X-Git-Url: http://git.megacz.com/?p=anneal.git;a=blobdiff_plain;f=src%2Fedu%2Fberkeley%2Fqfat%2FMesh.java;h=747599c59e3ff26c47a82543d461665574ba3909;hp=993f5e1945989a3ba6274898a89f3996413e01a8;hb=2f48eabf8a07e99905e1eae0b64b5a2abecb01fe;hpb=4b736bc17c9596c4cc1e7f80b750e1f58af60f2d

diff --git a/src/edu/berkeley/qfat/Mesh.java b/src/edu/berkeley/qfat/Mesh.java
index 993f5e1..747599c 100644
--- a/src/edu/berkeley/qfat/Mesh.java
+++ b/src/edu/berkeley/qfat/Mesh.java
@@ -11,12 +11,12 @@ import edu.berkeley.qfat.geom.Point;
 
 public class Mesh implements Iterable<Mesh.T> {
 
-    public static float EPSILON = (float)0.0001;
-    public static Random random = new Random();
+    public static final float EPSILON = (float)0.0001;
+    public static final 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<Vert> vertices() { return pointset; }
 
     public Iterable<E> edges() {
         return
@@ -37,14 +37,12 @@ public class Mesh implements Iterable<Mesh.T> {
     }
 
     public Iterator<T> iterator() {
-        for(Vert v : verts.values())
+        for(Vert v : pointset)
             if (v.e != null && v.e.t != null)
                 return new FaceIterator(v);
         return new FaceIterator();
     }
 
-    public Point origin() { return new Point(0, 0, 0); }
-
     public Mesh score_against = null;
     public double score = 0;
     public float score() { return (float)score; }
@@ -52,15 +50,14 @@ public class Mesh implements Iterable<Mesh.T> {
     public int numedges = 0;
     public float avgedge = 0;
 
-    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 +65,45 @@ public class Mesh implements Iterable<Mesh.T> {
         }
     }
 
-    public float rescore() {
-        int num = 0;
-        double dist = 0;
+    public void unApplyQuadricToNeighborAll() {
         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();
+                p.unApplyQuadricToNeighbor();
             }
-        /*
+    }
+    public void recomputeAllFundamentalQuadrics() {
+        HashSet<Vert> done = new HashSet<Vert>();
         for(T t : this)
-            for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() })
-                p.kdremove();
-        pointset.clear();
+            for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() }) {
+                if (done.contains(p)) continue;
+                done.add(p);
+                p.recomputeFundamentalQuadric();
+            }
+    }
+    public float applyQuadricToNeighborAll() {
+        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() })
-                p.kdinsert();
-        */
+            for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() }) {
+                if (done.contains(p)) continue;
+                done.add(p);
+                p.applyQuadricToNeighbor();
+                
+            }
         return (float)(dist/num);
     }
 
     public void transform(Matrix m) {
         ArrayList<Vert> set = new ArrayList<Vert>();
-        set.addAll(verts.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 : 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);
-    }
-
-    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 float volume() {
         double total = 0;
         for(T t : this) {
@@ -146,156 +116,153 @@ public class Mesh implements Iterable<Mesh.T> {
         return (float)total;
     }
 
+    public void rebuildPointSet() { pointset.rebuild(); }
+    public Vec diagonal() { return pointset.diagonal(); }
+    public Point centroid() { return pointset.centroid(); }
+    public Vert nearest(Point p) { return pointset.nearest(p); }
 
-    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 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;
+        E e;                // some edge *leaving* this point
+
+        /** the nearest vertex in the "score_against" mesh */
+        Vert   nearest_in_other_mesh;
+        /** the number of vertices in the other mesh for which this is the nearest_in_other_mesh */
+        int    quadric_count;
+        /** the total error quadric (contributions from all vertices in other mesh for which this is nearest) */
+        Matrix quadric = Matrix.ZERO;
+
+        Vert bound_to = this;
+        Matrix binding = new Matrix();
+        float oldscore = 0;
+        boolean quadricStale = false;
+
+        public Matrix errorQuadric() { return quadric; }
         public Point getPoint() { return p; }
+        public float score() { return oldscore; }
+
+        private Matrix fundamentalQuadric = null;
+        public Matrix fundamentalQuadric() {
+            if (fundamentalQuadric == null) recomputeFundamentalQuadric();
+            return fundamentalQuadric;
+        }
+
         private Vert(Point p) {
             this.p = p;
-            if (verts.get(p) != null) throw new Error();
-            verts.put(this.p, this);
+            if (pointset.get(p) != null) throw new Error();
             pointset.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 void recomputeFundamentalQuadric() {
+            if (!quadricStale && fundamentalQuadric != null) return;
+            quadricStale = false;
+            unApplyQuadricToNeighbor();
+            Matrix m = Matrix.ZERO;
+            E e = this.e;
+            do {
+                T t = e.t;
+                m = m.plus(t.norm().fundamentalQuadric(t.centroid()));
+                e = e.pair.next;
+            } while(e != this.e);
+            fundamentalQuadric = m;
+            applyQuadricToNeighbor();
         }
 
-        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 void unApplyQuadricToNeighbor() {
+            if (nearest_in_other_mesh == null) return;
+            if (fundamentalQuadric == null) return;
+            nearest_in_other_mesh.unComputeError();
+            nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.minus(fundamentalQuadric);
+            nearest_in_other_mesh.quadric_count--;
+            if (nearest_in_other_mesh.quadric_count==0)
+                nearest_in_other_mesh.quadric = Matrix.ZERO;
+            nearest_in_other_mesh.computeError();
+            nearest_in_other_mesh = 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() {
+
+        public void applyQuadricToNeighbor() {
             if (score_against == null) return;
 
