X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;ds=sidebyside;f=src%2Fedu%2Fberkeley%2Fqfat%2FMesh.java;h=3b39842b7d85fcd779470652d6977f832a6fa28f;hb=316044467afed9ea9df7fb373a0ab1ed2f7a901b;hp=1a1b9a30924c6047afa2cf8b34e11ad9d02f4b90;hpb=161d356850a765c2f6b83b42275095b777d7b2aa;p=anneal.git

diff --git a/src/edu/berkeley/qfat/Mesh.java b/src/edu/berkeley/qfat/Mesh.java
index 1a1b9a3..3b39842 100644
--- a/src/edu/berkeley/qfat/Mesh.java
+++ b/src/edu/berkeley/qfat/Mesh.java
@@ -11,32 +11,53 @@ import edu.berkeley.qfat.geom.Point;
 
 public class Mesh implements Iterable<Mesh.T> {
 
-    private KDTree kd = new KDTree(3);
-
     public static float EPSILON = (float)0.0001;
     public static Random random = new Random();
 
-    private HashMap<Point,Vert>  ps = new HashMap<Point,Vert>();
-    public  HashSet<E>    es = new HashSet<E>();
-    public  ArrayList<T>  ts = new ArrayList<T>();
-
-    public Iterator<T> iterator() { return ts.iterator(); }
+    private PointSet<Vert> pointset = new PointSet<Vert>();
+
+    public Iterable<Vert> vertices() { return pointset; }
+
+    public Iterable<E> edges() {
+        return
+            new Iterable<E>() {
+            public Iterator<E> iterator() {
+                // HACK
+                HashSet<E> hse = new HashSet<E>();
+                for(T t : Mesh.this) {
+                    hse.add(t.e1());
+                    hse.add(t.e2());
+                    hse.add(t.e3());
+                    hse.add(t.e1().pair);
+                    hse.add(t.e2().pair);
+                    hse.add(t.e3().pair);
+                }
+                return hse.iterator();
+            } };
+    }
 
-    public Point origin() { return new Point(0, 0, 0); }
+    public Iterator<T> iterator() {
+        for(Vert v : pointset)
+            if (v.e != null && v.e.t != null)
+                return new FaceIterator(v);
+        return new FaceIterator();
+    }
 
     public Mesh score_against = null;
     public double score = 0;
     public float score() { return (float)score; }
 
-    public void unbind() {
+    public int numedges = 0;
+    public float avgedge = 0;
 
+    public void unbind() {
         for(Mesh.T t : this) {
-            t.p1().unbind();
-            t.p2().unbind();
-            t.p3().unbind();
+            t.v1().unbind();
+            t.v2().unbind();
+            t.v3().unbind();
         }
-
     }
+
     public void bind() {
         for(Mesh.T t : this) {
             t.e1().dobind();
@@ -44,84 +65,30 @@ public class Mesh implements Iterable<Mesh.T> {
             t.e3().dobind();
         }
     }
-    public int numedges = 0;
-    public float avgedge = 0;
 
     public float rescore() {
         int num = 0;
         double dist = 0;
         HashSet<Vert> done = new HashSet<Vert>();
-        for(T t : ts)
-            for(Vert p : new Vert[] { t.p1(), t.p2(), t.p3() }) {
+        for(T t : this)
+            for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() }) {
                 if (done.contains(p)) continue;
                 done.add(p);
                 p.rescore();
             }
-        for(T t : ts)
-            for(Vert p : new Vert[] { t.p1(), t.p2(), t.p3() })
-                p.kdremove();
-        kd = new KDTree(3);
-        for(T t : ts)
-            for(Vert p : new Vert[] { t.p1(), t.p2(), t.p3() })
-                p.kdinsert();
         return (float)(dist/num);
     }
 
