X-Git-Url: http://git.megacz.com/?p=anneal.git;a=blobdiff_plain;f=src%2Fedu%2Fberkeley%2Fqfat%2FMesh.java;h=1484b662d59c2edd55abeae34e667798370a9adc;hp=993f5e1945989a3ba6274898a89f3996413e01a8;hb=a4491ca8f8b67e8693a44424c2300af10a404f17;hpb=4b736bc17c9596c4cc1e7f80b750e1f58af60f2d

diff --git a/src/edu/berkeley/qfat/Mesh.java b/src/edu/berkeley/qfat/Mesh.java
index 993f5e1..1484b66 100644
--- a/src/edu/berkeley/qfat/Mesh.java
+++ b/src/edu/berkeley/qfat/Mesh.java
@@ -8,59 +8,37 @@ import javax.media.opengl.glu.*;
 import edu.berkeley.qfat.geom.*;
 import edu.wlu.cs.levy.CG.KDTree;
 import edu.berkeley.qfat.geom.Point;
+import com.infomatiq.jsi.IntProcedure;
 
 public class Mesh implements Iterable<Mesh.T> {
 
-    public static float EPSILON = (float)0.0001;
-    public static Random random = new Random();
-
-    private PointSet<Vert> pointset = new PointSet<Vert>();
-    public Vert nearest(Point p) { return pointset.nearest(p); }
-    private HashMap<Point,Vert> verts = new HashMap<Point,Vert>();
-
-    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 static final float EPSILON = (float)0.0001;
+    public static final Random random = new Random();
 
-    public Iterator<T> iterator() {
-        for(Vert v : verts.values())
-            if (v.e != null && v.e.t != null)
-                return new FaceIterator(v);
-        return new FaceIterator();
-    }
+    private RTree<T>         triangles = new RTree<T>();
+    private PointSet<Vertex> vertices  = new PointSet<Vertex>();
+
+    public boolean immutableVertices;
+    public Mesh    error_against      = null;
+    public double  error              = 0;
 
-    public Point origin() { return new Point(0, 0, 0); }
+    public Mesh(boolean immutableVertices) { this.immutableVertices = immutableVertices; }
 
-    public Mesh score_against = null;
-    public double score = 0;
-    public float score() { return (float)score; }
+    public void makeVerticesImmutable() { this.immutableVertices = true; }
+    public float error() { return (float)error; }
 
-    public int numedges = 0;
-    public float avgedge = 0;
+    public int size() { return vertices.size(); }
+    public Iterable<Vertex> vertices() { return vertices; }
+    public Iterator<T> iterator() { return triangles.iterator(); }
 
-    public void unbind() {
+    public void rebindPoints() {
+        // unbind all points
         for(Mesh.T t : this) {
             t.v1().unbind();
             t.v2().unbind();
             t.v3().unbind();
         }
-    }
-
-    public void bind() {
+        // ask edges to re-implement their bindings
         for(Mesh.T t : this) {
             t.e1().dobind();
             t.e2().dobind();
@@ -68,72 +46,18 @@ public class Mesh implements Iterable<Mesh.T> {
         }
     }
 
-    public float rescore() {
-        int num = 0;
-        double dist = 0;
-        HashSet<Vert> done = new HashSet<Vert>();
-        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 : this)
-            for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() })
-                p.kdremove();
-        pointset.clear();
-        for(T t : this)
-            for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() })
-                p.kdinsert();
-        */
-        return (float)(dist/num);
-    }
-
     public void transform(Matrix m) {
-        ArrayList<Vert> set = new ArrayList<Vert>();
-        set.addAll(verts.values());
-        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 : verts.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);
+        ArrayList<Vertex> set = new ArrayList<Vertex>();
+        for(Vertex v : vertices) set.add(v);
+        for(Vertex v : set) v.transform(m.times(v.p), true);
     }
 
-    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 : verts.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 void rebuild() { /*vertices.rebuild();*/ }
+    public Vec diagonal() { return vertices.diagonal(); }
+    public Point centroid() { return vertices.centroid(); }
+    public Vertex nearest(Point p) { return vertices.nearest(p); }
 
+    /** compute the volume of the mesh */
     public float volume() {
         double total = 0;
         for(T t : this) {
@@ -147,342 +71,271 @@ public class Mesh implements Iterable<Mesh.T> {
     }
 
