checkpoint
[anneal.git] / src / edu / berkeley / qfat / Mesh.java
index 1e83eee..5240413 100644 (file)
@@ -11,6 +11,8 @@ import edu.wlu.cs.levy.CG.KDTree;
 import edu.berkeley.qfat.geom.Point;
 import com.infomatiq.jsi.IntProcedure;
 
+// EDGES RUN COUNTER-CLOCKWISE
+
 public class Mesh implements Iterable<Mesh.T> {
 
     public static final float EPSILON = (float)0.0001;
@@ -19,6 +21,53 @@ public class Mesh implements Iterable<Mesh.T> {
     private RTree<T>         triangles = new RTree<T>();
     private PointSet<Vertex> vertices  = new PointSet<Vertex>();
 
+    public boolean option_wireframe    = false;
+    public boolean option_errorNormals = false;
+    public boolean option_selectable   = true;
+
+    public void render(GL gl, Matrix m) {
+        if (option_wireframe) {
+            gl.glDisable(GL.GL_LIGHTING);
+            gl.glBegin(GL.GL_LINES);
+            gl.glColor3f(1, 1, 1);
+            for (T t : this) {
+                m.times(t.e1().p1.goodp).glVertex(gl);
+                m.times(t.e1().p2.goodp).glVertex(gl);
+                m.times(t.e2().p1.goodp).glVertex(gl);
+                m.times(t.e2().p2.goodp).glVertex(gl);
+                m.times(t.e3().p1.goodp).glVertex(gl);
+                m.times(t.e3().p2.goodp).glVertex(gl);
+            }
+            gl.glEnd();
+            gl.glEnable(GL.GL_LIGHTING);
+            return;
+        }
+        for(T t : this) {
+            gl.glColor4f((float)(0.25+(0.05*t.color)),
+                         (float)(0.25+(0.05*t.color)),
+                         (float)(0.75+(0.05*t.color)),
+                         (float)0.3); 
+            if (t.red) {
+            gl.glColor4f((float)(0.75+(0.05*t.color)),
+                         (float)(0.25+(0.05*t.color)),
+                         (float)(0.25+(0.05*t.color)),
+                         (float)0.3); 
+            }
+            t.glTriangle(gl, m);
+        }
+        if (option_errorNormals)
+            for(T t : this)
+                for(Mesh.Vertex p : new Mesh.Vertex[] { t.v1(), t.v2(), t.v3() }) {
+                    if (p.ok) {
+                        gl.glBegin(GL.GL_LINES);
+                        gl.glColor3f(1, 1, 1);
+                        p.p.glVertex(gl);
+                        p.p.plus(p.norm().times((float)p.error()*10)).glVertex(gl);
+                        gl.glEnd();
+                    }
+                }
+    }
+
     public boolean immutableVertices;
     public Mesh    error_against      = null;
     public double  error              = 0;
@@ -52,6 +101,7 @@ public class Mesh implements Iterable<Mesh.T> {
         ArrayList<Vertex> set = new ArrayList<Vertex>();
         for(Vertex v : vertices) set.add(v);
         for(Vertex v : set) v.transform(m.times(v.p), true, null);
+        for(Vertex v : set) v.goodp = v.p;
     }
 
     public void rebuild() { /*vertices.rebuild();*/ }
@@ -73,6 +123,74 @@ public class Mesh implements Iterable<Mesh.T> {
     }
 
