3 import java.awt.event.*;
5 import javax.media.opengl.*;
6 import javax.media.opengl.glu.*;
7 import edu.wlu.cs.levy.CG.KDTree;
9 public class Geom implements Iterable<Geom.T> {
11 private KDTree kd = new KDTree(3);
13 public static float EPSILON = (float)0.0001;
14 public static Random random = new Random();
16 private HashMap<P,V> ps = new HashMap<P,V>();
17 public HashSet<E> es = new HashSet<E>();
18 public ArrayList<T> ts = new ArrayList<T>();
20 public Iterator<T> iterator() { return ts.iterator(); }
22 public P origin() { return new P(0, 0, 0); }
24 public Geom score_against = null;
25 public double score = 0;
26 public float score() { return (float)score; }
28 public void unbind() {
30 for(Geom.T t : this) {
38 for(Geom.T t : this) {
44 public int numedges = 0;
45 public float avgedge = 0;
47 public float rescore() {
50 HashSet<V> done = new HashSet<V>();
52 for(V p : new V[] { t.p1(), t.p2(), t.p3() }) {
53 if (done.contains(p)) continue;
58 for(V p : new V[] { t.p1(), t.p2(), t.p3() })
62 for(V p : new V[] { t.p1(), t.p2(), t.p3() })
64 return (float)(dist/num);
67 public void transform(M m) {
68 ArrayList<V> set = new ArrayList<V>();
69 set.addAll(ps.values());
70 for(V v : set) v.transform(m);
73 public Vec diagonal() {
74 float min_x = Float.MAX_VALUE;
75 float min_y = Float.MAX_VALUE;
76 float min_z = Float.MAX_VALUE;
77 float max_x = Float.MIN_VALUE;
78 float max_y = Float.MIN_VALUE;
79 float max_z = Float.MIN_VALUE;
80 for(P p : ps.keySet()) {
81 if (p.x < min_x) min_x = p.x;
82 if (p.y < min_y) min_y = p.y;
83 if (p.z < min_z) min_z = p.z;
84 if (p.x > max_x) max_x = p.x;
85 if (p.y > max_y) max_y = p.y;
86 if (p.z > max_z) max_z = p.z;
88 return new Vec(max_x - min_x, max_y - min_y, max_z - min_z);
92 float min_x = Float.MAX_VALUE;
93 float min_y = Float.MAX_VALUE;
94 float min_z = Float.MAX_VALUE;
95 float max_x = Float.MIN_VALUE;
96 float max_y = Float.MIN_VALUE;
97 float max_z = Float.MIN_VALUE;
98 for(P p : ps.keySet()) {
99 if (p.x < min_x) min_x = p.x;
100 if (p.y < min_y) min_y = p.y;
101 if (p.z < min_z) min_z = p.z;
102 if (p.x > max_x) max_x = p.x;
103 if (p.y > max_y) max_y = p.y;
104 if (p.z > max_z) max_z = p.z;
106 return new P((float)(max_x + min_x)/2,
107 (float)(max_y + min_y)/2,
108 (float)(max_z + min_z)/2);
111 public T newT(V p12, V p23, V p31, Vec norm) {
112 Vec norm2 = p31.p.minus(p12.p).cross(p23.p.minus(p12.p));
113 float dot = norm.dot(norm2);
114 //if (Math.abs(dot) < EPSILON) throw new Error("dot products within epsilon of each other: "+norm+" "+norm2);
115 if (dot < 0) { V p = p12; p12=p23; p23 = p; }
116 return newT(p12, p23, p31);
119 public float volume() {
122 double area = t.area();
123 Vec origin_to_centroid = new Vec(new P(0, 0, 0), t.centroid());
124 boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
125 double height = Math.abs(t.norm().dot(origin_to_centroid));
126 total += ((facingAway ? 1 : -1) * area * height) / 3.0;
131 public V nearest(P p) {
133 try { results = kd.nearest(new double[]{p.x,p.y,p.z},1); } catch (Exception e) { throw new Error(e); }
134 return (V)results[0];
137 public T newT(V p1, V p2, V p3) {
138 E e12 = p1.makeE(p2);
139 E e23 = p2.makeE(p3);
140 E e31 = p3.makeE(p1);
141 while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
142 e12.makeAdjacent(e23);
143 e23.makeAdjacent(e31);
144 e31.makeAdjacent(e12);
147 if (e12.t == null) throw new Error();
148 if (e23.t == null) throw new Error();
149 if (e31.t == null) throw new Error();