 
-    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);
-            }
-        }
-    }
+    // Vertexices //////////////////////////////////////////////////////////////////////////////
+
+    /** a vertex in the mesh */
+    public final class Vertex extends HasQuadric implements Visitor {
+        public Point p, oldp;
+        E e;                // some edge *leaving* this point
+
+        Matrix binding = Matrix.ONE;
+        Vertex bound_to = this;
+        private boolean illegal = false;
 
-    public Vert register(Point p) { Vert v = verts.get(p); return v==null ? new Vert(p) : v; }
-    public final class Vert extends HasPoint {
-        public Point p;
         public Point getPoint() { return p; }
-        private Vert(Point p) {
+        public float error() { return olderror; }
+
+        private Vertex(Point p) {
             this.p = p;
-            if (verts.get(p) != null) throw new Error();
-            verts.put(this.p, this);
-            pointset.add(this);
+            if (vertices.get(p) != null) throw new Error();
+            vertices.add(this);
         }
+
         public void reinsert() {
-            pointset.remove(this);
-            pointset.add(this);
-        }
-        public void kdremove() {
-            if (!inserted) return;
-            inserted = false;
-            pointset.remove(this);
-        }
-        public void kdinsert() {
-            if (inserted) return;
-            inserted = true;
-            pointset.add(this);
-        }
-
-        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;
+            vertices.remove(this);
+            vertices.add(this);
+            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.t.reinsert();
+        }
+
+        public float olderror = 0;
+        public void setError(float nerror) {
+            error -= olderror;
+            olderror = nerror;
+            error += olderror;
+        }
+
+        public Matrix _recomputeFundamentalQuadric() {
+            Matrix m = Matrix.ZERO;
+            int count = 0;
+            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
+                m = m.plus(e.t.norm().fundamentalQuadric(e.t.centroid()));
+                count++;
             }
-            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 void rescore() {
-            if (score_against == null) return;
-
-            score -= oldscore;
-            oldscore = 0;
-
-            if (watch != null) unscore();
-            Vert po = this;
-            if (watch == null) {
-                watch = score_against.nearest(po.p);
-
-                // don't attract to vertices that face the other way
-                if (watch.e == null || 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++;
-                }
+            return m.times(1/(float)count);
+        }
+
+        public HasQuadric nearest() { return error_against==null ? null : error_against.vertices.nearest(p, this); }
+        public void computeError() {
+            float nerror =
+                quadric_count != 0
+                ? (quadric.preAndPostMultiply(p) * 100) / quadric_count
+                : nearest_in_other_mesh != null
+                ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p) * 100 * 10
+                : error_against != null
+                ? nearest().fundamentalQuadric().preAndPostMultiply(p) * 100 * 10
+                : 0;
+            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
+                double ang = Math.abs(e.crossAngle());
+                if (ang > Math.PI) throw new Error();
+                float minangle = (float)(Math.PI * 0.8);
+                if (ang > minangle) nerror += (ang - minangle);
             }
-
-            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;
+            setError(nerror);
         }
 
