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.geom.Point;
12 public class Mesh implements Iterable<Mesh.T> {
14 public static final float EPSILON = (float)0.0001;
15 public static final Random random = new Random();
17 private RTree<T> triangles = new RTree<T>();
18 private PointSet<Vertex> vertices = new PointSet<Vertex>();
20 public boolean immutableVertices;
21 public boolean ignorecollision = false;
22 public Mesh score_against = null;
23 public double score = 0;
25 public Mesh(boolean immutableVertices) { this.immutableVertices = immutableVertices; }
27 public void makeVerticesImmutable() { this.immutableVertices = true; }
28 public float score() { return (float)score; }
30 public int size() { return vertices.size(); }
31 public Iterable<Vertex> vertices() { return vertices; }
32 public Iterator<T> iterator() { return triangles.iterator(); }
34 public void rebindPoints() {
36 for(Mesh.T t : this) {
41 // ask edges to re-implement their bindings
42 for(Mesh.T t : this) {
49 public void transform(Matrix m) {
50 ArrayList<Vertex> set = new ArrayList<Vertex>();
51 for(Vertex v : vertices) set.add(v);
52 for(Vertex v : set) v.transform(m);
55 public void rebuild() { /*vertices.rebuild();*/ }
56 public Vec diagonal() { return vertices.diagonal(); }
57 public Point centroid() { return vertices.centroid(); }
58 public Vertex nearest(Point p) { return vertices.nearest(p); }
60 /** compute the volume of the mesh */
61 public float volume() {
64 double area = t.area();
65 Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
66 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
67 double height = Math.abs(t.norm().dot(origin_to_centroid));
68 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
74 // Vertexices //////////////////////////////////////////////////////////////////////////////
76 /** a vertex in the mesh */
77 public final class Vertex extends HasPoint implements Visitor<T> {
78 public String toString() { return p.toString(); }
80 E e; // some edge *leaving* this point
82 /** the nearest vertex in the "score_against" mesh */
83 Vertex nearest_in_other_mesh;
84 /** the number of vertices in the other mesh for which this is the nearest_in_other_mesh */
86 /** the total error quadric (contributions from all vertices in other mesh for which this is nearest) */
87 Matrix quadric = Matrix.ZERO;
89 Matrix binding = Matrix.ONE;
90 Vertex bound_to = this;
92 boolean quadricStale = false;
94 public Matrix errorQuadric() { return quadric; }
95 public Point getPoint() { return p; }
96 public float score() { return oldscore; }
98 private Matrix fundamentalQuadric = null;
99 public Matrix fundamentalQuadric() {
100 if (fundamentalQuadric == null) recomputeFundamentalQuadric();
101 return fundamentalQuadric;
104 private Vertex(Point p) {
106 if (vertices.get(p) != null) throw new Error();
110 private void glNormal(GL gl) {
112 gl.glNormal3f(norm.x, norm.y, norm.z);
115 public void recomputeFundamentalQuadric() {
116 if (!quadricStale && fundamentalQuadric != null) return;
117 quadricStale = false;
118 unApplyQuadricToNeighbor();
119 Matrix m = Matrix.ZERO;
121 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
123 m = m.plus(t.norm().fundamentalQuadric(t.centroid()));
126 fundamentalQuadric = m.times(1/(float)count);
127 applyQuadricToNeighbor();
130 public void unApplyQuadricToNeighbor() {
131 if (nearest_in_other_mesh == null) return;
132 if (fundamentalQuadric == null) return;
133 nearest_in_other_mesh.unComputeError();
134 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.minus(fundamentalQuadric);
135 nearest_in_other_mesh.quadric_count--;
136 if (nearest_in_other_mesh.quadric_count==0)
137 nearest_in_other_mesh.quadric = Matrix.ZERO;
138 nearest_in_other_mesh.computeError();
139 nearest_in_other_mesh = null;
142 public void applyQuadricToNeighbor() {
143 if (score_against == null) return;
145 Vertex new_nearest = score_against.nearest(p);
146 if (nearest_in_other_mesh != null && new_nearest == nearest_in_other_mesh) return;
148 if (nearest_in_other_mesh != null) unApplyQuadricToNeighbor();
