X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=src%2FGeom.java;fp=src%2FGeom.java;h=0000000000000000000000000000000000000000;hb=e3aa83b5505dcfbc200e29e5b1701664bb218709;hp=9f83c77d52ee47026690399e341e8f4a95f82e39;hpb=4b43602a6590a8c44a42e6d68cc1c33a4429eb4e;p=anneal.git

diff --git a/src/Geom.java b/src/Geom.java
deleted file mode 100644
index 9f83c77..0000000
--- a/src/Geom.java
+++ /dev/null
@@ -1,783 +0,0 @@
-import java.awt.*;
-import java.util.*;
-import java.awt.event.*;
-import javax.swing.*;
-import javax.media.opengl.*;
-import javax.media.opengl.glu.*;
-import edu.wlu.cs.levy.CG.KDTree;
-
-public class Geom implements Iterable<Geom.T> {
-
-    private KDTree kd = new KDTree(3);
-
-    public static float EPSILON = (float)0.0001;
-    public static Random random = new Random();
-
-    private HashMap<P,V>  ps = new HashMap<P,V>();
-    public  HashSet<E>    es = new HashSet<E>();
-    public  ArrayList<T>  ts = new ArrayList<T>();
-
-    public Iterator<T> iterator() { return ts.iterator(); }
-
-    public P origin() { return new P(0, 0, 0); }
-
-    public Geom score_against = null;
-    public double score = 0;
-    public float score() { return (float)score; }
-
-    public void unbind() {
-
-        for(Geom.T t : this) {
-            t.p1().unbind();
-            t.p2().unbind();
-            t.p3().unbind();
-        }
-
-    }
-    public void bind() {
-        for(Geom.T t : this) {
-            t.e1().dobind();
-            t.e2().dobind();
-            t.e3().dobind();
-        }
-    }
-    public int numedges = 0;
-    public float avgedge = 0;
-
-    public float rescore() {
-        int num = 0;
-        double dist = 0;
-        HashSet<V> done = new HashSet<V>();
-        for(T t : ts)
-            for(V p : new V[] { t.p1(), t.p2(), t.p3() }) {
-                if (done.contains(p)) continue;
-                done.add(p);
-                p.rescore();
-            }
-        for(T t : ts)
-            for(V p : new V[] { t.p1(), t.p2(), t.p3() })
-                p.kdremove();
-        kd = new KDTree(3);
-        for(T t : ts)
-            for(V p : new V[] { t.p1(), t.p2(), t.p3() })
-                p.kdinsert();
-        return (float)(dist/num);
-    }
-
-    public void transform(M m) {
-        ArrayList<V> set = new ArrayList<V>();
-        set.addAll(ps.values());
-        for(V v : set) v.transform(m);
-    }
-
-    public Vec diagonal() {
-        float min_x = Float.MAX_VALUE;
-        float min_y = Float.MAX_VALUE;
-        float min_z = Float.MAX_VALUE;
-        float max_x = Float.MIN_VALUE;
-        float max_y = Float.MIN_VALUE;
-        float max_z = Float.MIN_VALUE;
-        for(P p : ps.keySet()) {
-            if (p.x < min_x) min_x = p.x;
-            if (p.y < min_y) min_y = p.y;
-            if (p.z < min_z) min_z = p.z;
-            if (p.x > max_x) max_x = p.x;
-            if (p.y > max_y) max_y = p.y;
-            if (p.z > max_z) max_z = p.z;
-        }
-        return new Vec(max_x - min_x, max_y - min_y, max_z - min_z);
-    }
-
-    public P centroid() {
-        float min_x = Float.MAX_VALUE;
-        float min_y = Float.MAX_VALUE;
-        float min_z = Float.MAX_VALUE;
-        float max_x = Float.MIN_VALUE;
-        float max_y = Float.MIN_VALUE;
-        float max_z = Float.MIN_VALUE;
-        for(P p : ps.keySet()) {
-            if (p.x < min_x) min_x = p.x;
-            if (p.y < min_y) min_y = p.y;
-            if (p.z < min_z) min_z = p.z;
-            if (p.x > max_x) max_x = p.x;
-            if (p.y > max_y) max_y = p.y;
-            if (p.z > max_z) max_z = p.z;
-        }
-        return new P((float)(max_x + min_x)/2,
-                     (float)(max_y + min_y)/2,
-                     (float)(max_z + min_z)/2);
-    }
-
-    public T newT(V p12, V p23, V p31, Vec norm) {
-        Vec norm2 = p31.p.minus(p12.p).cross(p23.p.minus(p12.p));
-        float dot = norm.dot(norm2);
-        //if (Math.abs(dot) < EPSILON) throw new Error("dot products within epsilon of each other: "+norm+" "+norm2);
-        if (dot < 0) { V p = p12; p12=p23; p23 = p; }
-        return newT(p12, p23, p31);
-    }
-
-    public float volume() {
-        double total = 0;
-        for(T t : ts) {
-            double area = t.area();
-            Vec origin_to_centroid = new Vec(new P(0, 0, 0), t.centroid());
-            boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