         /** does NOT update bound pairs! */
-        public boolean transform(Matrix m) {
-            // FIXME: screws up kdtree 
-            // FIXME: screws up hashmap
-            unscore();
-            try {
-                if (verts.get(this.p)==null) throw new Error();
-                verts.remove(this.p);
-                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?
-                pointset.add(this);
-                verts.put(this.p,(Vert)this);
-            } catch (Exception e) {
-                throw new RuntimeException(e);
+        private boolean transform(Point newp, boolean ignoreProblems) {
+            this.oldp = this.p;
+            if (immutableVertices) throw new Error();
+
+            unApplyQuadricToNeighbor();
+            this.p = newp;
+            reinsert();
+            applyQuadricToNeighbor();
+
+            if (!ignoreProblems) {
+                illegal = false;
+                checkLegality();
             }
-            rescore();
-            boolean good = true;
-            /*
-            for(T t : this) {
-                for(E e = this.e; ;) {
-                    if (e.intersects(t)) { good = false; break; }
-                    e = e.pair.next;
-                    if (e == this.e) break;
-                }
+            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.p2.quadricStale = true;
+            return !illegal;
+        } 
+
+        public void checkLegality() {
+            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
+                if (Math.abs(e.crossAngle()) > (Math.PI * 0.9) || Math.abs(e.next.crossAngle()) > (Math.PI * 0.9)) illegal = true;
+                if (e.t.aspect() < 0.1) illegal = true;
             }
-            */
-            /*
-                if (t==this.t) continue;
-                if (this.intersects(t)) good = false;
+            if (illegal) triangles.range(oldp, this.p, (Visitor<T>)this);
+        }
+
+        public void reComputeErrorAround() {
+            reComputeError();
+            if (nearest_in_other_mesh != null)
+                nearest_in_other_mesh.reComputeError();
+            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
+                e.p2.reComputeError();
+        }
+
+        public boolean visit(Object o) {
+            if (o instanceof Vertex)
+                return ((Vertex)o).e != null && ((Vertex)o).norm().dot(Vertex.this.norm()) >= 0;
+            T t = (T)o;
+            if (illegal) return false;
+            for(E e = Vertex.this.e; e!=null; e=e.pair.next==Vertex.this.e?null:e.pair.next) {
+                if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { illegal = true; }
+                if (e.t != null) {
+                    if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { illegal = true; }
+                    if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { illegal = true; }
+                    if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { illegal = true; }
+                }
             }
-            */
-            return good;
+            return !illegal;
         }
-        public boolean move(Vec v) {
-            Matrix m = new Matrix(v);
-            Vert p = this;
+
+        public boolean move(Matrix m, boolean ignoreProblems) {
             boolean good = true;
-            do {
-                good &= p.transform(m);
-                v = v.times(binding); // bleh wrong
-                p = p.bound_to;
-            } while (p != this);
+            for(Vertex p = this; p != null; p = (p.bound_to==this)?null:p.bound_to)
+                good &= p.transform(m.times(p.p), ignoreProblems);
+            for(Vertex p = this; p != null; p = (p.bound_to==this)?null:p.bound_to)
+                if (good || ignoreProblems)  p.reComputeErrorAround();
+                else                         p.transform(p.oldp, true);
             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;
-            ret = getFreeIncident(e.pair.next, e.pair.next);
-            if (ret == null) throw new Error("unable to find free incident to " + this);
-            return ret;
+            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
+                System.out.println(e + " " + e.t);
+            throw new Error("unable to find free incident to " + this);
         }
 
         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);
+            for(E e = start; e!=null; e=e.pair.next==before?null:e.pair.next)
+                if (e.pair.p2 == this && e.pair.t == null && e.pair.next.t == null)
+                    return e.pair;
             return null;
         }
 
-        public E getE(Vert p2) {
-            E e = this.e;
-            do {
-                if (e==null) return null;
+        public E getE(Point p2) {
+            Vertex v = vertices.get(p2);
+            if (v==null) return null;
+            return getE(v);
+        }
+        public E getE(Vertex p2) {
+            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
                 if (e.p1 == this && e.p2 == p2) return e;
-                e = e.pair.next;
-            } while (e!=this.e);
             return null;
         }
 
-        public boolean isBoundTo(Vert p) {
-            Vert px = p;
-            do {
-                if (px==this) return true;
-                px = px.bound_to;
-            } while(px != p);
+        private void glNormal(GL gl) {
+            Vec norm = norm();
+            gl.glNormal3f(norm.x, norm.y, norm.z);
+        }
+        public Vec norm() {
+            Vec norm = new Vec(0, 0, 0);
+            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
+                if (e.t != null)
+                    norm = norm.plus(e.t.norm().times((float)e.prev.angle()));
+            return norm.norm();
+        }
+
+        public boolean isBoundTo(Vertex p) {
+            for(Vertex px = p; px!=null; px=(px.bound_to==p?null:px.bound_to))
+                if (px==this)
+                    return true;
             return false;
         }
 
