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;
11 import com.infomatiq.jsi.IntProcedure;
13 public class Mesh implements Iterable<Mesh.T> {
15 public static final float EPSILON = (float)0.0001;
16 public static final Random random = new Random();
18 private RTree<T> triangles = new RTree<T>();
19 private PointSet<Vertex> vertices = new PointSet<Vertex>();
21 public boolean immutableVertices;
22 public Mesh error_against = null;
23 public double error = 0;
25 public Mesh(boolean immutableVertices) { this.immutableVertices = immutableVertices; }
27 public void makeVerticesImmutable() { this.immutableVertices = true; }
28 public float error() { return (float)error; }
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.times(v.p), true);
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 HasQuadric implements Visitor {
79 E e; // some edge *leaving* this point
81 Matrix binding = Matrix.ONE;
82 Vertex bound_to = this;
83 private boolean illegal = false;
85 public Point getPoint() { return p; }
86 public float error() { return olderror; }
88 private Vertex(Point p) {
90 if (vertices.get(p) != null) throw new Error();
94 public void reinsert() {
95 vertices.remove(this);
97 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.t.reinsert();
100 public float olderror = 0;
101 public void setError(float nerror) {
107 public Matrix _recomputeFundamentalQuadric() {
108 Matrix m = Matrix.ZERO;
110 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
111 m = m.plus(e.t.norm().fundamentalQuadric(e.t.centroid()));
114 return m.times(1/(float)count);
117 public HasQuadric nearest() { return error_against==null ? null : error_against.vertices.nearest(p, this); }
118 public void computeError() {
121 ? (quadric.preAndPostMultiply(p) * 100) / quadric_count
122 : nearest_in_other_mesh != null
123 ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p) * 100 * 10
124 : error_against != null
125 ? nearest().fundamentalQuadric().preAndPostMultiply(p) * 100 * 10
127 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
128 double ang = Math.abs(e.crossAngle());
129 if (ang > Math.PI) throw new Error();
130 float minangle = (float)(Math.PI * 0.8);
131 if (ang > minangle) nerror += (ang - minangle);
136 /** does NOT update bound pairs! */
137 private boolean transform(Point newp, boolean ignoreProblems) {
139 if (immutableVertices) throw new Error();
141 unApplyQuadricToNeighbor();
144 applyQuadricToNeighbor();
146 if (!ignoreProblems) {
150 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.p2.quadricStale = true;
154 public void checkLegality() {
155 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
156 if (Math.abs(e.crossAngle()) > (Math.PI * 0.9) || Math.abs(e.next.crossAngle()) > (Math.PI * 0.9)) illegal = true;
157 if (e.t.aspect() < 0.1) illegal = true;
159 if (illegal) triangles.range(oldp, this.p, (Visitor<T>)this);
162 public void reComputeErrorAround() {
164 if (nearest_in_other_mesh != null)
165 nearest_in_other_mesh.reComputeError();
166 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
167 e.p2.reComputeError();
170 public boolean visit(Object o) {
171 if (o instanceof Vertex)
172 return ((Vertex)o).e != null && ((Vertex)o).norm().dot(Vertex.this.norm()) >= 0;
174 if (illegal) return false;
175 for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
176 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { illegal = true; }
178 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { illegal = true; }
179 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { illegal = true; }
180 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { illegal = true; }
186 public boolean move(Matrix m, boolean ignoreProblems) {
188 for(Vertex p = this; p != null; p = (p.bound_to==this)?null:p.bound_to)
189 good &= p.transform(m.times(p.p), ignoreProblems);
190 for(Vertex p = this; p != null; p = (p.bound_to==this)?null:p.bound_to)
191 if (good || ignoreProblems) p.reComputeErrorAround();
192 else p.transform(p.oldp, true);
196 public E getFreeIncident() {
197 E ret = getFreeIncident(e, e);
198 if (ret != null) return ret;
199 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
200 System.out.println(e + " " + e.t);
201 throw new Error("unable to find free incident to " + this);
204 public E getFreeIncident(E start, E before) {
205 for(E e = start; e!=null; e=e.pair.next==before?null:e.pair.next)
206 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null)
211 public E getE(Point p2) {
