X-Git-Url: http://git.megacz.com/?p=anneal.git;a=blobdiff_plain;f=src%2Fedu%2Fberkeley%2Fqfat%2FMesh.java;h=c50e34ccd2e9629cea45660a136c4122bd680946;hp=d1fda3c232d4e2273eb20bfd40406fa32228e41d;hb=f42953f58e189d611803dcb4661bb840d785c30a;hpb=be39f0f6c815c0e92b157fa18c568f0a034fd583

diff --git a/src/edu/berkeley/qfat/Mesh.java b/src/edu/berkeley/qfat/Mesh.java
index d1fda3c..c50e34c 100644
--- a/src/edu/berkeley/qfat/Mesh.java
+++ b/src/edu/berkeley/qfat/Mesh.java
@@ -11,54 +11,33 @@ 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 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 Iterator<T> iterator() {
-        for(Vert v : pointset)
-            if (v.e != null && v.e.t != null)
-                return new FaceIterator(v);
-        return new FaceIterator();
-    }
+    private RTree<T> tris = new RTree<T>();
+    private PointSet<Vert> vertices = new PointSet<Vert>();
 
     public Mesh score_against = null;
     public double score = 0;
     public float score() { return (float)score; }
-
     public int numedges = 0;
     public float avgedge = 0;
 
-    public void unbind() {
+    public int size() { return vertices.size(); }
+    public Iterable<Vert> vertices() { return vertices; }
+
+    public Iterator<T> iterator() {
+        return tris.iterator();
+    }
+
+    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();
@@ -66,7 +45,25 @@ public class Mesh implements Iterable<Mesh.T> {
         }
     }
 
-    public float rescore() {
+    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.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() }) {
+                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>();
@@ -74,14 +71,15 @@ public class Mesh implements Iterable<Mesh.T> {
             for(Vert p : new Vert[] { t.v1(), t.v2(), t.v3() }) {
                 if (done.contains(p)) continue;
                 done.add(p);
-                p.rescore();
+                p.applyQuadricToNeighbor();
+                
             }
         return (float)(dist/num);
     }
 
     public void transform(Matrix m) {
         ArrayList<Vert> set = new ArrayList<Vert>();
-        for (Vert v : pointset)
+        for (Vert v : vertices)
             set.add(v);
         for(Vert v : set) v.transform(m);
     }
@@ -98,128 +96,267 @@ public class Mesh implements Iterable<Mesh.T> {
         return (float)total;
     }
 
-
-    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 Vec diagonal() { return pointset.diagonal(); }
-    public Point centroid() { return pointset.centroid(); }
-    public Vert nearest(Point p) { return pointset.nearest(p); }
+    public void rebuild() { /*vertices.rebuild();*/ }
+    public Vec diagonal() { return vertices.diagonal(); }
+    public Point centroid() { return vertices.centroid(); }
+    public Vert nearest(Point p) { return vertices.nearest(p); }
 
     public final class Vert extends HasPoint {
+        public String toString() { return p.toString(); }
         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 = Matrix.ONE;
+        float oldscore = 0;
+        boolean quadricStale = false;
+
+        public Matrix errorQuadric() { return quadric; }
         public Point getPoint() { return p; }
-        private Vert(Point p, E e) { this(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 (pointset.get(p) != null) throw new Error();
-            pointset.add(this);
+            if (vertices.get(p) != null) throw new Error();
+            vertices.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;
-            }
-            watch = null;
+
+        private void glNormal(GL gl) {
+            Vec norm = norm();
+            gl.glNormal3f(norm.x, norm.y, norm.z);
+        }
+
+        public void recomputeFundamentalQuadric() {
+            //if (!quadricStale && fundamentalQuadric != null) return;
+            quadricStale = false;
+            unApplyQuadricToNeighbor();
+            Matrix m = Matrix.ZERO;
+            E e = this.e;
+            int count = 0;
+            do {
+                T t = e.t;
+                m = m.plus(t.norm().fundamentalQuadric(t.centroid()));
+                count++;
+                e = e.pair.next;
+            } while(e != this.e);
+            fundamentalQuadric = m.times(1/(float)count);
+            applyQuadricToNeighbor();
         }
-        public Vert partner() { return watch==null ? this : watch; }
-        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() {
+
+        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 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);
+            if (nearest_in_other_mesh != null) unApplyQuadricToNeighbor();
+            if (nearest_in_other_mesh != null) throw new Error();
 