-            double height = Math.abs(t.norm().dot(origin_to_centroid));
-            total += ((facingAway ? 1 : -1) * area * height) / 3.0;
-        }
-        return (float)total;
-    }
-
-    public V nearest(P p) {
-        Object[] results;
-        try { results = kd.nearest(new double[]{p.x,p.y,p.z},1); } catch (Exception e) { throw new Error(e); }
-        return (V)results[0];
-    }
-
-    public T newT(V p1, V p2, V p3) {
-        E e12 = p1.makeE(p2);
-        E e23 = p2.makeE(p3);
-        E e31 = p3.makeE(p1);
-        while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
-            e12.makeAdjacent(e23);
-            e23.makeAdjacent(e31);
-            e31.makeAdjacent(e12);
-        }
-        T ret = e12.makeT();
-        if (e12.t == null) throw new Error();
-        if (e23.t == null) throw new Error();
-        if (e31.t == null) throw new Error();
-        return ret;
-    }
-
-    public class BindingGroup {
-        public HashSet<E> es = new HashSet<E>();
-        public BindingGroup() { }
-        public BindingGroup(E e) {
-            es.add(e);
-        }
-        public void add(E e) {
-            if (e.bg != null) { merge(e.bg); return; }
-            es.add(e);
-            e.bg = this;
-        }
-        public void merge(BindingGroup bg) {
-            for(E e : bg.es) {
-                e.bg = null;
-                add(e);
-            }
-        }
-    }
-
-    public final class V {
-        public P p;
-        public V(P p) {
-            this.p = p;
-            if (ps.get(p) != null) throw new Error();
-            ps.put(this.p, this);
-        }
-        public void kdremove() {
-            if (!inserted) return;
-            inserted = false;
-            try { kd.delete(new double[]{p.x,p.y,p.z}); } catch (Exception e) { }
-        }
-        public void kdinsert() {
-            if (inserted) return;
-            inserted = true;
-            try { kd.insert(new double[]{p.x,p.y,p.z},this); } catch (Exception e) { throw new Error(e); }
-        }
-
-        public float score() { return oldscore; }
-        public void unscore() {
-            if (watch == null) return;
-            watch.watch_x -= p.x;
-            watch.watch_y -= p.y;
-            watch.watch_z -= p.z;
-            watch.watch_count--;
-            if (watch.watch_count==0) {
-                watch.watch_x = 0;
-                watch.watch_y = 0;
-                watch.watch_z = 0;
-            }
-            watch = null;
-        }
-        public V partner() { return watch==null ? this : watch; }
-        public V watchback() { return watch_count==0 ? partner() :
-                register(new P(watch_x/watch_count, watch_y/watch_count, watch_z/watch_count)); }
-        public void rescore() {
-            if (score_against == null) return;
-
-            score -= oldscore;
-            oldscore = 0;
-
-            if (watch != null) unscore();
-            V po = this;
-            if (watch == null) {
-                watch = score_against.nearest(po.p);
-
-                // don't attract to vertices that face the other way
-                if (watch.norm().dot(norm()) < 0) {
-                    watch = null;
-                } else {
-                    watch.watch_x += po.p.x;
-                    watch.watch_y += po.p.y;
-                    watch.watch_z += po.p.z;
-                    watch.watch_count++;
-                }
-            }
-
-            double s1, s2;
-            if (watch_count==0) s1 = 0;
-            else                s1 = p.distance(watch_x/watch_count, watch_y/watch_count, watch_z/watch_count);
-            s2 = watch==null ? 0 : po.p.distance(watch.p);
-            oldscore = (float)(s1 + s2);
-            score += oldscore;
-        }
-
-
-        /** does NOT update bound pairs! */
-        public boolean transform(M m) {
-            // FIXME: screws up kdtree 
-            // FIXME: screws up hashmap
-            unscore();
-            try {
-                if (ps.get(this.p)==null) throw new Error();
-                ps.remove(this.p);
-                float newx = m.a*p.x + m.b*p.y + m.c*p.z + m.d;
-                float newy = m.e*p.x + m.f*p.y + m.g*p.z + m.h;
-                float newz = m.i*p.x + m.j*p.y + m.k*p.z + m.l;
-                this.p = new P(newx, newy, newz);
-                // FIXME: what if we move onto exactly where another point is?
