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
173 Point pt = m.times(this.p);
174 for(Vertex v : (Iterable<Vertex>)getBoundPeers()) {
175 Point pt2 = v.getBindingMatrix(this).times(pt);
177 if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) > 5)
178 throw new Error(v.p+" "+pt2+"\n"+op+" "+pt+"\n"+v.getBindingMatrix(this));
179 if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) < 1/5) throw new Error();
181 good &= v.transform(pt2,
182 ignoreProblems, v.getBindingMatrix(this));
185 for(Vertex v : (Iterable<Vertex>)getBoundPeers())
186 v.recomputeFundamentalQuadricIfNeighborChanged();
190 /** does NOT update bound pairs! */
191 private boolean transform(Point newp, boolean ignoreProblems, Matrix yes) {
193 if (immutableVertices) throw new Error();
195 unApplyQuadricToNeighbor();
199 if (this.p.minus(newp).mag() > 0.1 && !ignoreProblems) {
202 throw new Exception(""+this.p.minus(newp).mag()+" "+ignoreProblems+" "+yes);
203 } catch(Exception e) {
212 applyQuadricToNeighbor();
214 if (!ignoreProblems) {
217 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
218 e.p2.quadricStale = true;
222 public void checkLegality() {
223 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
224 if (Math.abs(e.dihedralAngle()) > (Math.PI * 0.9) ||
225 Math.abs(e.next.dihedralAngle()) > (Math.PI * 0.9)) illegal = true;
226 if (e.t.aspect() < 0.2) illegal = true;
228 if (!illegal) triangles.range(oldp, this.p, (Visitor<T>)this);
231 public void reComputeErrorAround() {
233 if (nearest_in_other_mesh != null)
234 nearest_in_other_mesh.reComputeError();
235 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
236 e.p2.reComputeError();
239 public boolean visit(Object o) {
240 if (o instanceof Vertex)
241 return ((Vertex)o).e != null && ((Vertex)o).norm().dot(Vertex.this.norm()) >= 0;
243 if (illegal) return false;
244 for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
245 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { illegal = true; }
247 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { illegal = true; }
248 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { illegal = true; }
249 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { illegal = true; }
255 public E getFreeIncident() {
256 E ret = getFreeIncident(e, e);
257 if (ret != null) return ret;
258 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
259 System.out.println(e + " " + e.t);
260 throw new Error("unable to find free incident to " + this);
263 public E getFreeIncident(E start, E before) {
264 for(E e = start; e!=null; e=e.pair.next==before?null:e.pair.next)
265 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null)
270 public E getE(Point p2) {
271 Vertex v = vertices.get(p2);
272 if (v==null) return null;
275 public E getE(Vertex p2) {
276 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
277 if (e.p1 == this && e.p2 == p2) return e;
281 private void glNormal(GL gl) {
283 gl.glNormal3f(norm.x, norm.y, norm.z);
286 Vec norm = new Vec(0, 0, 0);
287 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
289 norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
293 public void bindTo(Vertex p) { bindTo(Matrix.ONE, p); }
297 /** [UNIQUE] an edge */
298 public final class E extends HasBindingGroup implements Comparable<E> {
300 public final Vertex p1, p2;
301 T t; // triangle to our "left"
302 E prev; // previous half-edge
303 E next; // next half-edge
304 E pair; // partner half-edge
305 boolean shattered = false;
307 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
309 public void bindingGroupChanged(edu.berkeley.qfat.geom.BindingGroup newBindingGroup_) {
311 edu.berkeley.qfat.geom.BindingGroup<E> newBindingGroup =
312 (edu.berkeley.qfat.geom.BindingGroup<E>)newBindingGroup_;
313 if (newBindingGroup==null) return;
314 if (this==newBindingGroup.getMaster()) return;
315 for(E eother : (Iterable<E>)newBindingGroup) {
316 if (next==null || prev==null) continue;
317 if (eother.next==null || eother.prev==null) continue;
318 if (next.isBoundTo(eother.pair.prev.pair) && !prev.isBoundTo(eother.pair.next.pair))