-        public void unbind() { bound_to = this; binding = new Matrix(); }
-        public void bind(Vert p) { bind(p, new Matrix()); }
-        public void bind(Vert p, Matrix binding) {
+        public void unbind() { bound_to = this; binding = Matrix.ONE; }
+        public void bind(Vertex p) { bind(p, Matrix.ONE); }
+        public void bind(Vertex p, Matrix binding) {
             if (isBoundTo(p)) return;
-            Vert temp_bound_to = p.bound_to;
+            Vertex temp_bound_to = p.bound_to;
             Matrix 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();
-        }
-
-        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 class BindingGroup {
+        private HashSet<E> set = new HashSet<E>();
+        public BindingGroup bind_others;
+        public BindingGroup other() { return bind_others; }
+        public BindingGroup(BindingGroup bind_others) { this.bind_others = bind_others; }
+        public BindingGroup() { this.bind_others = new BindingGroup(this); }
+        public BindingGroup(E e) { this(); set.add(e); }
+        public void add(E e) {
+            if (set.contains(e)) return;
+            set.add(e);
+            BindingGroup e_bind_peers = e.bind_peers;
+            BindingGroup e_bind_to    = e.bind_to;
+            e.bind_peers = this;
+            e.bind_to    = bind_others;
+            for (E epeer  : e_bind_peers.set) add(epeer);
+            for (E eother : e_bind_to.set)    bind_others.add(eother);
+
+            for(E eother : bind_others.set) {
+                if (e.next.bind_to.set.contains(eother.prev)) {
+                    e.next.next.bindEdge(eother.prev.prev);
+                }
+                if (e.prev.bind_to.set.contains(eother.next)) {
+                    e.prev.prev.bindEdge(eother.next.next);
+                }
+            }
 
-        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 int compareTo(E e) {
-            return e.length() > length() ? 1 : -1;
+        public void dobind(E e) {
+            for(E ebound : set) {
+                e.p1.bind(ebound.p2);
+                e.p2.bind(ebound.p1);
+            }
+        }
+        public void shatter(BindingGroup bg1, BindingGroup bg2) {
+            for(E e : set) {
+                e.shatter(e.midpoint(), bg1, bg2);
+            }
         }
+    }
+
+    /** [UNIQUE] an edge */
+    public final class E implements Comparable<E> {
 
-        public final Vert p1, p2;
+        public final Vertex 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 bind_peers  = new BindingGroup(this);
+        public BindingGroup bind_to     = bind_peers.other();
+        boolean shattered = false;
 
-
-        public BindingGroup bg = new BindingGroup(this);
-
-        public void bind(E e) { bind(e, new Matrix()); }
-        public void bind(E e, Matrix 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);
-            }
+        public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
+        public float comparator() {
+            Vertex nearest = error_against.nearest(midpoint());
+            return (float)Math.max(length(), midpoint().distance(nearest.p));
         }
+        public int compareTo(E e) {
+            return e.comparator() > comparator() ? 1 : -1;
+        }
+        public void bindEdge(E e) { bind_to.add(e); }
+        public void dobind() { bind_to.dobind(this); }
 
-        boolean shattered = false;
-        public Vert shatter() { return shatter(register(midpoint()), null, null); }
-        public Vert shatter(Vert mid, BindingGroup bg1, BindingGroup bg2) {
-            if (shattered) return mid;
+        public Point shatter() { return shatter(midpoint(), null, null); }
+        public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
+            if (shattered || destroyed) return mid;
             shattered = true;
 
-            Vert r = next.p2;
+            Vertex r = next.p2;
             E next = this.next;
             E prev = this.prev;
 
+            int old_colorclass = t==null ? 0 : t.colorclass;
             if (bg1==null) bg1 = new BindingGroup();
             if (bg2==null) bg2 = new BindingGroup();
-            for(E e : bg.es) e.shatter(register(e.midpoint()), bg1, bg2);
+            BindingGroup old_bind_to = bind_to;
+            bind_peers.shatter(bg1, bg2);
+            old_bind_to.shatter(bg2.other(), bg1.other());
             pair.shatter();
             destroy();
 
-            newT(r, p1, mid, null);
-            newT(r, mid, p2, null);
+            newT(r.p, p1.p, mid, null, old_colorclass);
+            newT(r.p, mid, p2.p, null, old_colorclass);
             bg1.add(p1.getE(mid));
-            bg2.add(mid.getE(p2));
+            bg2.add(p2.getE(mid).pair);
             return mid;
         }
 