 
+    public void subdivide() {
+        for (Vertex v : vertices()) v.original = true;
+        HashSet<E> edges = new HashSet<E>();
+        HashSet<E> flip = new HashSet<E>();
+        HashSet<T> tris = new HashSet<T>();
+        int count = 0;
+        for (T t : this) {
+            tris.add(t);
+            edges.add(t.e1());
+            edges.add(t.e2());
+            edges.add(t.e3());
+            count++;
+        }
+        System.out.println("triangles="+count);
+        count = 0;
+        for(E e : edges) {
+            if (e.destroyed || e.shattered) continue;
+            e.shatter().edge = true;
+            for(E ex : (Iterable<E>)e.getBoundPeers()) {
+                Vertex m = nearest(ex.midpoint());
+                m.edge = true;
+                E e3 = ex.p1.getE(m).next;
+                if (e3.p2.original)
+                    flip.add(e3);
+            }
+        }
+
+        int i=0;
+        for(E e : flip) {
+            e.flip();
+            System.out.println("flip!");
+            i++;
+            //if (i>2) break;
+        }
+        System.out.println("count="+count);
+        /*
+        for (E e : flip) {
+            if (e.p1.original && !e.p2.face && !e.p2.original)      e.flip();
+            else if (e.p2.original && !e.p1.face && !e.p1.original) e.flip();
+        }
+        HashSet<Vertex> verts = new HashSet<Vertex>();
+        for(Vertex v : vertices()) verts.add(v);
+        for(Vertex v : verts) {
+            if (!v.face) continue;
+            //v.move(v.recenter().minus(v.getPoint()), false);
+        }
+        */
+
+        /*
+        Queue<T> q = new LinkedList<T>();
+        OUTER: while(true) {
+            for (T t : this) {
+                if (t.old) { t.shatter(); continue OUTER; }
+            }
+            break;
+        }
+        */
+        /*
+        for (Vertex v : vertices())
+            clearWish();
+        for (Vertex v : vertices()) {
+            
+        }
+        for (Vertex v : vertices())
+            grantWish();
+        */
+    }
+
     // Vertexices //////////////////////////////////////////////////////////////////////////////
 
     /** a vertex in the mesh */
@@ -81,14 +199,21 @@ public class Mesh implements Iterable<Mesh.T> {
         public Point oldp;
         E e;                // some edge *leaving* this point
 
+        public boolean original = false;
+        public boolean edge = false;
+        public boolean face = false;
+
         private boolean illegal = false;
 
+        public boolean visible = false;
+
         public Point getPoint() { return p; }
         public float error() { return olderror; }
 
         private Vertex(Point p) {
             this.p = p;
             this.goodp = p;
+            this.oldp = p;
             if (vertices.get(p) != null) throw new Error();
             vertices.add(this);
         }
@@ -99,6 +224,17 @@ public class Mesh implements Iterable<Mesh.T> {
             for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.t.reinsert();
         }
 
+        // the average of all adjacent points
+        public Point recenter() {
+            int count = 0;
+            Vec vec = Vec.ZERO;
+            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
+                vec = vec.plus(e.getOther(this).getPoint().minus(Point.ZERO));
+                count++;
+            }
+            return Point.ZERO.plus(vec.div(count));
+        }
+
         public float olderror = 0;
         public void setError(float nerror) {
             error -= olderror;
@@ -106,6 +242,22 @@ public class Mesh implements Iterable<Mesh.T> {
             error += olderror;
         }
 
+        /*
+        public Vertex hack(GL gl, Point mouse) {
+            double dist = Double.MAX_VALUE;
+            Vertex cur = null;
+            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
+                Vertex v = e.getOther(this);
+                double dist2 = v.getPoint().glProject(gl).distance(mouse);
+                if ((cur==null || dist2 < dist) && v.visible) {
+                    dist = dist2;
+                    cur = v;
+                }
+            }
+            return cur;
+        }
+        */
+
         public float averageTriangleArea() {
             int count = 0;
             float ret = 0;
@@ -132,12 +284,17 @@ public class Mesh implements Iterable<Mesh.T> {
                 m = m.plus(e.t.norm().fundamentalQuadric(e.t.centroid()));
                 count++;
             }
+            if (count > 0) {
+                m = m.plus(norm().fundamentalQuadric(this.p).times(count));
+                count *= 2;
+            }
             return m.times(1/(float)count);
         }
 
         public HasQuadric nearest() { return error_against==null ? null : error_against.vertices.nearest(p, this); }
         public void computeError() {
             if (error_against==null) return;
+            if (nearest_in_other_mesh == null && nearest()==null) return;
             float nerror =
                 nearest_in_other_mesh != null
                 ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p)
@@ -145,23 +302,45 @@ public class Mesh implements Iterable<Mesh.T> {
             if (quadric_count != 0)
                 nerror = (nerror + quadric.preAndPostMultiply(p))/(quadric_count+1);
 