149 if (nearest_in_other_mesh != null) throw new Error();
151 nearest_in_other_mesh = new_nearest;
153 // don't attract to vertices that face the other way
154 if (nearest_in_other_mesh.e == null || nearest_in_other_mesh.norm().dot(norm()) < 0) {
155 nearest_in_other_mesh = null;
157 nearest_in_other_mesh.unComputeError();
158 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.plus(fundamentalQuadric());
159 nearest_in_other_mesh.quadric_count++;
160 nearest_in_other_mesh.computeError();
165 public void reComputeErrorAround() {
167 if (nearest_in_other_mesh != null) nearest_in_other_mesh.reComputeError();
168 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
169 e.p2.reComputeError();
171 public void reComputeError() {
175 public void unComputeError() {
179 public void computeError() {
182 ? (quadric.preAndPostMultiply(p) * 100) / quadric_count
185 : nearest_in_other_mesh != null
186 ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p) * 100 * 10
187 : score_against != null
188 ? score_against.nearest(p).fundamentalQuadric().preAndPostMultiply(p) * 100 * 10
190 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
191 double ang = Math.abs(e.crossAngle());
192 if (ang > Math.PI) throw new Error();
193 float minangle = (float)(Math.PI * 0.8);
195 oldscore += (ang - minangle);
200 private void removeTrianglesFromRTree() {
201 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
202 if (e.t != null) e.t.removeFromRTree();
204 private void addTrianglesToRTree() {
205 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
206 if (e.t != null) e.t.addToRTree();
209 /** does NOT update bound pairs! */
210 public boolean transform(Matrix m) {
211 if (immutableVertices) throw new Error();
213 unApplyQuadricToNeighbor();
216 if (vertices.get(this.p)==null) throw new Error();
217 vertices.remove(this);
218 removeTrianglesFromRTree();
219 float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
220 float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
221 float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
222 this.p = new Point(newx, newy, newz);
223 addTrianglesToRTree();
226 applyQuadricToNeighbor();
230 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
231 if (Math.abs(e.crossAngle()) > (Math.PI * 0.9) || Math.abs(e.next.crossAngle()) > (Math.PI * 0.9)) good = false;
232 if (e.t.aspect() < 0.1) good = false;
233 e.p2.quadricStale = true;
236 if (!ignorecollision && good) triangles.range(oldp, this.p, (Visitor<T>)this);
238 reComputeErrorAround();
242 public void visit(T t) {
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)) { good = false; }
247 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { good = false; }
248 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { good = false; }
249 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { good = false; }
253 private boolean good;
255 public boolean move(Vec v) {
256 Matrix m = Matrix.translate(v);
260 good &= p.transform(m);
266 public E getFreeIncident() {
267 E ret = getFreeIncident(e, e);
268 if (ret != null) return ret;
269 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
270 System.out.println(e + " " + e.t);
271 throw new Error("unable to find free incident to " + this);
274 public E getFreeIncident(E start, E before) {
275 for(E e = start; e!=null; e=e.pair.next==before?null:e.pair.next)
276 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null)
281 public E getE(Point p2) {
282 Vertex v = vertices.get(p2);
283 if (v==null) return null;
286 public E getE(Vertex p2) {
287 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
288 if (e.p1 == this && e.p2 == p2) return e;
293 Vec norm = new Vec(0, 0, 0);
294 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
296 norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
300 public boolean isBoundTo(Vertex p) {
301 for(Vertex px = p; px!=null; px=(px.bound_to==p?null:px.bound_to))
307 public void unbind() { bound_to = this; binding = Matrix.ONE; }
308 public void bind(Vertex p) { bind(p, Matrix.ONE); }
309 public void bind(Vertex p, Matrix binding) {