319 prev.bindTo(next.getBindingMatrix(eother.pair.prev.pair), eother.pair.next.pair);
320 if (!next.isBoundTo(eother.pair.prev.pair) && prev.isBoundTo(eother.pair.next.pair))
321 next.bindTo(prev.getBindingMatrix(eother.pair.next.pair), eother.pair.prev.pair);
326 public float stretchRatio() {
327 Vertex nearest = error_against.nearest(midpoint());
328 float nearest_distance = midpoint().distance(nearest.p);
329 float other_distance =
330 (p1.p.distance(error_against.nearest(p1.p).p)+
331 p2.p.distance(error_against.nearest(p2.p).p))/2;
332 return nearest_distance/other_distance;
334 public float comparator() {
336 //return t==null?0:(1/t.aspect());
338 public int compareTo(E e) {
339 return e.comparator() > comparator() ? 1 : -1;
341 public void bindEdge(E e, Matrix m) {
343 pair._bindEdge(e.pair, m);
345 public void _bindEdge(E e, Matrix m) {
348 //assumes edges are identical length at binding time
349 Vec reflectionPlaneNormal = e.p2.p.minus(e.p1.p).norm();
350 float a = reflectionPlaneNormal.x;
351 float b = reflectionPlaneNormal.y;
352 float c = reflectionPlaneNormal.z;
353 Matrix reflectionMatrix =
354 new Matrix( 1-2*a*a, -2*a*b, -2*a*c, 0,
355 -2*a*b, 1-2*b*b, -2*b*c, 0,
356 -2*a*c, -2*b*c, 1-2*c*c, 0,
358 m = m.times(Matrix.translate(e.midpoint().minus(Point.ORIGIN))
359 .times(reflectionMatrix)
360 .times(Matrix.translate(Point.ORIGIN.minus(e.midpoint()))));
361 System.out.println(reflectionPlaneNormal);
362 System.out.println(" " + p1.p + " " + m.times(e.p1.p));
363 System.out.println(" " + p2.p + " " + m.times(e.p2.p));
365 if (m.times(e.p1.p).minus(p1.p).mag() > EPSILON) throw new Error();
366 if (m.times(e.p2.p).minus(p2.p).mag() > EPSILON) throw new Error();
370 public void dobind() {
371 for(E e : (Iterable<E>)getBoundPeers()) {
372 if (e==this) continue;
373 p1.bindTo(getBindingMatrix(e), e.p1);
374 p2.bindTo(getBindingMatrix(e), e.p2);
378 public Point shatter() {
379 if (shattered || destroyed) return null;
385 for(E e : (Iterable<E>)getBoundPeers()) {
388 E pnext = e.pair.next;
389 E pprev = e.pair.prev;
390 Point mid = e.midpoint();
391 Vertex r = e.next.p2;
392 Vertex l = e.pair.next.p2;
395 newT(r.p, e.p1.p, mid, null, 0);
396 newT(r.p, mid, e.p2.p, null, 0);
397 newT(l.p, mid, e.p1.p, null, 0);
398 newT(l.p, e.p2.p, mid, null, 0);
400 for(E e : (Iterable<E>)getBoundPeers()) {
401 Point mid = e.midpoint();
403 first = e.p1.getE(mid);
406 firstq = e.p2.getE(mid).pair;
409 e.p1.getE(mid). bindTo(e.getBindingMatrix(firste), first);
410 e.p1.getE(mid).pair. bindTo(e.getBindingMatrix(firste), first.pair);
411 e.p2.getE(mid).pair. bindTo(e.getBindingMatrix(firste), firstq);
412 e.p2.getE(mid).pair.pair.bindTo(e.getBindingMatrix(firste), firstq.pair);
417 public boolean destroyed = false;
418 public void destroy() {
419 if (destroyed) return;
421 pair.destroyed = true;
423 if (t != null) t.destroy();
426 if (pair.t != null) pair.t.destroy();
429 if (next.t != null) next.t.destroy();
430 if (prev.t != null) prev.t.destroy();
434 if (pair.next.t != null) pair.next.t.destroy();
435 if (pair.prev.t != null) pair.next.t.destroy();
439 pair.prev.next = next;
440 next.prev = pair.prev;
441 prev.next = pair.next;
443 if (p1.e == this) p1.e = prev.next;
444 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
447 private void sync() {
448 this.prev.next = this;
449 this.next.prev = this;
450 this.pair.pair = this;
451 if (this.next.p1 != p2) throw new Error();
452 if (this.prev.p2 != p1) throw new Error();
453 if (this.p1.e == null) this.p1.e = this;
454 if (!added) added = true;
456 private boolean added = false;
458 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
460 public double dihedralAngle() {
461 Vec v1 = t.norm().times(-1);
462 Vec v2 = pair.t.norm().times(-1);
463 return Math.acos(v1.norm().dot(v2.norm()));
466 /** angle between this half-edge and the next */
467 public double angle() {
468 Vec v1 = next.p2.p.minus(p2.p);
469 Vec v2 = this.p1.p.minus(p2.p);
470 return Math.acos(v1.norm().dot(v2.norm()));
473 public void makeAdjacent(E e) {
474 if (this.next == e) return;
475 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
