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;
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() { vertices.remove(this); vertices.add(this); }
96 public float olderror = 0;
97 public void setError(float nerror) {
103 public Matrix _recomputeFundamentalQuadric() {
104 Matrix m = Matrix.ZERO;
106 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
107 m = m.plus(e.t.norm().fundamentalQuadric(e.t.centroid()));
110 return m.times(1/(float)count);
113 public HasQuadric nearest() { return error_against==null ? null : error_against.vertices.nearest(p, this); }
114 public void computeError() {
117 ? (quadric.preAndPostMultiply(p) * 100) / quadric_count
118 : nearest_in_other_mesh != null
119 ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p) * 100 * 10
120 : error_against != null
121 ? nearest().fundamentalQuadric().preAndPostMultiply(p) * 100 * 10
123 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
124 double ang = Math.abs(e.crossAngle());
125 if (ang > Math.PI) throw new Error();
126 float minangle = (float)(Math.PI * 0.8);
127 if (ang > minangle) nerror += (ang - minangle);
132 /** does NOT update bound pairs! */
133 private boolean transform(Point newp, boolean ignoreProblems) {
135 if (immutableVertices) throw new Error();
137 unApplyQuadricToNeighbor();
140 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.t.reinsert();
143 applyQuadricToNeighbor();
145 if (ignoreProblems) return true;
148 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
149 if (Math.abs(e.crossAngle()) > (Math.PI * 0.9) || Math.abs(e.next.crossAngle()) > (Math.PI * 0.9)) good = false;
150 if (e.t.aspect() < 0.1) good = false;
151 e.p2.quadricStale = true;
153 if (good) triangles.range(oldp, this.p, (Visitor<T>)this);
157 public void reComputeErrorAround() {
159 if (nearest_in_other_mesh != null)
160 nearest_in_other_mesh.reComputeError();
161 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
162 e.p2.reComputeError();
165 public boolean visit(Object o) {
166 if (o instanceof Vertex)
167 return ((Vertex)o).e != null && ((Vertex)o).norm().dot(Vertex.this.norm()) >= 0;
169 if (!good) return false;
170 for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
171 if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { good = false; }
173 if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { good = false; }
174 if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { good = false; }
175 if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { good = false; }
181 public boolean move(Matrix m, boolean ignoreProblems) {
183 for(Vertex p = this; p != null; p = (p.bound_to==this)?null:p.bound_to)
184 good &= p.transform(m.times(p.p), ignoreProblems);
185 for(Vertex p = this; p != null; p = (p.bound_to==this)?null:p.bound_to)
186 if (good || ignoreProblems) p.reComputeErrorAround();
187 else p.transform(p.oldp, true);
191 public E getFreeIncident() {
192 E ret = getFreeIncident(e, e);
193 if (ret != null) return ret;
194 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
195 System.out.println(e + " " + e.t);
196 throw new Error("unable to find free incident to " + this);
199 public E getFreeIncident(E start, E before) {
200 for(E e = start; e!=null; e=e.pair.next==before?null:e.pair.next)
201 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null)
206 public E getE(Point p2) {
207 Vertex v = vertices.get(p2);
208 if (v==null) return null;
211 public E getE(Vertex p2) {
212 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
213 if (e.p1 == this && e.p2 == p2) return e;
217 private void glNormal(GL gl) {
219 gl.glNormal3f(norm.x, norm.y, norm.z);
222 Vec norm = new Vec(0, 0, 0);
223 for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
225 norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
229 public boolean isBoundTo(Vertex p) {
230 for(Vertex px = p; px!=null; px=(px.bound_to==p?null:px.bound_to))
236 public void unbind() { bound_to = this; binding = Matrix.ONE; }
237 public void bind(Vertex p) { bind(p, Matrix.ONE); }
238 public void bind(Vertex p, Matrix binding) {
239 if (isBoundTo(p)) return;
240 Vertex temp_bound_to = p.bound_to;