-                ps.put(this.p,(V)this);
-            } catch (Exception e) {
-                throw new RuntimeException(e);
-            }
-            rescore();
-            boolean good = true;
-            /*
-            for(T t : ts) {
-                for(E e = this.e; ;) {
-                    if (e.intersects(t)) { good = false; break; }
-                    e = e.pair.next;
-                    if (e == this.e) break;
-                }
-            }
-            */
-            /*
-                if (t==this.t) continue;
-                if (this.intersects(t)) good = false;
-            }
-            */
-            return good;
-        }
-        public boolean move(Vec v) {
-            M m = new M(v);
-            V p = this;
-            boolean good = true;
-            do {
-                good &= p.transform(m);
-                v = v.times(binding); // bleh wrong
-                p = p.bound_to;
-            } while (p != this);
-            return good;
-        }
-
-        public E makeE(V p2) {
-            E e = getE(p2);
-            if (e != null) return e;
-            e = p2.getE(this);
-            if (this.e == null && p2.e == null) return this.e = new E(this, p2);
-            if (this.e == null && p2.e != null) return p2.makeE(this).pair;
-            return new E(getFreeIncident(), p2);
-        }
-
-        public E getFreeIncident() {
-            E ret = getFreeIncident(e, e);
-            if (ret != null) return ret;
-            ret = getFreeIncident(e.pair.next, e.pair.next);
-            if (ret == null) throw new Error("unable to find free incident to " + this);
-            return ret;
-        }
-
-        public E getFreeIncident(E start, E before) {
-            E e = start;
-            do {
-                if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null) return e.pair;
-                e = e.pair.next;
-            } while(e != before);
-            return null;
-        }
-
-        public E getE(V p2) {
-            E e = this.e;
-            do {
-                if (e==null) return null;
-                if (e.p1 == this && e.p2 == p2) return e;
-                e = e.pair.next;
-            } while (e!=this.e);
-            return null;
-        }
-
-        public boolean isBoundTo(V p) {
-            V px = p;
-            do {
-                if (px==this) return true;
-                px = px.bound_to;
-            } while(px != p);
-            return false;
-        }
-
-        public void unbind() { bound_to = this; binding = new M(); }
-        public void bind(V p) { bind(p, new M()); }
-        public void bind(V p, M binding) {
-            if (isBoundTo(p)) return;
-            V temp_bound_to = p.bound_to;
-            M temp_binding = p.binding;
-            p.bound_to = this.bound_to;
-            p.binding = binding.times(this.binding); // FIXME: may have order wrong here
-            this.bound_to = temp_bound_to;
-            this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
-        }
-        public Vec norm() {
-            Vec norm = new Vec(0, 0, 0);
-            E e = this.e;
-            do {
-                if (e.t != null) norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
-                e = e.pair.next;
-            } while(e != this.e);
-            return norm.norm();
-        }
-
-        V bound_to = this;
-        int watch_count;
-        float watch_x;
-        float watch_y;
-        float watch_z;
-        V watch;
-        E e;                // some edge *leaving* this point
-        M binding = new M();
-        float oldscore = 0;
-        boolean inserted = false;
