpoint();
418 Vertex r = e.next.p2;
419 Vertex l = e.pair.next.p2;
423 newT(r.p, e.p1.p, mid, null, 0);
424 newT(r.p, mid, e.p2.p, null, 0);
425 newT(l.p, mid, e.p1.p, null, 0);
426 newT(l.p, e.p2.p, mid, null, 0);
429 for(E e : (Iterable<E>)getBoundPeers()) {
430 Point mid = e.midpoint();
432 first = e.p1.getE(mid);
435 firstq = e.p2.getE(mid).pair;
438 e.p1.getE(mid). bindTo(e.getBindingMatrix(firste), first);
439 e.p1.getE(mid).pair. bindTo(e.getBindingMatrix(firste), first.pair);
440 e.p2.getE(mid).pair. bindTo(e.getBindingMatrix(firste), firstq);
441 e.p2.getE(mid).pair.pair.bindTo(e.getBindingMatrix(firste), firstq.pair);
442 first.bindingGroup.setKrank(e.bindingGroup.krank);
443 firstq.bindingGroup.setKrank(e.bindingGroup.krank);
444 first.pair.bindingGroup.setKrank(e.bindingGroup.krank);
445 firstq.pair.bindingGroup.setKrank(e.bindingGroup.krank);
450 public boolean destroyed = false;
451 public void destroy() {
452 if (destroyed) return;
454 pair.destroyed = true;
456 if (t != null) t.destroy();
459 if (pair.t != null) pair.t.destroy();
462 if (next.t != null) next.t.destroy();
463 if (prev.t != null) prev.t.destroy();
467 if (pair.next.t != null) pair.next.t.destroy();
468 if (pair.prev.t != null) pair.next.t.destroy();
472 pair.prev.next = next;
473 next.prev = pair.prev;
474 prev.next = pair.next;
476 if (p1.e == this) p1.e = prev.next;
477 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
480 private void sync() {
481 this.prev.next = this;
482 this.next.prev = this;
483 this.pair.pair = this;
484 if (this.next.p1 != p2) throw new Error();
485 if (this.prev.p2 != p1) throw new Error();
486 if (this.p1.e == null) this.p1.e = this;
487 if (!added) added = true;
489 private boolean added = false;
491 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
493 public double dihedralAngle() {
494 Vec v1 = t.norm().times(-1);
495 Vec v2 = pair.t.norm().times(-1);
496 return Math.acos(v1.norm().dot(v2.norm()));
499 /** angle between this half-edge and the next */
500 public double angle() {
501 Vec v1 = next.p2.p.minus(p2.p);
502 Vec v2 = this.p1.p.minus(p2.p);
503 return Math.acos(v1.norm().dot(v2.norm()));
506 public void makeAdjacent(E e) {
507 if (this.next == e) return;
508 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
509 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free ");
511 E freeIncident = p2.getFreeIncident(e, this);
513 e.prev.next = freeIncident.next;
514 freeIncident.next.prev = e.prev;
516 freeIncident.next = this.next;
517 this.next.prev = freeIncident;
526 /** creates an isolated edge out in the middle of space */
527 public E(Point p1, Point p2) {
528 if (vertices.get(p1) != null) throw new Error();
529 if (vertices.get(p2) != null) throw new Error();
530 this.p1 = new Vertex(p1);
531 this.p2 = new Vertex(p2);
532 this.prev = this.next = this.pair = new E(this, this, this);
534 this.p2.e = this.pair;
538 /** adds a new half-edge from prev.p2 to p2 */
539 public E(E prev, Point p) {
541 p2 = vertices.get(p);
542 if (p2 == null) p2 = new Vertex(p);
546 if (p2.getE(p1) != null) throw new Error();
548 this.next = this.pair = new E(this, this, prev.next);
550 E q = p2.getFreeIncident();
552 this.next.prev = this;
554 this.prev.next = this;
555 this.pair = new E(q, this, z);
557 if (p2.e==null) p2.e = this.pair;
561 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
562 public E(E prev, E pair, E next) {
570 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); }
571 public boolean has(Vertex v) { return v==p1 || v==p2; }
572 public float length() { return p1.p.minus(p2.p).mag(); }
573 public String toString() { return p1+"->"+p2; }
577 public E makeE(Point p1, Point p2) {
578 Vertex v1 = vertices.get(p1);
579 Vertex v2 = vertices.get(p2);
580 if (v1 != null && v2 != null) {
582 if (e != null) return e;
584 if (e != null) return e;
586 if (v1 != null) return new E(v1.getFreeIncident(), p2);
587 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
588 return new E(p1, p2);
590 public boolean coalesce = false;
591 private static float round(float f) {
592 return Math.round(f*1000)/1000f;
594 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
597 for(Vertex v : vertices) { if (p1.distance(v.p) < EPSILON) { p1 = v.p; break; } }
598 for(Vertex v : vertices) { if (p2.distance(v.p) < EPSILON) { p2 = v.p; break; } }
599 for(Vertex v : vertices) { if (p3.distance(v.p) < EPSILON) { p3 = v.p; break; } }
601 p1 = new Point(round(p1.x), round(p1.y), round(p1.z));
602 p2 = new Point(round(p2.x), round(p2.y), round(p2.z));
603 p3 = new Point(round(p3.x), round(p3.y), round(p3.z));
607 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
608 float dot = norm.dot(norm2);
609 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
610 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
612 E e12 = makeE(p1, p2);
613 E e23 = makeE(p2, p3);
614 E e31 = makeE(p3, p1);
615 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
616 e12.makeAdjacent(e23);
617 e23.makeAdjacent(e31);
618 e31.makeAdjacent(e12);
620 T ret = e12.makeT(colorclass);
621 if (e12.t == null) throw new Error();
622 if (e23.t == null) throw new Error();
623 if (e31.t == null) throw new Error();
627 /** [UNIQUE] a triangle (face) */
628 public final class T extends Triangle {
630 public final int color;
631 public final int colorclass;
633 T(E e1, int colorclass) {
637 if (e1==e2 || e1==e3) throw new Error();
638 if (e3.next!=e1) throw new Error();
639 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
642 e1.next.next.t = this;
644 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
646 int color = Math.abs(random.nextInt());
649 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
650 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
651 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
655 this.colorclass = colorclass;
658 public E e1() { return e1; }
659 public E e2() { return e1.next; }
660 public E e3() { return e1.prev; }
661 public Vertex v1() { return e1.p1; }
662 public Vertex v2() { return e1.p2; }
663 public Vertex v3() { return e1.next.p2; }
664 public Point p1() { return e1.p1.p; }
665 public Point p2() { return e1.p2.p; }
666 public Point p3() { return e1.next.p2.p; }
667 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
668 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
670 public void removeFromRTree() { triangles.remove(this); }
671 public void addToRTree() { triangles.insert(this); }
672 public void destroy() { triangles.remove(this); }
673 public void reinsert() { triangles.remove(this); triangles.add(this); }
675 public boolean shouldBeDrawn() {
677 if (e1().bindingGroupSize() <= 1) return false;
678 if (e2().bindingGroupSize() <= 1) return false;
679 if (e3().bindingGroupSize() <= 1) return false;
684 /** issue gl.glVertex() for each of the triangle's points */
685 public void glVertices(GL gl) {
686 if (!shouldBeDrawn()) return;
688 Point p1 = v1().goodp;
689 Point p2 = v2().goodp;
690 Point p3 = v3().goodp;