     public void transform(Matrix m) {
         ArrayList<Vert> set = new ArrayList<Vert>();
-        set.addAll(ps.values());
+        for (Vert v : pointset)
+            set.add(v);
         for(Vert 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(Point 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 Point 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(Point 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 Point((float)(max_x + min_x)/2,
-                     (float)(max_y + min_y)/2,
-                     (float)(max_z + min_z)/2);
-    }
-
-    public T newT(Vert p12, Vert p23, Vert 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) < EPointSILON) throw new Error("dot products within epsilon of each other: "+norm+" "+norm2);
-        if (dot < 0) { Vert p = p12; p12=p23; p23 = p; }
-        return newT(p12, p23, p31);
-    }
-
     public float volume() {
         double total = 0;
-        for(T t : ts) {
+        for(T t : this) {
             double area = t.area();
             Vec origin_to_centroid = new Vec(new Point(0, 0, 0), t.centroid());
             boolean facingAway = t.norm().dot(origin_to_centroid) > 0;
@@ -131,27 +98,6 @@ public class Mesh implements Iterable<Mesh.T> {
         return (float)total;
     }
 
-    public Vert nearest(Point p) {
-        Object[] results;
-        try { results = kd.nearest(new double[]{p.x,p.y,p.z},1); } catch (Exception e) { throw new Error(e); }
-        return (Vert)results[0];
-    }
-
-    public T newT(Vert p1, Vert p2, Vert 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>();
@@ -172,25 +118,32 @@ public class Mesh implements Iterable<Mesh.T> {
         }
     }
 
-    public Vert register(Point p) { Vert v = ps.get(p); return v==null ? new Vert(p) : v; }
-    public final class Vert {
+    public Vec diagonal() { return pointset.diagonal(); }
+    public Point centroid() { return pointset.centroid(); }
+    public Vert nearest(Point p) { return pointset.nearest(p); }
+
+    public final class Vert extends HasPoint {
         public Point p;
+        E e;                // some edge *leaving* this point
+
+        Vert bound_to = this;
+        int watch_count;
+        float watch_x;
+        float watch_y;
+        float watch_z;
+        Vert watch;
+        Matrix binding = new Matrix();
+        float oldscore = 0;
+        boolean inserted = false;
+
+        public Point getPoint() { return p; }
         private Vert(Point p) {
             this.p = p;
-            if (ps.get(p) != null) throw new Error();
-            ps.put(this.p, this);
+            //this.e = e;
+            //if (e==null) throw new Error();
+            if (pointset.get(p) != null) throw new Error();
+            pointset.add(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;
@@ -206,8 +159,8 @@ public class Mesh implements Iterable<Mesh.T> {
             watch = null;
         }
         public Vert partner() { return watch==null ? this : watch; }
-        public Vert watchback() { return watch_count==0 ? partner() :
-                register(new Point(watch_x/watch_count, watch_y/watch_count, watch_z/watch_count)); }
+        public Point watchback() { return watch_count==0 ? partner().p :
+                new Point(watch_x/watch_count, watch_y/watch_count, watch_z/watch_count); }
         public void rescore() {
             if (score_against == null) return;
 
@@ -220,7 +173,7 @@ public class Mesh implements Iterable<Mesh.T> {
                 watch = score_against.nearest(po.p);
 
                 // don't attract to vertices that face the other way
-                if (watch.norm().dot(norm()) < 0) {
+                if (watch.e == null || watch.norm().dot(norm()) < 0) {
                     watch = null;
                 } else {
                     watch.watch_x += po.p.x;
@@ -238,28 +191,27 @@ public class Mesh implements Iterable<Mesh.T> {
             score += oldscore;
         }
 