212 Vertex v = vertices.get(p2);
213 if (v==null) return null;
216 public E getE(Vertex p2) {
217 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
218 if (e.p1 == this && e.p2 == p2) return e;
222 private void glNormal(GL gl) {
224 gl.glNormal3f(norm.x, norm.y, norm.z);
227 Vec norm = new Vec(0, 0, 0);
228 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
230 norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
234 public boolean isBoundTo(Vertex p) {
235 for(Vertex px = p; px!=null; px=(px.bound_to==p?null:px.bound_to))
241 public void unbind() { bound_to = this; binding = Matrix.ONE; }
242 public void bind(Vertex p) { bind(p, Matrix.ONE); }
243 public void bind(Vertex p, Matrix binding) {
244 if (isBoundTo(p)) return;
245 Vertex temp_bound_to = p.bound_to;
246 Matrix temp_binding = p.binding;
247 p.bound_to = this.bound_to;
248 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
249 this.bound_to = temp_bound_to;
250 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
254 public class BindingGroup {
255 private HashSet<E> set = new HashSet<E>();
256 public BindingGroup bind_others;
257 public BindingGroup other() { return bind_others; }
258 public BindingGroup(BindingGroup bind_others) { this.bind_others = bind_others; }
259 public BindingGroup() { this.bind_others = new BindingGroup(this); }
260 public BindingGroup(E e) { this(); set.add(e); }
261 public void add(E e) {
262 if (set.contains(e)) return;
264 BindingGroup e_bind_peers = e.bind_peers;
265 BindingGroup e_bind_to = e.bind_to;
267 e.bind_to = bind_others;
268 for (E epeer : e_bind_peers.set) add(epeer);
269 for (E eother : e_bind_to.set) bind_others.add(eother);
271 for(E eother : bind_others.set) {
272 if (e.next.bind_to.set.contains(eother.prev)) {
273 e.next.next.bindEdge(eother.prev.prev);
275 if (e.prev.bind_to.set.contains(eother.next)) {
276 e.prev.prev.bindEdge(eother.next.next);
281 public void dobind(E e) {
282 for(E ebound : set) {
283 e.p1.bind(ebound.p2);
284 e.p2.bind(ebound.p1);
287 public void shatter(BindingGroup bg1, BindingGroup bg2) {
289 e.shatter(e.midpoint(), bg1, bg2);
294 /** [UNIQUE] an edge */
295 public final class E implements Comparable<E> {
297 public final Vertex p1, p2;
298 T t; // triangle to our "left"
299 E prev; // previous half-edge
300 E next; // next half-edge
301 E pair; // partner half-edge
302 public BindingGroup bind_peers = new BindingGroup(this);
303 public BindingGroup bind_to = bind_peers.other();
304 boolean shattered = false;
306 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
307 public float comparator() {
308 Vertex nearest = error_against.nearest(midpoint());
309 return (float)Math.max(length(), midpoint().distance(nearest.p));
311 public int compareTo(E e) {
312 return e.comparator() > comparator() ? 1 : -1;
314 public void bindEdge(E e) { bind_to.add(e); }
315 public void dobind() { bind_to.dobind(this); }
317 public Point shatter() { return shatter(midpoint(), null, null); }
318 public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
319 if (shattered || destroyed) return mid;
326 int old_colorclass = t==null ? 0 : t.colorclass;
327 if (bg1==null) bg1 = new BindingGroup();
328 if (bg2==null) bg2 = new BindingGroup();
329 BindingGroup old_bind_to = bind_to;
330 bind_peers.shatter(bg1, bg2);
331 old_bind_to.shatter(bg2.other(), bg1.other());
335 newT(r.p, p1.p, mid, null, old_colorclass);
336 newT(r.p, mid, p2.p, null, old_colorclass);
337 bg1.add(p1.getE(mid));
338 bg2.add(p2.getE(mid).pair);
342 public boolean destroyed = false;
343 public void destroy() {
344 if (destroyed) return;
346 pair.destroyed = true;
348 if (t != null) t.destroy();
351 if (pair.t != null) pair.t.destroy();
354 if (next.t != null) next.t.destroy();
355 if (prev.t != null) prev.t.destroy();
359 if (pair.next.t != null) pair.next.t.destroy();
360 if (pair.prev.t != null) pair.next.t.destroy();
366 this.bind_peers = null;
367 pair.bind_peers = null;
368 pair.prev.next = next;
369 next.prev = pair.prev;
370 prev.next = pair.next;
372 if (p1.e == this) p1.e = prev.next;
373 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
376 private void sync() {
377 this.prev.next = this;
378 this.next.prev = this;
379 this.pair.pair = this;
380 bind_peers.add(this);
381 if (this.next.p1 != p2) throw new Error();
382 if (this.prev.p2 != p1) throw new Error();
383 if (this.p1.e == null) this.p1.e = this;
384 if (!added) added = true;
386 private boolean added = false;
