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 recomputeFundamentalQuadricIfNeighborChanged() {
116 Vertex oldv = nearest_in_other_mesh;
117 Vertex newv = score_against.nearest(p);
118 if (oldv==newv) return;
119 recomputeFundamentalQuadric();
120 if (oldv!=null) oldv.recomputeFundamentalQuadricIfNeighborChanged();
121 //if (newv!=null) newv.recomputeFundamentalQuadricIfNeighborChanged();
123 public void recomputeFundamentalQuadric() {
124 unApplyQuadricToNeighbor();
125 if (quadricStale || fundamentalQuadric==null) {
126 Matrix m = Matrix.ZERO;
128 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
130 m = m.plus(t.norm().fundamentalQuadric(t.centroid()));
133 quadricStale = false;
134 fundamentalQuadric = m.times(1/(float)count);
136 applyQuadricToNeighbor();
139 public void unApplyQuadricToNeighbor() {
140 if (nearest_in_other_mesh == null) return;
141 if (fundamentalQuadric == null) return;
142 nearest_in_other_mesh.unComputeError();
143 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.minus(fundamentalQuadric);
144 nearest_in_other_mesh.quadric_count--;
145 if (nearest_in_other_mesh.quadric_count==0)
146 nearest_in_other_mesh.quadric = Matrix.ZERO;
147 nearest_in_other_mesh.computeError();
148 nearest_in_other_mesh = null;
151 public void applyQuadricToNeighbor() {
152 if (score_against == null) return;
154 Vertex new_nearest = score_against.nearest(p);
155 if (nearest_in_other_mesh != null && new_nearest == nearest_in_other_mesh) return;
157 if (nearest_in_other_mesh != null) unApplyQuadricToNeighbor();
158 if (nearest_in_other_mesh != null) throw new Error();
160 nearest_in_other_mesh = new_nearest;
162 // don't attract to vertices that face the other way
163 if (nearest_in_other_mesh.e == null || nearest_in_other_mesh.norm().dot(norm()) < 0) {
164 nearest_in_other_mesh = null;
166 nearest_in_other_mesh.unComputeError();
167 nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.plus(fundamentalQuadric());
168 nearest_in_other_mesh.quadric_count++;
169 nearest_in_other_mesh.computeError();
174 public void reComputeErrorAround() {
176 if (nearest_in_other_mesh != null) nearest_in_other_mesh.reComputeError();
177 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
178 e.p2.reComputeError();
180 public void reComputeError() {
184 public void unComputeError() {
188 public void computeError() {
191 ? (quadric.preAndPostMultiply(p) * 100) / quadric_count
194 : nearest_in_other_mesh != null
195 ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p) * 100 * 10
196 : score_against != null
197 ? score_against.nearest(p).fundamentalQuadric().preAndPostMultiply(p) * 100 * 10
199 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
200 double ang = Math.abs(e.crossAngle());
201 if (ang > Math.PI) throw new Error();
202 float minangle = (float)(Math.PI * 0.8);
204 oldscore += (ang - minangle);
209 private void removeTrianglesFromRTree() {
210 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
211 if (e.t != null) e.t.removeFromRTree();
213 private void addTrianglesToRTree() {
214 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
215 if (e.t != null) e.t.addToRTree();
218 /** does NOT update bound pairs! */
219 public boolean transform(Matrix m) {
220 if (immutableVertices) throw new Error();
222 unApplyQuadricToNeighbor();
225 if (vertices.get(this.p)==null) throw new Error();
226 vertices.remove(this);
227 removeTrianglesFromRTree();
228 float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
229 float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
230 float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
231 this.p = new Point(newx, newy, newz);
232 addTrianglesToRTree();
235 applyQuadricToNeighbor();
239 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
240 if (Math.abs(e.crossAngle()) > (Math.PI * 0.9) || Math.abs(e.next.crossAngle()) > (Math.PI * 0.9)) good = false;
241 if (e.t.aspect() < 0.1) good = false;
242 e.p2.quadricStale = true;
245 if (!ignorecollision && good) triangles.range(oldp, this.p, (Visitor<T>)this);
247 reComputeErrorAround();
251 public void visit(T t) {
253 for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
254 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { good = false; }
256 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { good = false; }