-                // don't attract to vertices that face the other way
-                if (watch.e == null || watch.norm().dot(norm()) < 0) {
-                    watch = null;
+            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();
+        }
+
+        public void reComputeErrorAround() {
+            reComputeError();
+            if (nearest_in_other_mesh != null) nearest_in_other_mesh.reComputeError();
+            E e = this.e;
+            do {
+                e.p2.reComputeError();
+                e = e.pair.next;
+            } while (e != this.e);
+        }
+        public void reComputeError() {
+            unComputeError();
+            computeError();
+        }
+        public void unComputeError() {
+            score -= oldscore;
+            oldscore = 0;
+        }
+        public void computeError() {
+            if (quadric_count == 0) {
+                if (!tilemesh) {
+                }
+                else if (nearest_in_other_mesh == null) {
+                    if (score_against != null) {
+                        Vert ne = score_against.nearest(p);
+                        oldscore = ne.fundamentalQuadric().preAndPostMultiply(p) * 100 * 10;
+                    } else {
+                        oldscore = 0;
+                    }
                 } else {
-                    watch.watch_x += po.p.x;
-                    watch.watch_y += po.p.y;
-                    watch.watch_z += po.p.z;
-                    watch.watch_count++;
+                    oldscore = nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p) * 100 * 10;
                 }
+            } else {
+                oldscore = (quadric.preAndPostMultiply(p) * 100) / quadric_count;
             }
 
-            double s1, s2;
-            if (watch_count==0) s1 = 0;
-            else                s1 = p.distance(watch_x/watch_count, watch_y/watch_count, watch_z/watch_count);
-            s2 = watch==null ? 0 : po.p.distance(watch.p);
-            oldscore = (float)(s1 + s2);
+            oldscore = oldscore;
+
+            int numaspects = 0;
+            float aspects = 0;
+            E e = this.e;
+            do {
+                //double ang = Math.abs(e.crossAngle());
+                double ang = Math.abs(e.crossAngle());
+                if (ang > Math.PI) throw new Error();
+                /*
+                if (e.t != null) {
+                    numaspects++;
+                    aspects += e.t.aspect()*e.t.aspect();
+                }
+                */
+
+                float minangle = (float)(Math.PI * 0.8);
+                if (ang > minangle)
+                    oldscore += (ang - minangle);
+
+                e = e.pair.next;
+            } while (e != this.e);
+            if (numaspects > 0) oldscore += (aspects / numaspects);
+
+            //System.out.println(oldscore);
+            //oldscore = oldscore*oldscore;
             score += oldscore;
         }
 