153 public class BindingGroup {
154 public HashSet<E> es = new HashSet<E>();
155 public BindingGroup() { }
156 public BindingGroup(E e) {
159 public void add(E e) {
160 if (e.bg != null) { merge(e.bg); return; }
164 public void merge(BindingGroup bg) {
172 public final class V {
176 if (ps.get(p) != null) throw new Error();
177 ps.put(this.p, this);
179 public void kdremove() {
180 if (!inserted) return;
182 try { kd.delete(new double[]{p.x,p.y,p.z}); } catch (Exception e) { }
184 public void kdinsert() {
185 if (inserted) return;
187 try { kd.insert(new double[]{p.x,p.y,p.z},this); } catch (Exception e) { throw new Error(e); }
190 public float score() { return oldscore; }
191 public void unscore() {
192 if (watch == null) return;
193 watch.watch_x -= p.x;
194 watch.watch_y -= p.y;
195 watch.watch_z -= p.z;
197 if (watch.watch_count==0) {
204 public V partner() { return watch==null ? this : watch; }
205 public V watchback() { return watch_count==0 ? partner() :
206 register(new P(watch_x/watch_count, watch_y/watch_count, watch_z/watch_count)); }
207 public void rescore() {
208 if (score_against == null) return;
213 if (watch != null) unscore();
216 watch = score_against.nearest(po.p);
218 // don't attract to vertices that face the other way
219 if (watch.norm().dot(norm()) < 0) {
222 watch.watch_x += po.p.x;
223 watch.watch_y += po.p.y;
224 watch.watch_z += po.p.z;
230 if (watch_count==0) s1 = 0;
231 else s1 = p.distance(watch_x/watch_count, watch_y/watch_count, watch_z/watch_count);
232 s2 = watch==null ? 0 : po.p.distance(watch.p);
233 oldscore = (float)(s1 + s2);
238 /** does NOT update bound pairs! */
239 public boolean transform(M m) {
240 // FIXME: screws up kdtree
241 // FIXME: screws up hashmap
244 if (ps.get(this.p)==null) throw new Error();
246 float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
247 float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
248 float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
249 this.p = new P(newx, newy, newz);
250 // FIXME: what if we move onto exactly where another point is?
251 ps.put(this.p,(V)this);
252 } catch (Exception e) {
253 throw new RuntimeException(e);
259 for(E e = this.e; ;) {
260 if (e.intersects(t)) { good = false; break; }
262 if (e == this.e) break;
267 if (t==this.t) continue;
268 if (this.intersects(t)) good = false;
273 public boolean move(Vec v) {
278 good &= p.transform(m);
279 v = v.times(binding); // bleh wrong
285 public E makeE(V p2) {
287 if (e != null) return e;
289 if (this.e == null && p2.e == null) return this.e = new E(this, p2);
290 if (this.e == null && p2.e != null) return p2.makeE(this).pair;
291 return new E(getFreeIncident(), p2);
294 public E getFreeIncident() {
295 E ret = getFreeIncident(e, e);
296 if (ret != null) return ret;
297 ret = getFreeIncident(e.pair.next, e.pair.next);
298 if (ret == null) throw new Error("unable to find free incident to " + this);
302 public E getFreeIncident(E start, E before) {
305 if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null) return e.pair;
307 } while(e != before);
311 public E getE(V p2) {
314 if (e==null) return null;
315 if (e.p1 == this && e.p2 == p2) return e;
321 public boolean isBoundTo(V p) {
324 if (px==this) return true;
330 public void unbind() { bound_to = this; binding = new M(); }
331 public void bind(V p) { bind(p, new M()); }
332 public void bind(V p, M binding) {
333 if (isBoundTo(p)) return;
334 V temp_bound_to = p.bound_to;
