X-Git-Url: http://git.megacz.com/?p=anneal.git;a=blobdiff_plain;f=src%2Fedu%2Fberkeley%2Fqfat%2FMesh.java;h=fb994880da734591fb6fefa0ec560273087f4e1b;hp=b0518165e5c6b2143a39417ec8d27b41783bad98;hb=6fe08d5c50c341f47ded8ce9acd670aad9362614;hpb=9a4c0a63db24cfe1787dbe798c2456271775fa88

diff --git a/src/edu/berkeley/qfat/Mesh.java b/src/edu/berkeley/qfat/Mesh.java
index b051816..fb99488 100644
--- a/src/edu/berkeley/qfat/Mesh.java
+++ b/src/edu/berkeley/qfat/Mesh.java
@@ -14,47 +14,22 @@ 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 int size() { return pointset.size(); }
-    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();
-            } };
-    }
+    private RTree<T>         triangles = new RTree<T>();
+    private PointSet<Vertex> vertices  = new PointSet<Vertex>();
 
-    public Iterator<T> iterator() {
-        /*
-        for(Vert v : pointset)
-            if (v.e != null && v.e.t != null)
-                return new FaceIterator(v);
-        return new FaceIterator();
-        */
-        return ts.iterator();
-    }
+    public boolean immutableVertices;
+    public boolean ignorecollision    = false;
+    public Mesh    score_against      = null;
+    public double  score              = 0;
 
-    public HashSet<T> ts = new HashSet<T>();
-    public RTree<T> tris = new RTree<T>();
+    public Mesh(boolean immutableVertices) { this.immutableVertices = immutableVertices; }
 
-    public Mesh score_against = null;
-    public double score = 0;
+    public void makeVerticesImmutable() { this.immutableVertices = true; }
     public float score() { return (float)score; }
 
-    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 rebindPoints() {
         // unbind all points
@@ -71,45 +46,18 @@ public class Mesh implements Iterable<Mesh.T> {
         }
     }
 
-    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>();
-        for(T t : this)
-            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>();
-        for (Vert v : pointset)
-            set.add(v);
-        for(Vert v : set) v.transform(m);
+        ArrayList<Vertex> set = new ArrayList<Vertex>();
+        for(Vertex v : vertices) set.add(v);
+        for(Vertex v : set) v.transform(m);
     }
 
+    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) {
@@ -122,25 +70,24 @@ 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 final class Vert extends HasPoint {
+    // Vertexices //////////////////////////////////////////////////////////////////////////////
+
+    /** a vertex in the mesh */
+    public final class Vertex extends HasPoint implements Visitor<T> {
         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;
+        Vertex   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;
+        Vertex bound_to = this;
         float oldscore = 0;
         boolean quadricStale = false;
 
@@ -154,10 +101,10 @@ public class Mesh implements Iterable<Mesh.T> {
             return fundamentalQuadric;
         }
 
-        private Vert(Point p) {
+        private Vertex(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) {
@@ -166,19 +113,18 @@ public class Mesh implements Iterable<Mesh.T> {
         }
 
         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);
+            if (quadricStale || fundamentalQuadric==null) {
+                Matrix m = Matrix.ZERO;
+                int count = 0;
+                for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
+                    T t = e.t;
+                    m = m.plus(t.norm().fundamentalQuadric(t.centroid()));
+                    count++;
+                }
+                quadricStale = false;
+                fundamentalQuadric = m.times(1/(float)count);
+            }
             applyQuadricToNeighbor();
         }
 
@@ -197,7 +143,7 @@ public class Mesh implements Iterable<Mesh.T> {
         public void applyQuadricToNeighbor() {
             if (score_against == null) return;
 
-            Vert new_nearest = score_against.nearest(p);
+            Vertex new_nearest = score_against.nearest(p);
             if (nearest_in_other_mesh != null && new_nearest == nearest_in_other_mesh) return;
 
