X-Git-Url: http://git.megacz.com/?p=anneal.git;a=blobdiff_plain;f=src%2Fedu%2Fberkeley%2Fqfat%2FMesh.java;h=ff48f424e3c324493150646b4ebcfafb1349adef;hp=f9c9b945551a3f292b503ee0bc78d209e937e338;hb=827bd30d02ef944697b7abc044c2782ab87f41ef;hpb=725965a06dc9a59f88b36e387f07ec3600b9364b

diff --git a/src/edu/berkeley/qfat/Mesh.java b/src/edu/berkeley/qfat/Mesh.java
index f9c9b94..ff48f42 100644
--- a/src/edu/berkeley/qfat/Mesh.java
+++ b/src/edu/berkeley/qfat/Mesh.java
@@ -14,41 +14,21 @@ public class Mesh implements Iterable<Mesh.T> {
     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 boolean tilemesh = false;
+    public boolean ignorecollision = false;
     public Mesh score_against = null;
     public double score = 0;
     public float score() { return (float)score; }
 
-    public int numedges = 0;
-    public float avgedge = 0;
+    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
@@ -99,7 +79,7 @@ public class Mesh implements Iterable<Mesh.T> {
 
     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);
     }
@@ -116,12 +96,13 @@ 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 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
 
@@ -133,7 +114,7 @@ public class Mesh implements Iterable<Mesh.T> {
         Matrix quadric = Matrix.ZERO;
 
         Vert bound_to = this;
-        Matrix binding = new Matrix();
+        Matrix binding = Matrix.ONE;
         float oldscore = 0;
         boolean quadricStale = false;
 
@@ -149,22 +130,29 @@ public class Mesh implements Iterable<Mesh.T> {
 
         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);
+        }
+
+        private void glNormal(GL gl) {
+            Vec norm = norm();
+            gl.glNormal3f(norm.x, norm.y, norm.z);
         }
 
         public void recomputeFundamentalQuadric() {
-            if (!quadricStale && fundamentalQuadric != null) return;
+            //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;
+            fundamentalQuadric = m.times(1/(float)count);
             applyQuadricToNeighbor();
         }
 
@@ -203,6 +191,15 @@ public class Mesh implements Iterable<Mesh.T> {
             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();
@@ -212,40 +209,150 @@ public class Mesh implements Iterable<Mesh.T> {
             oldscore = 0;
         }
         public void computeError() {
-            oldscore = quadric_count == 0 ? 0 : (quadric.preAndPostMultiply(p) / quadric_count);
+            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 {
+                    oldscore = nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p) * 100 * 10;
+                }
+            } else {
+                oldscore = (quadric.preAndPostMultiply(p) * 100) / quadric_count;
+            }
+
+            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) {
             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);
-                pointset.add(this);
+                addTrianglesToRTree();
+                vertices.add(this);
             } catch (Exception e) {
                 throw new RuntimeException(e);
             }
             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);
 
 
-            // FIXME: intersection test needed?
-            return true;
+            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);
+                }
+                */
+            }
+
+
+            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 {
@@ -259,7 +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;
         }
 
@@ -273,7 +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);
         }
@@ -305,8 +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;
@@ -323,23 +437,24 @@ public class Mesh implements Iterable<Mesh.T> {
         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() { 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;
-                set.add(epeer);
-            }
-            for (E eother : e.bind_to.set) {
-                eother.bind_to = bind_others;
-                bind_others.add(eother);
-            }
-
-            for(E ex : (!swap ? right : left)) {
-                if (e.prev.isBoundTo(ex.prev)) {
-                    System.out.println("hit!");
+            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);
                 }
             }
 
@@ -352,7 +467,7 @@ public class Mesh implements Iterable<Mesh.T> {
         }
         public void shatter(BindingGroup bg1, BindingGroup bg2) {
             for(E e : set) {
-                e.shatter(e.midpoint(), bg1, bg2, false);
+                e.shatter(e.midpoint(), bg1, bg2);
             }
         }
     }
@@ -365,32 +480,54 @@ public class Mesh implements Iterable<Mesh.T> {
         E prev;  // previous half-edge
         E next;  // next half-edge
         E pair;  // partner half-edge
-        public BindingGroup bind_peers  = new BindingGroup();
+        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 boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
+        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); }
 
-        public Point shatter() { return shatter(midpoint(), null, null, false); }
-        public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2, boolean swap) {
-            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;
             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();
+            BindingGroup old_bind_to = bind_to;
             bind_peers.shatter(bg1, bg2);
-            bind_to.shatter(bg2.other(), bg1.other());
+            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;
@@ -401,12 +538,23 @@ 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.bind_to = null;
             pair.bind_to = null;
             this.bind_peers = null;
@@ -417,10 +565,6 @@ public class Mesh implements Iterable<Mesh.T> {
             pair.next = prev;
             if (p1.e == this) p1.e = prev.next;
             if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
-            avgedge -= this.length();
-            avgedge -= pair.length();
-            numedges--;
-            numedges--;
         }
 