335 M temp_binding = p.binding;
336 p.bound_to = this.bound_to;
337 p.binding = binding.times(this.binding); // FIXME: may have order wrong here
338 this.bound_to = temp_bound_to;
339 this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
342 Vec norm = new Vec(0, 0, 0);
345 if (e.t != null) norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
347 } while(e != this.e);
357 E e; // some edge *leaving* this point
360 boolean inserted = false;
363 /** [UNIQUE] an edge */
364 public final class E implements Comparable<E> {
366 public boolean intersects(T t) {
367 double A0=t.p1().p.x, A1=t.p1().p.y, A2=t.p1().p.z;
368 double B0=t.p2().p.x, B1=t.p2().p.y, B2=t.p2().p.z;
369 double C0=t.p3().p.x, C1=t.p3().p.y, C2=t.p3().p.z;
370 double j0=p1.p.x, j1=p1.p.y, j2=p1.p.z;
371 double k0=p2.p.x, k1=p2.p.y, k2=p2.p.z;
379 double R00, R01, R02, R03,
393 /* c = a × b */
394 c0 = a1 * b2 - a2 * b1;
395 c1 = a2 * b0 - a0 * b2;
396 c2 = a0 * b1 - a1 * b0;
398 /* M^(-1) = (1/det(M)) * adj(M) */
399 in_det = 1 / (c0 * c0 + c1 * c1 + c2 * c2);
400 R00 = (b1 * c2 - b2 * c1) * in_det;
401 R01 = (b2 * c0 - b0 * c2) * in_det;
402 R02 = (b0 * c1 - b1 * c0) * in_det;
403 R10 = (c1 * a2 - c2 * a1) * in_det;
404 R11 = (c2 * a0 - c0 * a2) * in_det;
405 R12 = (c0 * a1 - c1 * a0) * in_det;
411 R03 = -(R00 * A0 + R01 * A1 + R02 * A2);
412 R13 = -(R10 * A0 + R11 * A1 + R12 * A2);
413 R23 = -(R20 * A0 + R21 * A1 + R22 * A2);
415 /* fill in last row of 4x4 matrix */
419 J2 = R20 * j0 + R21 * j1 + R22 * j2 + R23;
420 K2 = R20 * k0 + R21 * k1 + R22 * k2 + R23;
421 if (J2 * K2 >= 0) return false;
423 J0 = R00 * j0 + R01 * j1 + R02 * j2 + R03;
424 K0 = R00 * k0 + R01 * k1 + R02 * k2 + R03;
425 i0 = J0 + J2 * ((K0 - J0) / (J2 - K2));
426 if (i0 < 0 || i0 > 1) return false;
428 J1 = R10 * j0 + R11 * j1 + R12 * j2 + R13;
429 K1 = R10 * k0 + R11 * k1 + R12 * k2 + R13;
430 i1 = J1 + J2 * ((K1 - J1) / (J2 - K2));
431 if (i1 < 0 || i1 > 1 || i0 + i1 > 1) return false;
436 public int compareTo(E e) {
437 return e.length() > length() ? 1 : -1;
440 public final V p1, p2;
441 T t; // triangle to our "left"
442 E prev; // previous half-edge
443 E next; // next half-edge
444 E pair; // partner half-edge
447 public BindingGroup bg = new BindingGroup(this);
449 public void bind(E e) { bind(e, new M()); }
450 public void bind(E e, M m) { e.bg.add(this); }
452 public void dobind() {
453 if (bg==null) return;
455 if (ex==this) continue;
461 boolean shattered = false;
462 public V shatter() { return shatter(register(midpoint()), null, null); }
463 public V shatter(V mid, BindingGroup bg1, BindingGroup bg2) {
464 if (shattered) return mid;
471 if (bg1==null) bg1 = new BindingGroup();
472 if (bg2==null) bg2 = new BindingGroup();
473 for(E e : bg.es) e.shatter(register(e.midpoint()), bg1, bg2);
479 bg1.add(p1.getE(mid));
480 bg2.add(mid.getE(p2));
484 public boolean destroyed = false;
485 public void destroy() {
486 if (destroyed) return;
488 pair.destroyed = true;
489 if (next.t != null) next.t.destroy();
490 if (prev.t != null) prev.t.destroy();
491 if (pair.next.t != null) ts.remove(pair.next.t);
492 if (pair.prev.t != null) ts.remove(pair.prev.t);
499 pair.prev.next = next;
500 next.prev = pair.prev;
501 prev.next = pair.next;
503 if (p1.e == this) p1.e = prev.next;
504 if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
507 avgedge -= this.length();
508 avgedge -= pair.length();
513 private void sync() {
514 this.prev.next = this;