-
         /** does NOT update bound pairs! */
         public boolean transform(Matrix m) {
             // FIXME: screws up kdtree 
             // FIXME: screws up hashmap
             unscore();
             try {
-                if (ps.get(this.p)==null) throw new Error();
-                ps.remove(this.p);
+                if (pointset.get(this.p)==null) throw new Error();
+                pointset.remove(this);
                 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 Point(newx, newy, newz);
                 // FIXME: what if we move onto exactly where another point is?
-                ps.put(this.p,(Vert)this);
+                pointset.add(this);
             } catch (Exception e) {
                 throw new RuntimeException(e);
             }
             rescore();
             boolean good = true;
             /*
-            for(T t : ts) {
+            for(T t : this) {
                 for(E e = this.e; ;) {
                     if (e.intersects(t)) { good = false; break; }
                     e = e.pair.next;
@@ -286,15 +238,6 @@ public class Mesh implements Iterable<Mesh.T> {
             return good;
         }
 
-        public E makeE(Vert 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;
@@ -312,6 +255,11 @@ public class Mesh implements Iterable<Mesh.T> {
             return null;
         }
 
+        public E getE(Point p2) {
+            Vert v = pointset.get(p2);
+            if (v==null) return null;
+            return getE(v);
+        }
         public E getE(Vert p2) {
             E e = this.e;
             do {
@@ -351,105 +299,20 @@ public class Mesh implements Iterable<Mesh.T> {
             } while(e != this.e);
             return norm.norm();
         }
-
-        Vert bound_to = this;
-        int watch_count;
-        float watch_x;
-        float watch_y;
-        float watch_z;
-        Vert watch;
-        E e;                // some edge *leaving* this point
-        Matrix binding = new Matrix();
-        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 Vert 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 int compareTo(E e) { return e.length() > length() ? 1 : -1; }
+
         public void bind(E e) { bind(e, new Matrix()); }
         public void bind(E e, Matrix m) { e.bg.add(this); }
 
@@ -463,8 +326,8 @@ public class Mesh implements Iterable<Mesh.T> {
         }
 
         boolean shattered = false;
-        public Vert shatter() { return shatter(register(midpoint()), null, null); }
-        public Vert shatter(Vert mid, BindingGroup bg1, BindingGroup bg2) {
+        public Point shatter() { return shatter(midpoint(), null, null); }
+        public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
             if (shattered) return mid;
             shattered = true;
 
@@ -474,14 +337,14 @@ public class Mesh implements Iterable<Mesh.T> {
 
             if (bg1==null) bg1 = new BindingGroup();
             if (bg2==null) bg2 = new BindingGroup();
-            for(E e : bg.es) e.shatter(register(e.midpoint()), bg1, bg2);
+            for(E e : bg.es) e.shatter(e.midpoint(), bg1, bg2);
             pair.shatter();
             destroy();
 
-            newT(r, p1, mid);
-            newT(r, mid, p2);
+            newT(r.p, p1.p, mid, null);
+            newT(r.p, mid, p2.p, null);
             bg1.add(p1.getE(mid));
-            bg2.add(mid.getE(p2));
+            bg2.add(p2.getE(mid).pair);
             return mid;
         }
 
@@ -492,8 +355,6 @@ public class Mesh implements Iterable<Mesh.T> {
             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;
@@ -506,8 +367,6 @@ public class Mesh implements Iterable<Mesh.T> {
             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--;
@@ -521,7 +380,6 @@ public class Mesh implements Iterable<Mesh.T> {
             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++;
@@ -560,16 +418,22 @@ public class Mesh implements Iterable<Mesh.T> {
         }
 
         /** creates an isolated edge out in the middle of space */
-        public E(Vert p1, Vert p2) {
-            if (p1==p2) throw new Error("attempt to create edge with single vertex: " + p1);
-            this.p1 = p1;
-            this.p2 = p2;
+        public E(Point p1, Point p2) {
+            if (pointset.get(p1) != null) throw new Error();
+            if (pointset.get(p2) != null) throw new Error();
+            this.p1 = new Vert(p1);
+            this.p2 = new Vert(p2);
             this.prev = this.next = this.pair = new E(this, this, this);
+            this.p1.e = this;
+            this.p2.e = this.pair;
             sync();
         }
 