-            score -= oldscore;
-            oldscore = 0;
+            Vert new_nearest = score_against.nearest(p);
+            if (nearest_in_other_mesh != null && new_nearest == nearest_in_other_mesh) return;
 
-            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++;
-                }
+            if (nearest_in_other_mesh != null) unApplyQuadricToNeighbor();
+            if (nearest_in_other_mesh != null) throw new Error();
+
+            nearest_in_other_mesh = new_nearest;
+                
+            // don't attract to vertices that face the other way
+            if (nearest_in_other_mesh.e == null || nearest_in_other_mesh.norm().dot(norm()) < 0) {
+                nearest_in_other_mesh = null;
+            } else {
+                nearest_in_other_mesh.unComputeError();
+                nearest_in_other_mesh.quadric = nearest_in_other_mesh.quadric.plus(fundamentalQuadric());
+                nearest_in_other_mesh.quadric_count++;
+                nearest_in_other_mesh.computeError();
             }
+            reComputeError();
+        }
 
-            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);
+        public void reComputeError() {
+            unComputeError();
+            computeError();
+        }
+        public void unComputeError() {
+            score -= oldscore;
+            oldscore = 0;
+        }
+        public void computeError() {
+            oldscore = quadric_count == 0 ? 0 : (quadric.preAndPostMultiply(p) / quadric_count);
             score += oldscore;
         }
 
         /** does NOT update bound pairs! */
         public boolean transform(Matrix m) {
-            // FIXME: screws up kdtree 
-            // FIXME: screws up hashmap
-            unscore();
+            unApplyQuadricToNeighbor();
             try {
-                if (verts.get(this.p)==null) throw new Error();
-                verts.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?
                 pointset.add(this);
-                verts.put(this.p,(Vert)this);
             } catch (Exception e) {
                 throw new RuntimeException(e);
             }
-            rescore();
+            applyQuadricToNeighbor();
+
+            // should recompute fundamental quadrics of all vertices sharing a face, but we defer...
+            E e = this.e;
+            do {
+                e.p2.quadricStale = true;
+                e = e.pair.next;
+            } while(e != this.e);
+
+            // FIXME: intersection test needed?
             boolean good = true;
-            /*
-            for(T t : this) {
-                for(E e = this.e; ;) {
-                    if (e.intersects(t)) { good = false; break; }
+            for(T t : Mesh.this) {
+                if (!good) break;
+                e = this.e;
+                do {
+                    if (!t.has(e.p1) && !t.has(e.p2) && e.t != null && e.intersects(t)) { good = false; break; }
                     e = e.pair.next;
-                    if (e == this.e) break;
-                }
+                } while(e != this.e);
             }
-            */
-            /*
-                if (t==this.t) continue;
-                if (this.intersects(t)) good = false;
-            }
-            */
             return good;
         }
+
         public boolean move(Vec v) {
             Matrix m = new Matrix(v);
             Vert 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(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;
@@ -313,6 +280,11 @@ 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 {
@@ -323,6 +295,16 @@ public class Mesh implements Iterable<Mesh.T> {
             return null;
         }
 
+        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();
+        }
+
         public boolean isBoundTo(Vert p) {
             Vert px = p;
             do {
@@ -331,7 +313,6 @@ public class Mesh implements Iterable<Mesh.T> {
             } while(px != p);
             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) {
@@ -343,129 +324,64 @@ public class Mesh implements Iterable<Mesh.T> {
             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 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;
+    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;
+            for (E epeer : e.bind_peers.set) {
+                epeer.bind_peers = this;
+                epeer.bind_to    = bind_others;
+                set.add(epeer);
+            }
+            for (E eother : e.bind_to.set) {
+                bind_others.add(eother);
+            }
 
-            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;
+            for(E eother : bind_others.set) {
+                if (e.next.bind_to.set.contains(eother.prev)) {
+                    e.next.next.bindEdge(eother.prev.prev);
+                }
+            }
 
-            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;
         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 int compareTo(E e) { return e.length() > length() ? 1 : -1; }
+        public void bindEdge(E e) { bind_to.add(e); }
+        public void dobind() { bind_to.dobind(this); }
 
-        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);
-            }
-        }
-
-        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;
 
@@ -475,14 +391,15 @@ 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);
+            bind_peers.shatter(bg1, bg2);
+            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);
+            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;
         }
 
@@ -497,8 +414,12 @@ public class Mesh implements Iterable<Mesh.T> {
             prev.t = null;
             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;
@@ -515,6 +436,7 @@ public class Mesh implements Iterable<Mesh.T> {
             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;
@@ -556,16 +478,22 @@ 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;
@@ -580,6 +508,7 @@ 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();
         }
 
@@ -596,18 +525,101 @@ 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 T newT(Vert p1, Vert p2, Vert p3, Vec norm) {
+    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.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);
@@ -672,10 +684,6 @@ public class Mesh implements Iterable<Mesh.T> {
                 break;
             }
             this.color = color;
-
-            v1().kdinsert();
-            v2().kdinsert();
-            v3().kdinsert();
         }
         public E e1() { return e1; }
         public E e2() { return e1.next; }