+        private void removeTrianglesFromRTree() {
+            E e = this.e;
+            do {
+                if (e.t != null) e.t.removeFromRTree();
+                e = e.pair.next;
+            } while(e != this.e);
+        }
+        private void addTrianglesToRTree() {
+            E e = this.e;
+            do {
+                if (e.t != null) e.t.addToRTree();
+                e = e.pair.next;
+            } while(e != this.e);
+        }
+
         /** does NOT update bound pairs! */
         public boolean transform(Matrix m) {
-            // FIXME: screws up kdtree 
-            // FIXME: screws up hashmap
-            unscore();
+            unApplyQuadricToNeighbor();
+            Point oldp = this.p;
             try {
-                if (pointset.get(this.p)==null) throw new Error();
-                pointset.remove(this);
+                if (vertices.get(this.p)==null) throw new Error();
+                vertices.remove(this);
+                removeTrianglesFromRTree();
                 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);
+                addTrianglesToRTree();
+                vertices.add(this);
             } catch (Exception e) {
                 throw new RuntimeException(e);
             }
-            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;
+            applyQuadricToNeighbor();
+
+            // FIXME: intersection test needed?
+            good = true;
+
+            // should recompute fundamental quadrics of all vertices sharing a face, but we defer...
+            E e = this.e;
+            do {
+                /*
+                if (Math.abs(e.crossAngle()) > (Math.PI * 0.9) ||
+                    Math.abs(e.next.crossAngle()) > (Math.PI * 0.9)) {
+                    good = false;
                 }
+                if (e.t.aspect() < 0.1) {
+                    good = false;
+                }
+                */
+                e.p2.quadricStale = true;
+                e = e.pair.next;
+            } while(e != this.e);
+
+
+            if (!ignorecollision && good) {
+
+                tris.range(new Segment(oldp, this.p),
+                            new Visitor<T>() {
+                                public void visit(T t) {
+                                    if (!good) return;
+                                    E e = Vert.this.e;
+                                    do {
+                                        if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { good = false; }
+                                        if (e.t != null) {
+                                            if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { good = false; }
+                                            if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { good = false; }
+                                            if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { good = false; }
+                                        }
+                                        e = e.pair.next;
+                                    } while(e != Vert.this.e);
+                                }
+                            });
+
+                /*
+                for(T t : Mesh.this) {
+                    if (!good) break;
+                    e = this.e;
+                    do {
+                        if (!t.has(e.p1) && !t.has(e.p2) && e.intersects(t)) { good = false; break; }
+                        if (e.t != null) {
+                            if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { good = false; break; }
+                            if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { good = false; break; }
+                            if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { good = false; break; }
+                        }
+                        e = e.pair.next;
+                    } while(e != this.e);
+                }
+                */
             }
-            */
-            /*
-                if (t==this.t) continue;
-                if (this.intersects(t)) good = false;
-            }
-            */
+
+
+            reComputeErrorAround();
             return good;
         }
+        private boolean good;
+
         public boolean move(Vec v) {
-            Matrix m = new Matrix(v);
+            Matrix m = Matrix.translate(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;
@@ -229,7 +366,14 @@ public class Mesh implements Iterable<Mesh.T> {
             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);
+            if (ret == null) {
+                E ex = e;
+                do {
+                    System.out.println(ex + " " + ex.t);
+                    ex = ex.pair.next;
+                } while (ex != e);
+                throw new Error("unable to find free incident to " + this);
+            }
             return ret;
         }
 
@@ -243,7 +387,7 @@ public class Mesh implements Iterable<Mesh.T> {
         }
 
         public E getE(Point p2) {
-            Vert v = pointset.get(p2);
+            Vert v = vertices.get(p2);
             if (v==null) return null;
             return getE(v);
         }
@@ -257,6 +401,16 @@ 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 {
@@ -265,9 +419,8 @@ 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 unbind() { bound_to = this; binding = Matrix.ONE; }
+        public void bind(Vert p) { bind(p, Matrix.ONE); }
         public void bind(Vert p, Matrix binding) {
             if (isBoundTo(p)) return;
             Vert temp_bound_to = p.bound_to;
@@ -277,26 +430,46 @@ 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;
+    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 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 */
@@ -307,40 +480,53 @@ public class Mesh implements Iterable<Mesh.T> {
         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); }
+        public BindingGroup bind_peers  = new BindingGroup(this);
+        public BindingGroup bind_to     = bind_peers.other();
+        boolean shattered = false;
 