388 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
390 public double crossAngle() {
391 Vec v1 = t.norm().times(-1);
392 Vec v2 = pair.t.norm().times(-1);
393 return Math.acos(v1.norm().dot(v2.norm()));
396 /** angle between this half-edge and the next */
397 public double angle() {
398 Vec v1 = next.p2.p.minus(p2.p);
399 Vec v2 = this.p1.p.minus(p2.p);
400 return Math.acos(v1.norm().dot(v2.norm()));
403 public void makeAdjacent(E e) {
404 if (this.next == e) return;
405 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
406 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
408 E freeIncident = p2.getFreeIncident(e, this);
410 e.prev.next = freeIncident.next;
411 freeIncident.next.prev = e.prev;
413 freeIncident.next = this.next;
414 this.next.prev = freeIncident;
423 /** creates an isolated edge out in the middle of space */
424 public E(Point p1, Point p2) {
425 if (vertices.get(p1) != null) throw new Error();
426 if (vertices.get(p2) != null) throw new Error();
427 this.p1 = new Vertex(p1);
428 this.p2 = new Vertex(p2);
429 this.prev = this.next = this.pair = new E(this, this, this);
431 this.p2.e = this.pair;
435 /** adds a new half-edge from prev.p2 to p2 */
436 public E(E prev, Point p) {
438 p2 = vertices.get(p);
439 if (p2 == null) p2 = new Vertex(p);
443 if (p2.getE(p1) != null) throw new Error();
445 this.next = this.pair = new E(this, this, prev.next);
447 E q = p2.getFreeIncident();
449 this.next.prev = this;
451 this.prev.next = this;
452 this.pair = new E(q, this, z);
454 if (p2.e==null) p2.e = this.pair;
458 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
459 public E(E prev, E pair, E next) {
467 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); }
468 public boolean has(Vertex v) { return v==p1 || v==p2; }
469 public float length() { return p1.p.minus(p2.p).mag(); }
470 public String toString() { return p1+"->"+p2; }
474 public E makeE(Point p1, Point p2) {
475 Vertex v1 = vertices.get(p1);
476 Vertex v2 = vertices.get(p2);
477 if (v1 != null && v2 != null) {
479 if (e != null) return e;
481 if (e != null) return e;
483 if (v1 != null) return new E(v1.getFreeIncident(), p2);
484 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
485 return new E(p1, p2);
487 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
489 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
490 float dot = norm.dot(norm2);
491 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
492 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
494 E e12 = makeE(p1, p2);
495 E e23 = makeE(p2, p3);
496 E e31 = makeE(p3, p1);
497 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
498 e12.makeAdjacent(e23);
499 e23.makeAdjacent(e31);
500 e31.makeAdjacent(e12);
502 T ret = e12.makeT(colorclass);
503 if (e12.t == null) throw new Error();
504 if (e23.t == null) throw new Error();
505 if (e31.t == null) throw new Error();
509 /** [UNIQUE] a triangle (face) */
510 public final class T extends Triangle {
512 public final int color;
513 public final int colorclass;
515 T(E e1, int colorclass) {
519 if (e1==e2 || e1==e3) throw new Error();
520 if (e3.next!=e1) throw new Error();
521 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
524 e1.next.next.t = this;
526 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
528 int color = Math.abs(random.nextInt());
531 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
532 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
533 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
537 this.colorclass = colorclass;
540 public E e1() { return e1; }
541 public E e2() { return e1.next; }
542 public E e3() { return e1.prev; }
543 public Vertex v1() { return e1.p1; }
544 public Vertex v2() { return e1.p2; }
545 public Vertex v3() { return e1.next.p2; }
546 public Point p1() { return e1.p1.p; }
547 public Point p2() { return e1.p2.p; }
548 public Point p3() { return e1.next.p2.p; }
549 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
550 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
552 public void removeFromRTree() { triangles.remove(this); }
553 public void addToRTree() { triangles.insert(this); }
554 public void destroy() { triangles.remove(this); }
555 public void reinsert() { triangles.remove(this); triangles.add(this); }
557 public boolean shouldBeDrawn() {
558 if (e1().bind_to.set.size() == 0) return false;
559 if (e2().bind_to.set.size() == 0) return false;
560 if (e3().bind_to.set.size() == 0) return false;