@@ -491,42 +344,54 @@ public class Mesh implements Iterable<Mesh.T> {
             if (destroyed) return;
             destroyed = true;
             pair.destroyed = true;
+
+            if (t != null) t.destroy();
+            t = null;
+
+            if (pair.t != null) pair.t.destroy();
+            pair.t = null;
+
             if (next.t != null) next.t.destroy();
             if (prev.t != null) prev.t.destroy();
             next.t = null;
             prev.t = null;
+
+            if (pair.next.t != null) pair.next.t.destroy();
+            if (pair.prev.t != null) pair.next.t.destroy();
             pair.next.t = null;
             pair.prev.t = null;
-            this.bg = null;
-            pair.bg = null;
+
+            this.bind_to = null;
+            pair.bind_to = null;
+            this.bind_peers = null;
+            pair.bind_peers = 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;
-            avgedge -= this.length();
-            avgedge -= pair.length();
-            numedges--;
-            numedges--;
         }
 
         private void sync() {
             this.prev.next = this;
             this.next.prev = this;
             this.pair.pair = this;
+            bind_peers.add(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;
-            if (!added) {
-                added = true;
-                numedges++;
-                avgedge += length();
-            }
+            if (!added) added = true;
         }
         private boolean added = false;
 
-        public T makeT() { return t==null ? (t = new T(this)) : t; }
+        public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
+
+        public double crossAngle() {
+            Vec v1 = t.norm().times(-1);
+            Vec v2 = pair.t.norm().times(-1);
+            return Math.acos(v1.norm().dot(v2.norm()));
+        }
 
         /** angle between this half-edge and the next */
         public double angle() {
@@ -556,16 +421,22 @@ 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 (vertices.get(p1) != null) throw new Error();
+            if (vertices.get(p2) != null) throw new Error();
+            this.p1 = new Vertex(p1);
+            this.p2 = new Vertex(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) {
+            Vertex p2;
+            p2 = vertices.get(p);
+            if (p2 == null) p2 = new Vertex(p);
             this.p1 = prev.p2;
             this.p2 = p2;
             this.prev = prev;
@@ -580,6 +451,7 @@ 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();
         }
 
@@ -593,64 +465,54 @@ public class Mesh implements Iterable<Mesh.T> {
             sync();
         }
         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); }
-        public boolean has(Vert v) { return v==p1 || v==p2; }
+        public boolean has(Vertex v) { return v==p1 || v==p2; }
         public float length() { return p1.p.minus(p2.p).mag(); }
         public String toString() { return p1+"->"+p2; }
+
     }
 
-    public T newT(Vert p1, Vert p2, Vert p3, Vec norm) {
+    public E makeE(Point p1, Point p2) {
+        Vertex v1 = vertices.get(p1);
+        Vertex v2 = vertices.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, int colorclass) {
         if (norm != null) {
-            Vec norm2 = p3.p.minus(p1.p).cross(p2.p.minus(p1.p));
+            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) { Vert p = p1; p1=p2; p2 = p; }
+            if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
         }
-        E e12 = p1.makeE(p2);
-        E e23 = p2.makeE(p3);
-        E e31 = p3.makeE(p1);
+        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();
+        T ret = e12.makeT(colorclass);
         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 extends Triangle {
         public final E e1;
         public final int color;
+        public final int colorclass;
 
-        public void destroy() {
-        }
-
-        T(E e1) {
+        T(E e1, int colorclass) {
             this.e1 = e1;
             E e2 = e1.next;
             E e3 = e2.next;
@@ -672,22 +534,32 @@ public class Mesh implements Iterable<Mesh.T> {
                 break;
             }
             this.color = color;
-
-            v1().kdinsert();
-            v2().kdinsert();
-            v3().kdinsert();
+            this.colorclass = colorclass;
+            triangles.add(this);
         }
         public E e1() { return e1; }
         public E e2() { return e1.next; }
         public E e3() { return e1.prev; }
-        public Vert v1() { return e1.p1; }
-        public Vert v2() { return e1.p2; }
-        public Vert v3() { return e1.next.p2; }
+        public Vertex v1() { return e1.p1; }
+        public Vertex v2() { return e1.p2; }
+        public Vertex 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 v1()==v || v2()==v || v3()==v; }
-    }
+        public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
+
+        public void removeFromRTree() { triangles.remove(this); }
+        public void addToRTree() { triangles.insert(this); }
+        public void destroy() { triangles.remove(this); }
+        public void reinsert() { triangles.remove(this); triangles.add(this); }
 
+        public boolean shouldBeDrawn() {
+            if (e1().bind_to.set.size() == 0) return false;
+            if (e2().bind_to.set.size() == 0) return false;
+            if (e3().bind_to.set.size() == 0) return false;
+            return true;
+        }
+
+    }
 }