515 this.next.prev = this;
516 this.pair.pair = this;
517 if (this.next.p1 != p2) throw new Error();
518 if (this.prev.p2 != p1) throw new Error();
519 if (this.p1.e == null) this.p1.e = this;
527 private boolean added = false;
529 public T makeT() { return t==null ? (t = new T(this)) : t; }
531 /** angle between this half-edge and the next */
532 public double angle() {
533 Vec v1 = next.p2.p.minus(p2.p);
534 Vec v2 = this.p1.p.minus(p2.p);
535 return Math.acos(v1.norm().dot(v2.norm()));
538 public void makeAdjacent(E e) {
539 if (this.next == e) return;
540 if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
541 if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
543 E freeIncident = p2.getFreeIncident(e, this);
545 e.prev.next = freeIncident.next;
546 freeIncident.next.prev = e.prev;
548 freeIncident.next = this.next;
549 this.next.prev = freeIncident;
558 /** creates an isolated edge out in the middle of space */
559 public E(V p1, V p2) {
560 if (p1==p2) throw new Error("attempt to create edge with single vertex: " + p1);
563 this.prev = this.next = this.pair = new E(this, this, this);
567 /** adds a new half-edge from prev.p2 to p2 */
568 public E(E prev, V p2) {
572 if (p2.getE(p1) != null) throw new Error();
574 this.next = this.pair = new E(this, this, prev.next);
576 E q = p2.getFreeIncident();
578 this.next.prev = this;
580 this.prev.next = this;
581 this.pair = new E(q, this, z);
586 /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
587 public E(E prev, E pair, E next) {
595 public P midpoint() { return new P((p1.p.x+p2.p.x)/2, (p1.p.y+p2.p.y)/2, (p1.p.z+p2.p.z)/2); }
596 public boolean has(V v) { return v==p1 || v==p2; }
597 public float length() { return p1.p.minus(p2.p).mag(); }
598 public String toString() { return p1+"->"+p2; }
601 /** [UNIQUE] a triangle (face) */
602 public final class T {
604 public final int color;
606 public void destroy() {
610 public V nearest(P p) {
611 float d1 = p1().p.distance(p);
612 float d2 = p2().p.distance(p);
613 float d3 = p3().p.distance(p);
614 if (d1 < d2 && d1 < d3) return p1();
615 if (d2 < d3) return p2();
623 if (e1==e2 || e1==e3) throw new Error();
624 if (e3.next!=e1) throw new Error();
625 if (e1.t!=null || e2.t!=null || e3.t!=null)
626 throw new Error("non-manifold surface or disagreeing normals");
629 e1.next.next.t = this;
631 // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
633 int color = Math.abs(random.nextInt());
636 if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
637 if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
638 if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
650 public V p1() { return e1.p1; }
651 public V p2() { return e1.p2; }
652 public V p3() { return e1.next.p2; }
653 public E e1() { return e1; }
654 public E e2() { return e1.next; }
655 public E e3() { return e1.prev; }
656 public Vec norm() { return p2().p.minus(p1().p).cross(p3().p.minus(p1().p)).norm(); }
657 public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
658 public boolean has(V v) { return p1()==v || p2()==v || p3()==v; }
660 public float area() {
661 return (float)Math.abs(0.5 * e1().length() * new Vec(p1().p, p2().p).norm().dot(new Vec(p2().p, p3().p)));
664 public void glVertices(GL gl) {
670 public P centroid() { return new P((p1().p.x+p2().p.x+p3().p.x)/3,
671 (p1().p.y+p2().p.y+p3().p.y)/3,
672 (p1().p.z+p2().p.z+p3().p.z)/3); }
673 public float diameter() {
674 // FIXME: what is this supposed to be?