310 if (isBoundTo(p)) return;
311 Vertex temp_bound_to = p.bound_to;
312 Matrix temp_binding = p.binding;
313 p.bound_to = this.bound_to;
314 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
315 this.bound_to = temp_bound_to;
316 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
320 public class BindingGroup {
321 private HashSet<E> set = new HashSet<E>();
322 public BindingGroup bind_others;
323 public BindingGroup other() { return bind_others; }
324 public BindingGroup(BindingGroup bind_others) { this.bind_others = bind_others; }
325 public BindingGroup() { this.bind_others = new BindingGroup(this); }
326 public BindingGroup(E e) { this(); set.add(e); }
327 public void add(E e) {
328 if (set.contains(e)) return;
330 BindingGroup e_bind_peers = e.bind_peers;
331 BindingGroup e_bind_to = e.bind_to;
333 e.bind_to = bind_others;
334 for (E epeer : e_bind_peers.set) add(epeer);
335 for (E eother : e_bind_to.set) bind_others.add(eother);
337 for(E eother : bind_others.set) {
338 if (e.next.bind_to.set.contains(eother.prev)) {
339 e.next.next.bindEdge(eother.prev.prev);
341 if (e.prev.bind_to.set.contains(eother.next)) {
342 e.prev.prev.bindEdge(eother.next.next);
347 public void dobind(E e) {
348 for(E ebound : set) {
349 e.p1.bind(ebound.p2);
350 e.p2.bind(ebound.p1);
353 public void shatter(BindingGroup bg1, BindingGroup bg2) {
355 e.shatter(e.midpoint(), bg1, bg2);
360 /** [UNIQUE] an edge */
361 public final class E implements Comparable<E> {
363 public final Vertex p1, p2;
364 T t; // triangle to our "left"
365 E prev; // previous half-edge
366 E next; // next half-edge
367 E pair; // partner half-edge
368 public BindingGroup bind_peers = new BindingGroup(this);
369 public BindingGroup bind_to = bind_peers.other();
370 boolean shattered = false;
372 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
373 public float comparator() {
374 Vertex nearest = score_against.nearest(midpoint());
375 return (float)Math.max(length(), midpoint().distance(nearest.p));
377 public int compareTo(E e) {
378 return e.comparator() > comparator() ? 1 : -1;
380 public void bindEdge(E e) { bind_to.add(e); }
381 public void dobind() { bind_to.dobind(this); }
383 public Point shatter() { return shatter(midpoint(), null, null); }
384 public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
385 if (shattered || destroyed) return mid;
392 int old_colorclass = t==null ? 0 : t.colorclass;
393 if (bg1==null) bg1 = new BindingGroup();
394 if (bg2==null) bg2 = new BindingGroup();
395 BindingGroup old_bind_to = bind_to;
396 bind_peers.shatter(bg1, bg2);
397 old_bind_to.shatter(bg2.other(), bg1.other());
401 newT(r.p, p1.p, mid, null, old_colorclass);
402 newT(r.p, mid, p2.p, null, old_colorclass);
403 bg1.add(p1.getE(mid));
404 bg2.add(p2.getE(mid).pair);
408 public boolean destroyed = false;
409 public void destroy() {
410 if (destroyed) return;
412 pair.destroyed = true;
414 if (t != null) t.destroy();
417 if (pair.t != null) pair.t.destroy();
420 if (next.t != null) next.t.destroy();
421 if (prev.t != null) prev.t.destroy();
425 if (pair.next.t != null) pair.next.t.destroy();
426 if (pair.prev.t != null) pair.next.t.destroy();
432 this.bind_peers = null;
433 pair.bind_peers = null;
434 pair.prev.next = next;
435 next.prev = pair.prev;
436 prev.next = pair.next;
438 if (p1.e == this) p1.e = prev.next;
439 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
442 private void sync() {
443 this.prev.next = this;
444 this.next.prev = this;
445 this.pair.pair = this;
446 bind_peers.add(this);
447 if (this.next.p1 != p2) throw new Error();
448 if (this.prev.p2 != p1) throw new Error();
449 if (this.p1.e == null) this.p1.e = this;
450 if (!added) added = true;
452 private boolean added = false;
454 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
456 public double crossAngle() {
457 Vec v1 = t.norm().times(-1);
458 Vec v2 = pair.t.norm().times(-1);
459 return Math.acos(v1.norm().dot(v2.norm()));
462 /** angle between this half-edge and the next */
463 public double angle() {
464 Vec v1 = next.p2.p.minus(p2.p);