         private void sync() {
@@ -431,15 +575,17 @@ public class Mesh implements Iterable<Mesh.T> {
             if (this.next.p1 != p2) throw new Error();
             if (this.prev.p2 != p1) throw new Error();
             if (this.p1.e == null) this.p1.e = this;
-            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() {
@@ -470,8 +616,8 @@ 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();
+            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);
@@ -483,7 +629,7 @@ public class Mesh implements Iterable<Mesh.T> {
         /** adds a new half-edge from prev.p2 to p2 */
         public E(E prev, Point p) {
             Vert p2;
-            p2 = pointset.get(p);
+            p2 = vertices.get(p);
             if (p2 == null) p2 = new Vert(p);
             this.p1 = prev.p2;
             this.p2 = p2;
@@ -517,80 +663,11 @@ public class Mesh implements Iterable<Mesh.T> {
         public float length() { return p1.p.minus(p2.p).mag(); }
         public String toString() { return p1+"->"+p2; }
 
-        public boolean intersects(T t) {
-            double A0=t.v1().p.x, A1=t.v1().p.y, A2=t.v1().p.z;
-            double B0=t.v2().p.x, B1=t.v2().p.y, B2=t.v2().p.z;
-            double C0=t.v3().p.x, C1=t.v3().p.y, C2=t.v3().p.z;
-            double j0=p1.p.x, j1=p1.p.y, j2=p1.p.z;
-            double k0=p2.p.x, k1=p2.p.y, k2=p2.p.z;
-            double J0, J1, J2;
-            double K0, K1, K2;
-            double i0, i1, i2;
-            double a0, a1, a2;
-            double b0, b1, b2;
-            double c0, c1, c2;
-            double in_det;
-            double R00, R01, R02, R03,
-                R10, R11, R12, R13,
-                R20, R21, R22, R23,
-                R30, R31, R32, R33;
-
-
-            /* a = B - A */
-            a0 = B0 - A0; 
-            a1 = B1 - A1; 
-            a2 = B2 - A2;
-            /* b = C - B */
-            b0 = C0 - A0;
-            b1 = C1 - A1;
-            b2 = C2 - A2;
-            /* c = a &times; b */
-            c0 = a1 * b2 - a2 * b1;
-            c1 = a2 * b0 - a0 * b2;
-            c2 = a0 * b1 - a1 * b0;
- 
-            /* M^(-1) = (1/det(M)) * adj(M) */
-            in_det = 1 / (c0 * c0 + c1 * c1 + c2 * c2);
-            R00 = (b1 * c2 - b2 * c1) * in_det;
-            R01 = (b2 * c0 - b0 * c2) * in_det;
-            R02 = (b0 * c1 - b1 * c0) * in_det;
-            R10 = (c1 * a2 - c2 * a1) * in_det;
-            R11 = (c2 * a0 - c0 * a2) * in_det;
-            R12 = (c0 * a1 - c1 * a0) * in_det;
-            R20 = (c0) * in_det;
-            R21 = (c1) * in_det;
-            R22 = (c2) * in_det;
-  
-            /* O = M^(-1) * A */
-            R03 = -(R00 * A0 + R01 * A1 + R02 * A2);
-            R13 = -(R10 * A0 + R11 * A1 + R12 * A2);
-            R23 = -(R20 * A0 + R21 * A1 + R22 * A2);
- 
-            /* fill in last row of 4x4 matrix */
-            R30 = R31 = R32 = 0;
-            R33 = 1;
-  
-            J2 = R20 * j0 + R21 * j1 + R22 * j2 + R23;
-            K2 = R20 * k0 + R21 * k1 + R22 * k2 + R23;
-            if (J2 * K2 >= 0) return false;
-
-            J0 = R00 * j0 + R01 * j1 + R02 * j2 + R03;
-            K0 = R00 * k0 + R01 * k1 + R02 * k2 + R03;
-            i0 = J0 + J2 * ((K0 - J0) / (J2 - K2));
-            if (i0 < 0 || i0 > 1) return false;
-  
-            J1 = R10 * j0 + R11 * j1 + R12 * j2 + R13;
-            K1 = R10 * k0 + R11 * k1 + R12 * k2 + R13;
-            i1 = J1 + J2 * ((K1 - J1) / (J2 - K2));
-            if (i1 < 0 || i1 > 1 || i0 + i1 > 1) return false;
-
-            return true;            
-        }
     }
 
     public E makeE(Point p1, Point p2) {
-        Vert v1 = pointset.get(p1);
-        Vert v2 = pointset.get(p2);
+        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;
@@ -601,7 +678,7 @@ 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);
@@ -616,7 +693,7 @@ 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();
@@ -624,36 +701,18 @@ public class Mesh implements Iterable<Mesh.T> {
     }
 
 
-    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() {
-        }
+        public void removeFromRTree() { tris.remove(this); }
+        public void addToRTree() { tris.insert(this); }
+
+        public void destroy() { tris.remove(this); }
 
-        T(E e1) {
+        T(E e1, int colorclass) {
             this.e1 = e1;
             E e2 = e1.next;
             E e3 = e2.next;
@@ -675,6 +734,8 @@ 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; }
@@ -687,6 +748,13 @@ 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 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;
+        }
+
+    }
 }