             if (nearest_in_other_mesh != null) unApplyQuadricToNeighbor();
@@ -220,11 +166,8 @@ public class Mesh implements Iterable<Mesh.T> {
         public void reComputeErrorAround() {
             reComputeError();
             if (nearest_in_other_mesh != null) nearest_in_other_mesh.reComputeError();
-            E e = this.e;
-            do {
+            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
                 e.p2.reComputeError();
-                e = e.pair.next;
-            } while (e != this.e);
         }
         public void reComputeError() {
             unComputeError();
@@ -235,151 +178,84 @@ public class Mesh implements Iterable<Mesh.T> {
             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 {
-                    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());
+            oldscore =
+                quadric_count != 0
+                ? (quadric.preAndPostMultiply(p) * 100) / quadric_count
+                : immutableVertices
+                ? oldscore
+                : nearest_in_other_mesh != null
+                ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p) * 100 * 10
+                : score_against != null
+                ? score_against.nearest(p).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();
-                /*
-                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 {
+            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
                 if (e.t != null) e.t.removeFromRTree();
-                e = e.pair.next;
-            } while(e != this.e);
         }
         private void addTrianglesToRTree() {
-            E e = this.e;
-            do {
+            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
                 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) {
+            if (immutableVertices) throw new Error();
+
             unApplyQuadricToNeighbor();
             Point oldp = this.p;
-            try {
-                if (pointset.get(this.p)==null) throw new Error();
-                pointset.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);
-                addTrianglesToRTree();
-                pointset.add(this);
-            } catch (Exception e) {
-                throw new RuntimeException(e);
-            }
+
+            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);
+            addTrianglesToRTree();
+            vertices.add(this);
+
             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;
-                }
-                */
+            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)) 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 (!ignorecollision && good) triangles.range(oldp, this.p, (Visitor<T>)this);
 
             reComputeErrorAround();
             return good;
         }
+
+        public void visit(T t) {
+            if (!good) return;
+            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)) { 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; }
+                }
+            }
+        }
         private boolean good;
 
         public boolean move(Vec v) {
             Matrix m = Matrix.translate(v);
-            Vert p = this;
+            Vertex p = this;
             boolean good = true;
             do {
                 good &= p.transform(m);
@@ -391,65 +267,49 @@ public class Mesh implements Iterable<Mesh.T> {
         public E getFreeIncident() {
             E ret = getFreeIncident(e, e);
             if (ret != null) return ret;
-            ret = getFreeIncident(e.pair.next, e.pair.next);
-            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;
+            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(Point p2) {
-            Vert v = pointset.get(p2);
+            Vertex v = vertices.get(p2);
             if (v==null) return null;
             return getE(v);
         }
-        public E getE(Vert p2) {
-            E e = this.e;
-            do {
-                if (e==null) return null;
+        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 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);
+            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(Vert p) {
-            Vert px = p;
-            do {
-                if (px==this) return true;
-                px = px.bound_to;
-            } while(px != p);
+        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 = Matrix.ONE; }
-        public void bind(Vert p) { bind(p, Matrix.ONE); }
-        public void bind(Vert p, Matrix binding) {
+        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
@@ -501,7 +361,7 @@ public class Mesh implements Iterable<Mesh.T> {
     /** [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
@@ -510,22 +370,10 @@ public class Mesh implements Iterable<Mesh.T> {
         public BindingGroup bind_to     = bind_peers.other();
         boolean shattered = false;
 
+        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();
-            */
+            Vertex nearest = score_against.nearest(midpoint());
             return (float)Math.max(length(), midpoint().distance(nearest.p));
-            //return length();
         }
         public int compareTo(E e) {
             return e.comparator() > comparator() ? 1 : -1;
@@ -538,7 +386,7 @@ public class Mesh implements Iterable<Mesh.T> {
             if (shattered || destroyed) return mid;
             shattered = true;
 
-            Vert r = next.p2;
+            Vertex r = next.p2;
             E next = this.next;
             E prev = this.prev;
 
@@ -590,10 +438,6 @@ 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() {
@@ -604,11 +448,7 @@ 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;
 
@@ -649,10 +489,10 @@ 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.p2 = new Vert(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;
@@ -661,9 +501,9 @@ 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);
-            if (p2 == null) p2 = new Vert(p);
+            Vertex p2;
+            p2 = vertices.get(p);
+            if (p2 == null) p2 = new Vertex(p);
             this.p1 = prev.p2;
             this.p2 = p2;
             this.prev = prev;
@@ -692,84 +532,15 @@ 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 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);
+        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;
@@ -803,40 +574,16 @@ 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 removeFromRTree() { tris.remove(this); }
-        public void addToRTree() { tris.insert(this); }
+        public void removeFromRTree() { triangles.remove(this); }
+        public void addToRTree() { triangles.insert(this); }
 
-        public void destroy() {
-            tris.remove(this);
-            ts.remove(this);
-        }
+        public void destroy() { triangles.remove(this); }
 
         T(E e1, int colorclass) {
             this.e1 = e1;
@@ -861,33 +608,26 @@ public class Mesh implements Iterable<Mesh.T> {
             }
             this.color = color;
             this.colorclass = colorclass;
-            ts.add(this);
-            tris.add(this);
+            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 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 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;
         }
+
     }
-    public boolean tilemesh = false;
-    public boolean ignorecollision = false;
 }