-    }
-
-    /** [UNIQUE] an edge */
-    public final class E implements Comparable<E> {
-
-        public boolean intersects(T t) {
-            double A0=t.p1().p.x, A1=t.p1().p.y, A2=t.p1().p.z;
-            double B0=t.p2().p.x, B1=t.p2().p.y, B2=t.p2().p.z;
-            double C0=t.p3().p.x, C1=t.p3().p.y, C2=t.p3().p.z;
-            double j0=p1.p.x, j1=p1.p.y, j2=p1.p.z;
-            double k0=p2.p.x, k1=p2.p.y, k2=p2.p.z;
-            double J0, J1, J2;
-            double K0, K1, K2;
-            double i0, i1, i2;
-            double a0, a1, a2;
-            double b0, b1, b2;
-            double c0, c1, c2;
-            double in_det;
-            double R00, R01, R02, R03,
-                R10, R11, R12, R13,
-                R20, R21, R22, R23,
-                R30, R31, R32, R33;
-
-
-            /* a = B - A */
-            a0 = B0 - A0; 
-            a1 = B1 - A1; 
-            a2 = B2 - A2;
-            /* b = C - B */
-            b0 = C0 - A0;
-            b1 = C1 - A1;
-            b2 = C2 - A2;
-            /* c = a &times; b */
-            c0 = a1 * b2 - a2 * b1;
-            c1 = a2 * b0 - a0 * b2;
-            c2 = a0 * b1 - a1 * b0;
- 
-            /* M^(-1) = (1/det(M)) * adj(M) */
-            in_det = 1 / (c0 * c0 + c1 * c1 + c2 * c2);
-            R00 = (b1 * c2 - b2 * c1) * in_det;
-            R01 = (b2 * c0 - b0 * c2) * in_det;
-            R02 = (b0 * c1 - b1 * c0) * in_det;
-            R10 = (c1 * a2 - c2 * a1) * in_det;
-            R11 = (c2 * a0 - c0 * a2) * in_det;
-            R12 = (c0 * a1 - c1 * a0) * in_det;
-            R20 = (c0) * in_det;
-            R21 = (c1) * in_det;
-            R22 = (c2) * in_det;
-  
-            /* O = M^(-1) * A */
-            R03 = -(R00 * A0 + R01 * A1 + R02 * A2);
-            R13 = -(R10 * A0 + R11 * A1 + R12 * A2);
-            R23 = -(R20 * A0 + R21 * A1 + R22 * A2);
- 
-            /* fill in last row of 4x4 matrix */
-            R30 = R31 = R32 = 0;
-            R33 = 1;
-  
-            J2 = R20 * j0 + R21 * j1 + R22 * j2 + R23;
-            K2 = R20 * k0 + R21 * k1 + R22 * k2 + R23;
-            if (J2 * K2 >= 0) return false;
-
-            J0 = R00 * j0 + R01 * j1 + R02 * j2 + R03;
-            K0 = R00 * k0 + R01 * k1 + R02 * k2 + R03;
-            i0 = J0 + J2 * ((K0 - J0) / (J2 - K2));
-            if (i0 < 0 || i0 > 1) return false;
-  
-            J1 = R10 * j0 + R11 * j1 + R12 * j2 + R13;
-            K1 = R10 * k0 + R11 * k1 + R12 * k2 + R13;
-            i1 = J1 + J2 * ((K1 - J1) / (J2 - K2));
-            if (i1 < 0 || i1 > 1 || i0 + i1 > 1) return false;
-
-            return true;            
-        }
-
-        public int compareTo(E e) {
-            return e.length() > length() ? 1 : -1;
-        }
-
-        public final V p1, p2;
-        T t;     // triangle to our "left"
-        E prev;  // previous half-edge
-        E next;  // next half-edge
-        E pair;  // partner half-edge
-
-
-        public BindingGroup bg = new BindingGroup(this);
-
-        public void bind(E e) { bind(e, new M()); }
-        public void bind(E e, M m) { e.bg.add(this); }
-
-        public void dobind() {
-            if (bg==null) return;
-            for(E ex : bg.es) {
-                if (ex==this) continue;
-                p1.bind(ex.p1);
-                p2.bind(ex.p2);
-            }
-        }
-
-        boolean shattered = false;
-        public V shatter() { return shatter(register(midpoint()), null, null); }
-        public V shatter(V mid, BindingGroup bg1, BindingGroup bg2) {
-            if (shattered) return mid;
-            shattered = true;
-
-            V r = next.p2;