-        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 float comparator() {
+            Vert nearest = score_against.nearest(midpoint());
+            //if (t==null) return length();
+            /*
+            double ang = Math.abs(crossAngle());
+            float minangle = (float)(Math.PI * 0.9);
+            if (ang > minangle)
+                return 300;
+            */
+            /*
+            if ((length() * length()) / t.area() > 10)
+                return (float)(length()*Math.sqrt(t.area()));
+            return length()*t.area();
+            */
+            return (float)Math.max(length(), midpoint().distance(nearest.p));
+            //return length();
+        }
+        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 Point shatter() { return shatter(midpoint(), null, null); }
         public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
-            if (shattered) return mid;
+            if (shattered || destroyed) return mid;
             shattered = true;
 
             Vert 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(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.p, p1.p, mid, null);
-            newT(r.p, mid, p2.p, 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(p2.getE(mid).pair);
             return mid;
@@ -351,14 +537,27 @@ 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;
@@ -375,6 +574,7 @@ 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;
@@ -386,7 +586,13 @@ public class Mesh implements Iterable<Mesh.T> {
         }
         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() {
@@ -417,19 +623,21 @@ public class Mesh implements Iterable<Mesh.T> {
 
         /** creates an isolated edge out in the middle of space */
         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);
-            this.p2 = new Vert(p2, this);
+            if (vertices.get(p1) != null) throw new Error();
+            if (vertices.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, Point p) {
             Vert p2;
-            p2 = pointset.get(p);
-            if (p2 == null) p2 = new Vert(p, this);
+            p2 = vertices.get(p);
+            if (p2 == null) p2 = new Vert(p);
             this.p1 = prev.p2;
             this.p2 = p2;
             this.prev = prev;
@@ -444,6 +652,7 @@ 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();
         }
 
@@ -532,13 +741,9 @@ public class Mesh implements Iterable<Mesh.T> {
         }
     }
 
-    private Vert register(Point p) {
-        Vert v = pointset.get(p);
-        return v==null ? new Vert(p) : v;
-    }
     public E makeE(Point p1, Point p2) {
-        Vert v1 = pointset.get(p1);
-        Vert v2 = pointset.get(p2);
+        Vert v1 = vertices.get(p1);
+        Vert v2 = vertices.get(p2);
         if (v1 != null && v2 != null) {
             E e = v1.getE(v2);
             if (e != null) return e;
@@ -549,7 +754,7 @@ public class Mesh implements Iterable<Mesh.T> {
         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) {
+    public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
         if (norm != null) {
             Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
             float dot = norm.dot(norm2);
@@ -564,7 +769,7 @@ public class Mesh implements Iterable<Mesh.T> {
             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();
@@ -597,11 +802,14 @@ public class Mesh implements Iterable<Mesh.T> {
     public final class T extends Triangle {
         public final E e1;
         public final int color;
+        public final int colorclass;
 
-        public void destroy() {
-        }
+        public void removeFromRTree() { tris.remove(this); }
+        public void addToRTree() { tris.insert(this); }
 
-        T(E e1) {
+        public void destroy() { tris.remove(this); }
+
+        T(E e1, int colorclass) {
             this.e1 = e1;
             E e2 = e1.next;
             E e3 = e2.next;
@@ -623,6 +831,8 @@ public class Mesh implements Iterable<Mesh.T> {
                 break;
             }
             this.color = color;
+            this.colorclass = colorclass;
+            tris.add(this);
         }
         public E e1() { return e1; }
         public E e2() { return e1.next; }
@@ -635,6 +845,21 @@ public class Mesh implements Iterable<Mesh.T> {
         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 void glVertices(GL gl) {
+
+            /*
+            if (e1().bind_to.set.size() == 0) return;
+            if (e2().bind_to.set.size() == 0) return;
+            if (e3().bind_to.set.size() == 0) return;
+            */
+
+            norm().glNormal(gl);
+            p1().glVertex(gl);
+            p2().glVertex(gl);
+            p3().glVertex(gl);
+        }
+    }
+    public boolean tilemesh = false;
+    public boolean ignorecollision = false;
 }