476 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free ");
478 E freeIncident = p2.getFreeIncident(e, this);
480 e.prev.next = freeIncident.next;
481 freeIncident.next.prev = e.prev;
483 freeIncident.next = this.next;
484 this.next.prev = freeIncident;
493 /** creates an isolated edge out in the middle of space */
494 public E(Point p1, Point p2) {
495 if (vertices.get(p1) != null) throw new Error();
496 if (vertices.get(p2) != null) throw new Error();
497 this.p1 = new Vertex(p1);
498 this.p2 = new Vertex(p2);
499 this.prev = this.next = this.pair = new E(this, this, this);
501 this.p2.e = this.pair;
505 /** adds a new half-edge from prev.p2 to p2 */
506 public E(E prev, Point p) {
508 p2 = vertices.get(p);
509 if (p2 == null) p2 = new Vertex(p);
513 if (p2.getE(p1) != null) throw new Error();
515 this.next = this.pair = new E(this, this, prev.next);
517 E q = p2.getFreeIncident();
519 this.next.prev = this;
521 this.prev.next = this;
522 this.pair = new E(q, this, z);
524 if (p2.e==null) p2.e = this.pair;
528 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
529 public E(E prev, E pair, E next) {
537 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); }
538 public boolean has(Vertex v) { return v==p1 || v==p2; }
539 public float length() { return p1.p.minus(p2.p).mag(); }
540 public String toString() { return p1+"->"+p2; }
544 public E makeE(Point p1, Point p2) {
545 Vertex v1 = vertices.get(p1);
546 Vertex v2 = vertices.get(p2);
547 if (v1 != null && v2 != null) {
549 if (e != null) return e;
551 if (e != null) return e;
553 if (v1 != null) return new E(v1.getFreeIncident(), p2);
554 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
555 return new E(p1, p2);
557 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
559 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
560 float dot = norm.dot(norm2);
561 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
562 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
564 E e12 = makeE(p1, p2);
565 E e23 = makeE(p2, p3);
566 E e31 = makeE(p3, p1);
567 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
568 e12.makeAdjacent(e23);
569 e23.makeAdjacent(e31);
570 e31.makeAdjacent(e12);
572 T ret = e12.makeT(colorclass);
573 if (e12.t == null) throw new Error();
574 if (e23.t == null) throw new Error();
575 if (e31.t == null) throw new Error();
579 /** [UNIQUE] a triangle (face) */
580 public final class T extends Triangle {
582 public final int color;
583 public final int colorclass;
585 T(E e1, int colorclass) {
589 if (e1==e2 || e1==e3) throw new Error();
590 if (e3.next!=e1) throw new Error();
591 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
594 e1.next.next.t = this;
596 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
598 int color = Math.abs(random.nextInt());
601 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
602 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
603 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
607 this.colorclass = colorclass;
610 public E e1() { return e1; }
611 public E e2() { return e1.next; }
612 public E e3() { return e1.prev; }
613 public Vertex v1() { return e1.p1; }
614 public Vertex v2() { return e1.p2; }
615 public Vertex v3() { return e1.next.p2; }
616 public Point p1() { return e1.p1.p; }
617 public Point p2() { return e1.p2.p; }
618 public Point p3() { return e1.next.p2.p; }
619 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
620 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
622 public void removeFromRTree() { triangles.remove(this); }
623 public void addToRTree() { triangles.insert(this); }
624 public void destroy() { triangles.remove(this); }
625 public void reinsert() { triangles.remove(this); triangles.add(this); }
627 public boolean shouldBeDrawn() {
629 if (e1().bindingGroupSize() <= 1) return false;
630 if (e2().bindingGroupSize() <= 1) return false;
631 if (e3().bindingGroupSize() <= 1) return false;
636 /** issue gl.glVertex() for each of the triangle's points */
637 public void glVertices(GL gl) {
638 if (!shouldBeDrawn()) return;
640 Point p1 = v1().goodp;
641 Point p2 = v2().goodp;
642 Point p3 = v3().goodp;