-            E next = this.next;
-            E prev = this.prev;
-
-            if (bg1==null) bg1 = new BindingGroup();
-            if (bg2==null) bg2 = new BindingGroup();
-            for(E e : bg.es) e.shatter(register(e.midpoint()), bg1, bg2);
-            pair.shatter();
-            destroy();
-
-            newT(r, p1, mid);
-            newT(r, mid, p2);
-            bg1.add(p1.getE(mid));
-            bg2.add(mid.getE(p2));
-            return mid;
-        }
-
-        public boolean destroyed = false;
-        public void destroy() {
-            if (destroyed) return;
-            destroyed = true;
-            pair.destroyed = true;
-            if (next.t != null) next.t.destroy();
-            if (prev.t != null) prev.t.destroy();
-            if (pair.next.t != null) ts.remove(pair.next.t);
-            if (pair.prev.t != null) ts.remove(pair.prev.t);
-            next.t = null;
-            prev.t = null;
-            pair.next.t = null;
-            pair.prev.t = null;
-            this.bg = null;
-            pair.bg = null;
-            pair.prev.next = next;
-            next.prev = pair.prev;
-            prev.next = pair.next;
-            pair.next = prev;
-            if (p1.e == this) p1.e = prev.next;
-            if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
-            es.remove(this);
-            es.remove(pair);
-            avgedge -= this.length();
-            avgedge -= pair.length();
-            numedges--;
-            numedges--;
-        }
-
-        private void sync() {
-            this.prev.next = this;
-            this.next.prev = this;
-            this.pair.pair = this;
-            if (this.next.p1 != p2) throw new Error();
-            if (this.prev.p2 != p1) throw new Error();
-            if (this.p1.e == null) this.p1.e = this;
-            es.add(this);
-            if (!added) {
-                added = true;
-                numedges++;
-                avgedge += length();
-            }
-        }
-        private boolean added = false;
-
-        public T makeT() { return t==null ? (t = new T(this)) : t; }
-
-        /** angle between this half-edge and the next */
-        public double angle() {
-            Vec v1 = next.p2.p.minus(p2.p);
-            Vec v2 = this.p1.p.minus(p2.p);
-            return Math.acos(v1.norm().dot(v2.norm()));
-        }
-
-        public void makeAdjacent(E e) {
-            if (this.next == e) return;
-            if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
-            if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free");
-
-            E freeIncident = p2.getFreeIncident(e, this);
-
-            e.prev.next = freeIncident.next;
-            freeIncident.next.prev = e.prev;
-
-            freeIncident.next = this.next;
-            this.next.prev = freeIncident;
-            
-            this.next = e;
-            e.prev = this;
-
-            sync();
-            freeIncident.sync();
-        }
-
-        /** creates an isolated edge out in the middle of space */
-        public E(V p1, V p2) {
-            if (p1==p2) throw new Error("attempt to create edge with single vertex: " + p1);
-            this.p1 = p1;
-            this.p2 = p2;
-            this.prev = this.next = this.pair = new E(this, this, this);
-            sync();
-        }
-
-        /** adds a new half-edge from prev.p2 to p2 */
-        public E(E prev, V p2) {
-            this.p1 = prev.p2;
-            this.p2 = p2;
-            this.prev = prev;
-            if (p2.getE(p1) != null) throw new Error();
-            if (p2.e==null) {
-                this.next = this.pair = new E(this, this, prev.next);