257 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { good = false; }
258 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { good = false; }
262 private boolean good;
264 public boolean move(Vec v) {
265 Matrix m = Matrix.translate(v);
269 good &= p.transform(m);
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;
302 Vec norm = new Vec(0, 0, 0);
303 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
305 norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
309 public boolean isBoundTo(Vertex p) {
310 for(Vertex px = p; px!=null; px=(px.bound_to==p?null:px.bound_to))
316 public void unbind() { bound_to = this; binding = Matrix.ONE; }
317 public void bind(Vertex p) { bind(p, Matrix.ONE); }
318 public void bind(Vertex p, Matrix binding) {
319 if (isBoundTo(p)) return;
320 Vertex temp_bound_to = p.bound_to;
321 Matrix temp_binding = p.binding;
322 p.bound_to = this.bound_to;
323 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
324 this.bound_to = temp_bound_to;
325 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
329 public class BindingGroup {
330 private HashSet<E> set = new HashSet<E>();
331 public BindingGroup bind_others;
332 public BindingGroup other() { return bind_others; }
333 public BindingGroup(BindingGroup bind_others) { this.bind_others = bind_others; }
334 public BindingGroup() { this.bind_others = new BindingGroup(this); }
335 public BindingGroup(E e) { this(); set.add(e); }
336 public void add(E e) {
337 if (set.contains(e)) return;
339 BindingGroup e_bind_peers = e.bind_peers;
340 BindingGroup e_bind_to = e.bind_to;
342 e.bind_to = bind_others;
343 for (E epeer : e_bind_peers.set) add(epeer);
344 for (E eother : e_bind_to.set) bind_others.add(eother);
346 for(E eother : bind_others.set) {
347 if (e.next.bind_to.set.contains(eother.prev)) {
348 e.next.next.bindEdge(eother.prev.prev);
350 if (e.prev.bind_to.set.contains(eother.next)) {
351 e.prev.prev.bindEdge(eother.next.next);
356 public void dobind(E e) {
357 for(E ebound : set) {
358 e.p1.bind(ebound.p2);
359 e.p2.bind(ebound.p1);
362 public void shatter(BindingGroup bg1, BindingGroup bg2) {
364 e.shatter(e.midpoint(), bg1, bg2);
369 /** [UNIQUE] an edge */
370 public final class E implements Comparable<E> {
372 public final Vertex p1, p2;
373 T t; // triangle to our "left"
374 E prev; // previous half-edge
375 E next; // next half-edge
376 E pair; // partner half-edge
377 public BindingGroup bind_peers = new BindingGroup(this);
378 public BindingGroup bind_to = bind_peers.other();
379 boolean shattered = false;
381 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
382 public float comparator() {
383 Vertex nearest = score_against.nearest(midpoint());
384 return (float)Math.max(length(), midpoint().distance(nearest.p));
386 public int compareTo(E e) {
387 return e.comparator() > comparator() ? 1 : -1;
389 public void bindEdge(E e) { bind_to.add(e); }
390 public void dobind() { bind_to.dobind(this); }
392 public Point shatter() { return shatter(midpoint(), null, null); }
393 public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
394 if (shattered || destroyed) return mid;
401 int old_colorclass = t==null ? 0 : t.colorclass;
402 if (bg1==null) bg1 = new BindingGroup();
403 if (bg2==null) bg2 = new BindingGroup();
404 BindingGroup old_bind_to = bind_to;
405 bind_peers.shatter(bg1, bg2);
406 old_bind_to.shatter(bg2.other(), bg1.other());
410 newT(r.p, p1.p, mid, null, old_colorclass);
411 newT(r.p, mid, p2.p, null, old_colorclass);
412 bg1.add(p1.getE(mid));
413 bg2.add(p2.getE(mid).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();
441 this.bind_peers = null;
442 pair.bind_peers = null;
443 pair.prev.next = next;
444 next.prev = pair.prev;
445 prev.next = pair.next;
447 if (p1.e == this) p1.e = prev.next;
448 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
451 private void sync() {
452 this.prev.next = this;
453 this.next.prev = this;
454 this.pair.pair = this;
455 bind_peers.add(this);
456 if (this.next.p1 != p2) throw new Error();
457 if (this.prev.p2 != p1) throw new Error();
458 if (this.p1.e == null) this.p1.e = this;
459 if (!added) added = true;
461 private boolean added = false;
463 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
465 public double crossAngle() {