241 Matrix temp_binding = p.binding;
242 p.bound_to = this.bound_to;
243 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
244 this.bound_to = temp_bound_to;
245 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
249 public class BindingGroup {
250 private HashSet<E> set = new HashSet<E>();
251 public BindingGroup bind_others;
252 public BindingGroup other() { return bind_others; }
253 public BindingGroup(BindingGroup bind_others) { this.bind_others = bind_others; }
254 public BindingGroup() { this.bind_others = new BindingGroup(this); }
255 public BindingGroup(E e) { this(); set.add(e); }
256 public void add(E e) {
257 if (set.contains(e)) return;
259 BindingGroup e_bind_peers = e.bind_peers;
260 BindingGroup e_bind_to = e.bind_to;
262 e.bind_to = bind_others;
263 for (E epeer : e_bind_peers.set) add(epeer);
264 for (E eother : e_bind_to.set) bind_others.add(eother);
266 for(E eother : bind_others.set) {
267 if (e.next.bind_to.set.contains(eother.prev)) {
268 e.next.next.bindEdge(eother.prev.prev);
270 if (e.prev.bind_to.set.contains(eother.next)) {
271 e.prev.prev.bindEdge(eother.next.next);
276 public void dobind(E e) {
277 for(E ebound : set) {
278 e.p1.bind(ebound.p2);
279 e.p2.bind(ebound.p1);
282 public void shatter(BindingGroup bg1, BindingGroup bg2) {
284 e.shatter(e.midpoint(), bg1, bg2);
289 /** [UNIQUE] an edge */
290 public final class E implements Comparable<E> {
292 public final Vertex p1, p2;
293 T t; // triangle to our "left"
294 E prev; // previous half-edge
295 E next; // next half-edge
296 E pair; // partner half-edge
297 public BindingGroup bind_peers = new BindingGroup(this);
298 public BindingGroup bind_to = bind_peers.other();
299 boolean shattered = false;
301 public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
302 public float comparator() {
303 Vertex nearest = error_against.nearest(midpoint());
304 return (float)Math.max(length(), midpoint().distance(nearest.p));
306 public int compareTo(E e) {
307 return e.comparator() > comparator() ? 1 : -1;
309 public void bindEdge(E e) { bind_to.add(e); }
310 public void dobind() { bind_to.dobind(this); }
312 public Point shatter() { return shatter(midpoint(), null, null); }
313 public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
314 if (shattered || destroyed) return mid;
321 int old_colorclass = t==null ? 0 : t.colorclass;
322 if (bg1==null) bg1 = new BindingGroup();
323 if (bg2==null) bg2 = new BindingGroup();
324 BindingGroup old_bind_to = bind_to;
325 bind_peers.shatter(bg1, bg2);
326 old_bind_to.shatter(bg2.other(), bg1.other());
330 newT(r.p, p1.p, mid, null, old_colorclass);
331 newT(r.p, mid, p2.p, null, old_colorclass);
332 bg1.add(p1.getE(mid));
333 bg2.add(p2.getE(mid).pair);
337 public boolean destroyed = false;
338 public void destroy() {
339 if (destroyed) return;
341 pair.destroyed = true;
343 if (t != null) t.destroy();
346 if (pair.t != null) pair.t.destroy();
349 if (next.t != null) next.t.destroy();
350 if (prev.t != null) prev.t.destroy();
354 if (pair.next.t != null) pair.next.t.destroy();
355 if (pair.prev.t != null) pair.next.t.destroy();
361 this.bind_peers = null;
362 pair.bind_peers = null;
363 pair.prev.next = next;
364 next.prev = pair.prev;
365 prev.next = pair.next;
367 if (p1.e == this) p1.e = prev.next;
368 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
371 private void sync() {
372 this.prev.next = this;
373 this.next.prev = this;
374 this.pair.pair = this;
375 bind_peers.add(this);
376 if (this.next.p1 != p2) throw new Error();
377 if (this.prev.p2 != p1) throw new Error();
378 if (this.p1.e == null) this.p1.e = this;
379 if (!added) added = true;
381 private boolean added = false;
383 public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
385 public double crossAngle() {
386 Vec v1 = t.norm().times(-1);
387 Vec v2 = pair.t.norm().times(-1);
388 return Math.acos(v1.norm().dot(v2.norm()));
391 /** angle between this half-edge and the next */
392 public double angle() {
393 Vec v1 = next.p2.p.minus(p2.p);
394 Vec v2 = this.p1.p.minus(p2.p);
395 return Math.acos(v1.norm().dot(v2.norm()));