-            } else {
-                E q = p2.getFreeIncident();
-                this.next = q.next;
-                this.next.prev = this;
-                E z = prev.next;
-                this.prev.next = this;
-                this.pair = new E(q, this, z);
-            }
-            sync();
-        }
-
-        /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
-        public E(E prev, E pair, E next) {
-            this.p1 = prev.p2;
-            this.p2 = next.p1;
-            this.prev = prev;
-            this.next = next;
-            this.pair = pair;
-            sync();
-        }
-        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); }
-        public boolean has(V v) { return v==p1 || v==p2; }
-        public float length() { return p1.p.minus(p2.p).mag(); }
-        public String toString() { return p1+"->"+p2; }
-    }
-
-    /** [UNIQUE] a triangle (face) */
-    public final class T {
-        public final E e1;
-        public final int color;
-
-        public void destroy() {
-            ts.remove(this);
-        }
-
-        public V nearest(P p) {
-            float d1 = p1().p.distance(p);
-            float d2 = p2().p.distance(p);
-            float d3 = p3().p.distance(p);
-            if (d1 < d2 && d1 < d3) return p1();
-            if (d2 < d3) return p2();
-            return p3();
-        }
-
-        T(E e1) {
-            this.e1 = e1;
-            E e2 = e1.next;
-            E e3 = e2.next;
-            if (e1==e2     || e1==e3) throw new Error();
-            if (e3.next!=e1) throw new Error();
-            if (e1.t!=null || e2.t!=null || e3.t!=null)
-                throw new Error("non-manifold surface or disagreeing normals");
-            e1.t = this;
-            e1.next.t = this;
-            e1.next.next.t = this;
-
-            // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
-
-            int color = Math.abs(random.nextInt());
-            while(true) {
-                color = color % 4;
-                if (e1().pair.t != null && color == e1().pair.t.color) { color++; continue; }
-                if (e2().pair.t != null && color == e2().pair.t.color) { color++; continue; }
-                if (e3().pair.t != null && color == e3().pair.t.color) { color++; continue; }
-                break;
-            }
-
-            // FIXME unnecssary
-            ts.add(this);
-            p1().kdinsert();
-            p2().kdinsert();
-            p3().kdinsert();
-
-            this.color = color;
-        }
-        public V p1() { return e1.p1; }
-        public V p2() { return e1.p2; }
-        public V p3() { return e1.next.p2; }
-        public E e1() { return e1; }
-        public E e2() { return e1.next; }
-        public E e3() { return e1.prev; }
-        public Vec norm() { return p2().p.minus(p1().p).cross(p3().p.minus(p1().p)).norm(); }
-        public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
-        public boolean has(V v) { return p1()==v || p2()==v || p3()==v; }
-
-        public float area() {
-            return (float)Math.abs(0.5 * e1().length() * new Vec(p1().p, p2().p).norm().dot(new Vec(p2().p, p3().p)));
-        }
-
-        public void glVertices(GL gl) {
-            p1().p.glVertex(gl);
-            p2().p.glVertex(gl);
-            p3().p.glVertex(gl);
-        }
-
-        public P centroid() { return new P((p1().p.x+p2().p.x+p3().p.x)/3,
-                                          (p1().p.y+p2().p.y+p3().p.y)/3, 
-                                          (p1().p.z+p2().p.z+p3().p.z)/3); }
-        public float diameter() {
-            // FIXME: what is this supposed to be?