         /** adds a new half-edge from prev.p2 to p2 */
-        public E(E prev, Vert p2) {
+        public E(E prev, Point p) {
+            Vert p2;
+            p2 = pointset.get(p);
+            if (p2 == null) p2 = new Vert(p);
             this.p1 = prev.p2;
             this.p2 = p2;
             this.prev = prev;
@@ -584,6 +448,7 @@ public class Mesh implements Iterable<Mesh.T> {
                 this.prev.next = this;
                 this.pair = new E(q, this, z);
             }
+            if (p2.e==null) p2.e = this.pair;
             sync();
         }
 
@@ -600,34 +465,150 @@ public class Mesh implements Iterable<Mesh.T> {
         public boolean has(Vert v) { return v==p1 || v==p2; }
         public float length() { return p1.p.minus(p2.p).mag(); }
         public String toString() { return p1+"->"+p2; }
+
+        public boolean intersects(T t) {
+            double A0=t.v1().p.x, A1=t.v1().p.y, A2=t.v1().p.z;
+            double B0=t.v2().p.x, B1=t.v2().p.y, B2=t.v2().p.z;
+            double C0=t.v3().p.x, C1=t.v3().p.y, C2=t.v3().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 E makeE(Point p1, Point p2) {
+        Vert v1 = pointset.get(p1);
+        Vert v2 = pointset.get(p2);
+        if (v1 != null && v2 != null) {
+            E e = v1.getE(v2);
+            if (e != null) return e;
+            e = v2.getE(v1);
+            if (e != null) return e;
+        }
+        if (v1 != null) return new E(v1.getFreeIncident(), p2);
+        if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
+        return new E(p1, p2);
+    }
+    public T newT(Point p1, Point p2, Point p3, Vec norm) {
+        if (norm != null) {
+            Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
+            float dot = norm.dot(norm2);
+            //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
+            if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
+        }
+        E e12 = makeE(p1, p2);
+        E e23 = makeE(p2, p3);
+        E e31 = makeE(p3, 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 FaceIterator implements Iterator<T> {
+        private HashSet<T> visited = new HashSet<T>();
+        private LinkedList<T> next = new LinkedList<T>();
+        public FaceIterator() { }
+        public FaceIterator(Vert v) { next.addFirst(v.e.t); }
+        public boolean hasNext() { return next.peek()!=null; }
+        public void remove() { throw new Error(); }
+        public T next() {
+            T ret = next.removeFirst();
+            if (ret == null) return null;
+            visited.add(ret);
+            T t1 = ret.e1().pair.t;
+            T t2 = ret.e2().pair.t;
+            T t3 = ret.e3().pair.t;
+            if (t1 != null && !visited.contains(t1)) next.addFirst(t1);
+            if (t2 != null && !visited.contains(t2)) next.addFirst(t2);
+            if (t3 != null && !visited.contains(t3)) next.addFirst(t3);
+            return ret;
+        }
     }
 
     /** [UNIQUE] a triangle (face) */
-    public final class T {
+    public final class T extends Triangle {
         public final E e1;
         public final int color;
 
         public void destroy() {
-            ts.remove(this);
-        }
-
-        public Vert nearest(Point 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 (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");
+            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;
@@ -642,45 +623,19 @@ public class Mesh implements Iterable<Mesh.T> {
                 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 Vert p1() { return e1.p1; }
-        public Vert p2() { return e1.p2; }
-        public Vert 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 Vert v1() { return e1.p1; }
+        public Vert v2() { return e1.p2; }
+        public Vert v3() { return e1.next.p2; }
+        public Point p1() { return e1.p1.p; }
+        public Point p2() { return e1.p2.p; }
+        public Point p3() { return e1.next.p2.p; }
         public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
-        public boolean has(Vert 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 Point centroid() { return new Point((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 boolean has(Vert v) { return v1()==v || v2()==v || v3()==v; }
     }
-    
 
 }