675 return Math.max(Math.max(e1().length(), e2().length()), e3().length()) / 2;
681 public V register(P p) { V v = ps.get(p); return v==null ? new V(p) : v; }
683 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
685 /** point in 3-space; immutable */
686 public static final class P {
687 public final float x, y, z;
688 public P(double x, double y, double z) { this((float)x, (float)y, (float)z); }
689 public P(float x, float y, float z) { this.x = x; this.y = y; this.z = z; }
690 public float distance(P p) { return distance(p.x, p.y, p.z); }
691 public float distance(float ox, float oy, float oz) { return (float)Math.sqrt((x-ox)*(x-ox)+(y-oy)*(y-oy)+(z-oz)*(z-oz)); }
692 public P times(M m) { return m.times(this); }
693 public Vec minus(P p) { return new Vec(x-p.x, y-p.y, z-p.z); }
694 public P plus(Vec v) { return new P(x+v.x, y+v.y, z+v.z); }
695 public boolean equals(Object o) { return o!=null && (o instanceof P) && ((P)o).x==x && ((P)o).y==y && ((P)o).z==z; }
696 public void glVertex(GL gl) { _glVertex(gl); }
697 private void _glVertex(GL gl) { gl.glVertex3f(x, y, z); }
698 public String toString() { return "("+x+","+y+","+z+")"; }
699 public int hashCode() { return Float.floatToIntBits(x) ^ Float.floatToIntBits(y) ^ Float.floatToIntBits(z); }
702 /** vector in 3-space; immutable */
703 public static final class Vec {
704 public final float x, y, z;
705 public Vec(double x, double y, double z) { this((float)x, (float)y, (float)z); }
706 public Vec(float x, float y, float z) { this.x = x; this.y = y; this.z = z; }
707 public Vec(P p1, P p2) { this(p2.x-p1.x, p2.y-p1.y, p2.z-p1.z); }
708 public Vec cross(Vec v) { return new Vec(y*v.z-z*v.y, z*v.x-x*v.z, x*v.y-y*v.x); }
709 public Vec plus(Vec v) { return new Vec(x+v.x, y+v.y, z+v.z); }
710 public Vec norm() { return mag()==0 ? this : div(mag()); }
711 public Vec times(M m) { return m.apply(this); }
712 public float mag() { return (float)Math.sqrt(x*x+y*y+z*z); }
713 public float dot(Vec v) { return x*v.x + y*v.y + z*v.z; }
714 public Vec times(float mag) { return new Vec(x*mag, y*mag, z*mag); }
715 public Vec div(float mag) { return new Vec(x/mag, y/mag, z/mag); }
716 public String toString() { return "<"+x+","+y+","+z+">"; }
720 public static class M {
727 public final float a, b, c, d, e, f, g, h, i, j, k, l;
728 public M() { this(1); }
729 public M(float scale) {
731 l = h = d = e = b = i = c = j = g = 0;
733 public M(float scalex, float scaley, float scalez) {
737 l = h = d = e = b = i = c = j = g = 0;
739 public M(Vec translate) {
740 d = translate.x; h = translate.y; l = translate.z;
742 b = c = e = g = i = j = 0;
744 public M(float a, float b, float c, float d, float e, float f, float g, float h, float i, float j, float k, float l) {
745 this.a = a; this.b = b; this.c = c; this.d = d; this.e = e; this.f = f; this.g = g; this.h = h; this.i = i;
746 this.j = j; this.k = k; this.l = l;
748 public M times(float x) {
749 return new M(a*x, b*x, c*x, d*x, e*x, f*x, g*x, h*x, i*x, j*x, k*x, l*x);
751 public M(Vec axis, float angle) {
752 double q = Math.cos(angle);
753 double s = Math.sin(angle);
755 a = (float)(q + axis.x*axis.x*t);
756 f = (float)(q + axis.y*axis.y*t);
757 k = (float)(q + axis.z*axis.z*t);
758 double tmp1 = axis.x*axis.y*t;
759 double tmp2 = axis.z*s;
760 e = (float)(tmp1 + tmp2);
761 b = (float)(tmp1 - tmp2);
762 tmp1 = axis.x*axis.z*t;
764 i = (float)(tmp1 - tmp2);
765 c = (float)(tmp1 + tmp2);
766 tmp1 = axis.y*axis.z*t;
768 j = (float)(tmp1 + tmp2);
769 g = (float)(tmp1 - tmp2);
772 public P times(P p) {
773 return new P(a*p.x + b*p.y + c*p.z + d,
774 e*p.x + f*p.y + g*p.z + h,
775 i*p.x + j*p.y + k*p.z + l);
777 public P apply(P p) { return p; }
778 public Vec apply(Vec v) { return v; }
779 public M invert() { return this; }
780 public M times(M m) { return this; }