-            return Math.max(Math.max(e1().length(), e2().length()), e3().length()) / 2;
-        }
-
-
-    }
-    
-    public V register(P p) { V v = ps.get(p); return v==null ? new V(p) : v; }
-
-    //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-
-    /** point in 3-space; immutable */
-    public static final class P {
-        public final float x, y, z;
-        public P(double x, double y, double z) { this((float)x, (float)y, (float)z); }
-        public P(float x, float y, float z) { this.x = x; this.y = y; this.z = z; }
-        public float distance(P p) { return distance(p.x, p.y, p.z); }
-        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)); }
-        public P times(M m) { return m.times(this); }
-        public Vec minus(P p) { return new Vec(x-p.x, y-p.y, z-p.z); }
-        public P plus(Vec v) { return new P(x+v.x, y+v.y, z+v.z); }
-        public boolean equals(Object o) { return o!=null && (o instanceof P) && ((P)o).x==x && ((P)o).y==y && ((P)o).z==z; }
-        public void glVertex(GL gl) { _glVertex(gl); }
-        private void _glVertex(GL gl) { gl.glVertex3f(x, y, z); }
-        public String toString() { return "("+x+","+y+","+z+")"; }
-        public int hashCode() { return Float.floatToIntBits(x) ^ Float.floatToIntBits(y) ^ Float.floatToIntBits(z); }
-    }
-
-    /** vector in 3-space; immutable */
-    public static final class Vec {
-        public final float x, y, z;
-        public Vec(double x, double y, double z) { this((float)x, (float)y, (float)z); }
-        public Vec(float x, float y, float z) { this.x = x; this.y = y; this.z = z; }
-        public Vec(P p1, P p2) { this(p2.x-p1.x, p2.y-p1.y, p2.z-p1.z); }
-        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); }
-        public Vec plus(Vec v) { return new Vec(x+v.x, y+v.y, z+v.z); }
-        public Vec norm() { return mag()==0 ? this : div(mag()); }
-        public Vec times(M m) { return m.apply(this); }
-        public float mag() { return (float)Math.sqrt(x*x+y*y+z*z); }
-        public float dot(Vec v) { return x*v.x + y*v.y + z*v.z; }
-        public Vec times(float mag) { return new Vec(x*mag, y*mag, z*mag); }
-        public Vec div(float mag) { return new Vec(x/mag, y/mag, z/mag); }
-        public String toString() { return "<"+x+","+y+","+z+">"; }
-    }
-
-    /** affine matrix */
-    public static class M {
-        //
-        //  [ a b c d ]   [ x ]
-        //  [ e f g h ]   [ y ]
-        //  [ i j k l ]   [ z ]
-        //  [ 0 0 0 1 ]   [ 1 ]
-        //
-        public final float a, b, c, d, e, f, g, h, i, j, k, l;
-        public M() { this(1); }
-        public M(float scale) {
-            a = f = k = scale;
-            l = h = d = e = b = i = c = j = g = 0;            
-        }
-        public M(float scalex, float scaley, float scalez) {
-            a = scalex;
-            f = scaley;
-            k = scalez;
-            l = h = d = e = b = i = c = j = g = 0;            
-        }
-        public M(Vec translate) {
-            d = translate.x; h = translate.y; l = translate.z;
-            a = f = k = 1;
-            b = c = e = g = i = j = 0;
-        }
-        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) {
-            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;
-            this.j = j; this.k = k; this.l = l;
-        }
-        public M times(float x) {
-            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);
-        }
-        public M(Vec axis, float angle) {
-            double q = Math.cos(angle);
-            double s = Math.sin(angle);
-            double t = 1.0 - q;
-            a = (float)(q + axis.x*axis.x*t);
-            f = (float)(q + axis.y*axis.y*t);
-            k = (float)(q + axis.z*axis.z*t);
-            double tmp1 = axis.x*axis.y*t;
-            double tmp2 = axis.z*s;
-            e = (float)(tmp1 + tmp2);
-            b = (float)(tmp1 - tmp2);
-            tmp1 = axis.x*axis.z*t;
-            tmp2 = axis.y*s;
-            i = (float)(tmp1 - tmp2);
-            c = (float)(tmp1 + tmp2);
-            tmp1 = axis.y*axis.z*t;
-            tmp2 = axis.x*s;
-            j = (float)(tmp1 + tmp2);
-            g = (float)(tmp1 - tmp2);
-            d = h = l = 0;
-        }
-        public P times(P p) {
-            return new P(a*p.x + b*p.y + c*p.z + d,
-                        e*p.x + f*p.y + g*p.z + h,
-                        i*p.x + j*p.y + k*p.z + l);
-        }
-        public P apply(P p) { return p; }
-        public Vec apply(Vec v) { return v; }
-        public M invert() { return this; }
-        public M times(M m) { return this; }
-    }
-
-}