465 Vec v2 = this.p1.p.minus(p2.p);
466 return Math.acos(v1.norm().dot(v2.norm()));
469 public void makeAdjacent(E e) {
470 if (this.next == e) return;
471 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
472 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
474 E freeIncident = p2.getFreeIncident(e, this);
476 e.prev.next = freeIncident.next;
477 freeIncident.next.prev = e.prev;
479 freeIncident.next = this.next;
480 this.next.prev = freeIncident;
489 /** creates an isolated edge out in the middle of space */
490 public E(Point p1, Point p2) {
491 if (vertices.get(p1) != null) throw new Error();
492 if (vertices.get(p2) != null) throw new Error();
493 this.p1 = new Vertex(p1);
494 this.p2 = new Vertex(p2);
495 this.prev = this.next = this.pair = new E(this, this, this);
497 this.p2.e = this.pair;
501 /** adds a new half-edge from prev.p2 to p2 */
502 public E(E prev, Point p) {
504 p2 = vertices.get(p);
505 if (p2 == null) p2 = new Vertex(p);
509 if (p2.getE(p1) != null) throw new Error();
511 this.next = this.pair = new E(this, this, prev.next);
513 E q = p2.getFreeIncident();
515 this.next.prev = this;
517 this.prev.next = this;
518 this.pair = new E(q, this, z);
520 if (p2.e==null) p2.e = this.pair;
524 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
525 public E(E prev, E pair, E next) {
533 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); }
534 public boolean has(Vertex v) { return v==p1 || v==p2; }
535 public float length() { return p1.p.minus(p2.p).mag(); }
536 public String toString() { return p1+"->"+p2; }
540 public E makeE(Point p1, Point p2) {
541 Vertex v1 = vertices.get(p1);
542 Vertex v2 = vertices.get(p2);
543 if (v1 != null && v2 != null) {
545 if (e != null) return e;
547 if (e != null) return e;
549 if (v1 != null) return new E(v1.getFreeIncident(), p2);
550 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
551 return new E(p1, p2);
553 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
555 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
556 float dot = norm.dot(norm2);
557 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
558 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
560 E e12 = makeE(p1, p2);
561 E e23 = makeE(p2, p3);
562 E e31 = makeE(p3, p1);
563 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
564 e12.makeAdjacent(e23);
565 e23.makeAdjacent(e31);
566 e31.makeAdjacent(e12);
568 T ret = e12.makeT(colorclass);
569 if (e12.t == null) throw new Error();
570 if (e23.t == null) throw new Error();
571 if (e31.t == null) throw new Error();
576 /** [UNIQUE] a triangle (face) */
577 public final class T extends Triangle {
579 public final int color;
580 public final int colorclass;
582 public void removeFromRTree() { triangles.remove(this); }
583 public void addToRTree() { triangles.insert(this); }
585 public void destroy() { triangles.remove(this); }
587 T(E e1, int colorclass) {
591 if (e1==e2 || e1==e3) throw new Error();
592 if (e3.next!=e1) throw new Error();
593 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
596 e1.next.next.t = this;
598 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
600 int color = Math.abs(random.nextInt());
603 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
604 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
605 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
609 this.colorclass = colorclass;
612 public E e1() { return e1; }
613 public E e2() { return e1.next; }
614 public E e3() { return e1.prev; }
615 public Vertex v1() { return e1.p1; }
616 public Vertex v2() { return e1.p2; }
617 public Vertex v3() { return e1.next.p2; }
618 public Point p1() { return e1.p1.p; }
619 public Point p2() { return e1.p2.p; }
620 public Point p3() { return e1.next.p2.p; }
621 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
622 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
624 public boolean shouldBeDrawn() {
625 if (e1().bind_to.set.size() == 0) return false;
626 if (e2().bind_to.set.size() == 0) return false;
627 if (e3().bind_to.set.size() == 0) return false;