466 Vec v1 = t.norm().times(-1);
467 Vec v2 = pair.t.norm().times(-1);
468 return Math.acos(v1.norm().dot(v2.norm()));
471 /** angle between this half-edge and the next */
472 public double angle() {
473 Vec v1 = next.p2.p.minus(p2.p);
474 Vec v2 = this.p1.p.minus(p2.p);
475 return Math.acos(v1.norm().dot(v2.norm()));
478 public void makeAdjacent(E e) {
479 if (this.next == e) return;
480 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
481 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
483 E freeIncident = p2.getFreeIncident(e, this);
485 e.prev.next = freeIncident.next;
486 freeIncident.next.prev = e.prev;
488 freeIncident.next = this.next;
489 this.next.prev = freeIncident;
498 /** creates an isolated edge out in the middle of space */
499 public E(Point p1, Point p2) {
500 if (vertices.get(p1) != null) throw new Error();
501 if (vertices.get(p2) != null) throw new Error();
502 this.p1 = new Vertex(p1);
503 this.p2 = new Vertex(p2);
504 this.prev = this.next = this.pair = new E(this, this, this);
506 this.p2.e = this.pair;
510 /** adds a new half-edge from prev.p2 to p2 */
511 public E(E prev, Point p) {
513 p2 = vertices.get(p);
514 if (p2 == null) p2 = new Vertex(p);
518 if (p2.getE(p1) != null) throw new Error();
520 this.next = this.pair = new E(this, this, prev.next);
522 E q = p2.getFreeIncident();
524 this.next.prev = this;
526 this.prev.next = this;
527 this.pair = new E(q, this, z);
529 if (p2.e==null) p2.e = this.pair;
533 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
534 public E(E prev, E pair, E next) {
542 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); }
543 public boolean has(Vertex v) { return v==p1 || v==p2; }
544 public float length() { return p1.p.minus(p2.p).mag(); }
545 public String toString() { return p1+"->"+p2; }
549 public E makeE(Point p1, Point p2) {
550 Vertex v1 = vertices.get(p1);
551 Vertex v2 = vertices.get(p2);
552 if (v1 != null && v2 != null) {
554 if (e != null) return e;
556 if (e != null) return e;
558 if (v1 != null) return new E(v1.getFreeIncident(), p2);
559 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
560 return new E(p1, p2);
562 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
564 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
565 float dot = norm.dot(norm2);
566 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
567 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
569 E e12 = makeE(p1, p2);
570 E e23 = makeE(p2, p3);
571 E e31 = makeE(p3, p1);
572 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
573 e12.makeAdjacent(e23);
574 e23.makeAdjacent(e31);
575 e31.makeAdjacent(e12);
577 T ret = e12.makeT(colorclass);
578 if (e12.t == null) throw new Error();
579 if (e23.t == null) throw new Error();
580 if (e31.t == null) throw new Error();
585 /** [UNIQUE] a triangle (face) */
586 public final class T extends Triangle {
588 public final int color;
589 public final int colorclass;
591 public void removeFromRTree() { triangles.remove(this); }
592 public void addToRTree() { triangles.insert(this); }
594 public void destroy() { triangles.remove(this); }
596 T(E e1, int colorclass) {
600 if (e1==e2 || e1==e3) throw new Error();
601 if (e3.next!=e1) throw new Error();
602 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
605 e1.next.next.t = this;
607 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
609 int color = Math.abs(random.nextInt());
612 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
613 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
614 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
618 this.colorclass = colorclass;
621 public E e1() { return e1; }
622 public E e2() { return e1.next; }
623 public E e3() { return e1.prev; }
624 public Vertex v1() { return e1.p1; }
625 public Vertex v2() { return e1.p2; }
626 public Vertex v3() { return e1.next.p2; }
627 public Point p1() { return e1.p1.p; }
628 public Point p2() { return e1.p2.p; }
629 public Point p3() { return e1.next.p2.p; }
630 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
631 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
633 public boolean shouldBeDrawn() {
634 if (e1().bind_to.set.size() == 0) return false;
635 if (e2().bind_to.set.size() == 0) return false;
636 if (e3().bind_to.set.size() == 0) return false;