398 public void makeAdjacent(E e) {
399 if (this.next == e) return;
400 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
401 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
403 E freeIncident = p2.getFreeIncident(e, this);
405 e.prev.next = freeIncident.next;
406 freeIncident.next.prev = e.prev;
408 freeIncident.next = this.next;
409 this.next.prev = freeIncident;
418 /** creates an isolated edge out in the middle of space */
419 public E(Point p1, Point p2) {
420 if (vertices.get(p1) != null) throw new Error();
421 if (vertices.get(p2) != null) throw new Error();
422 this.p1 = new Vertex(p1);
423 this.p2 = new Vertex(p2);
424 this.prev = this.next = this.pair = new E(this, this, this);
426 this.p2.e = this.pair;
430 /** adds a new half-edge from prev.p2 to p2 */
431 public E(E prev, Point p) {
433 p2 = vertices.get(p);
434 if (p2 == null) p2 = new Vertex(p);
438 if (p2.getE(p1) != null) throw new Error();
440 this.next = this.pair = new E(this, this, prev.next);
442 E q = p2.getFreeIncident();
444 this.next.prev = this;
446 this.prev.next = this;
447 this.pair = new E(q, this, z);
449 if (p2.e==null) p2.e = this.pair;
453 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
454 public E(E prev, E pair, E next) {
462 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); }
463 public boolean has(Vertex v) { return v==p1 || v==p2; }
464 public float length() { return p1.p.minus(p2.p).mag(); }
465 public String toString() { return p1+"->"+p2; }
469 public E makeE(Point p1, Point p2) {
470 Vertex v1 = vertices.get(p1);
471 Vertex v2 = vertices.get(p2);
472 if (v1 != null && v2 != null) {
474 if (e != null) return e;
476 if (e != null) return e;
478 if (v1 != null) return new E(v1.getFreeIncident(), p2);
479 if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
480 return new E(p1, p2);
482 public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
484 Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
485 float dot = norm.dot(norm2);
486 //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
487 if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
489 E e12 = makeE(p1, p2);
490 E e23 = makeE(p2, p3);
491 E e31 = makeE(p3, p1);
492 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
493 e12.makeAdjacent(e23);
494 e23.makeAdjacent(e31);
495 e31.makeAdjacent(e12);
497 T ret = e12.makeT(colorclass);
498 if (e12.t == null) throw new Error();
499 if (e23.t == null) throw new Error();
500 if (e31.t == null) throw new Error();
504 /** [UNIQUE] a triangle (face) */
505 public final class T extends Triangle {
507 public final int color;
508 public final int colorclass;
510 T(E e1, int colorclass) {
514 if (e1==e2 || e1==e3) throw new Error();
515 if (e3.next!=e1) throw new Error();
516 if (e1.t!=null || e2.t!=null || e3.t!=null) throw new Error("non-manifold surface or disagreeing normals");
519 e1.next.next.t = this;
521 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
523 int color = Math.abs(random.nextInt());
526 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
527 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
528 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
532 this.colorclass = colorclass;
535 public E e1() { return e1; }
536 public E e2() { return e1.next; }
537 public E e3() { return e1.prev; }
538 public Vertex v1() { return e1.p1; }
539 public Vertex v2() { return e1.p2; }
540 public Vertex v3() { return e1.next.p2; }
541 public Point p1() { return e1.p1.p; }
542 public Point p2() { return e1.p2.p; }
543 public Point p3() { return e1.next.p2.p; }
544 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
545 public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
547 public void removeFromRTree() { triangles.remove(this); }
548 public void addToRTree() { triangles.insert(this); }
549 public void destroy() { triangles.remove(this); }
550 public void reinsert() { triangles.remove(this); triangles.add(this); }
552 public boolean shouldBeDrawn() {
553 if (e1().bind_to.set.size() == 0) return false;
554 if (e2().bind_to.set.size() == 0) return false;
555 if (e3().bind_to.set.size() == 0) return false;