-            if (!immutableVertices && quadric_count == 0)
-                nerror *= 2;
-                
+            if (!immutableVertices && quadric_count == 0) {
+                //nerror = Math.max(nerror, 0.4f);
+                //nerror *= 2;
+            }
+            //System.out.println(nerror);
             for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
-                double ang = Math.abs(e.dihedralAngle());
+                double ang = e.dihedralAngle();
                 if (ang > Math.PI) throw new Error();
+                if (ang < -Math.PI) throw new Error();
                 float minangle = (float)(Math.PI * 0.8);
+                //nerror += ((ang / Math.PI)*(ang/Math.PI)) * e.length() * 0.05;
+
+                nerror += (1-e.t.quality())*0.0001;
                 if (ang > minangle) nerror += (ang - minangle);
+
+                //System.out.println(((ang / Math.PI)*(ang/Math.PI)) * 0.000001);
+                /*
                 if (e.t.aspect() < 0.2) {
                     nerror += (0.2-e.t.aspect()) * 10;
                 }
+                */
+            }
+            if (!immutableVertices) {
+                Vertex n = (Vertex)nearest();
+                float d = norm().dot(n.norm());
+                if (d > 1 || d < -1) throw new Error();
+                if (d >= 0) {
+                    nerror *= (2.0f - d);
+                } else {
+                    nerror += 0.0003 * (2.0f + d);
+                    nerror *= (2.0f + d);
+                }
             }
 
             setError(nerror);
         }
 
-        public boolean move(Matrix m, boolean ignoreProblems) {
+        public boolean move(Vec vv, boolean ignoreProblems) {
+
             boolean good = true;
 
             //     t1' = M * t1
@@ -169,22 +348,28 @@ public class Mesh implements Iterable<Mesh.T> {
             //     t2' = t2.getMatrix(t1) * M * t1
             //     t1 =     t1.getMatrix(t2) * t2
             // M * t1 = M * t1.getMatrix(t2) * t2
+
             if (bindingGroup!=null && this != bindingGroup.getMaster()) {
-                Matrix v = getBindingMatrix(bindingGroup.getMaster());
-                return ((Vertex)bindingGroup.getMaster()).move(v.inverse().times(m).times(v), ignoreProblems);
+                Matrix m2 = getBindingMatrix(bindingGroup.getMaster());
+                Vec v2 = m2.times(vv.plus(getPoint())).minus(m2.times(getPoint()));
+                return ((Vertex)bindingGroup.getMaster()).move(v2, ignoreProblems);
             }
 
+            Point op = this.p;
+            Point pp = vv.plus(getPoint());
             if (bindingGroup != null) {
-                Matrix m2 = null;
-                for(int i=0; i<20 && !m.equals(m2); i++) {
-                    m2 = m.times(bindingGroup.krank);
+                /*
+                for(int i=0; i<20 ; i++) {
+                    Point p2 = getConstraint().times(pp);
+                    pp = pp.midpoint(p2);
                     //System.out.println(m.minus(m2));
                 }
-                if (!m.equals(m2)) return true;
+            */
+                //pp = getConstraint().times(pp);
             }
-
-            Point op = this.p;
-            Point pt = m.times(this.p);
+            //pp = pp.minus(op).norm().times(vv.mag()).plus(op);
+            ok = false;
+            Point pt = pp;
             for(Vertex v : (Iterable<Vertex>)getBoundPeers()) {
                 Point pt2 = v.getBindingMatrix(this).times(pt);
                 /*
@@ -195,7 +380,7 @@ public class Mesh implements Iterable<Mesh.T> {
                 good &= v.transform(pt2, ignoreProblems, v.getBindingMatrix(this));
             }
 
-            if (!good) {
+            if (!good && !ignoreProblems) {
                 for(Vertex v : (Iterable<Vertex>)getBoundPeers()) 
                     v.transform(v.oldp, true, null);
             }
@@ -204,8 +389,10 @@ public class Mesh implements Iterable<Mesh.T> {
                 v.recomputeFundamentalQuadricIfNeighborChanged();
             for(Vertex v : (Iterable<Vertex>)getBoundPeers())
                 v.reComputeErrorAround();
+            ok = true;
             return good;
         }
+        public boolean ok = true;
 
         /** does NOT update bound pairs! */
         private boolean transform(Point newp, boolean ignoreProblems, Matrix yes) {
@@ -214,18 +401,18 @@ public class Mesh implements Iterable<Mesh.T> {
 
             unApplyQuadricToNeighbor();
 
-
+            boolean illegalbefore = illegal;
             illegal = false;
-            if (this.p.minus(newp).mag() > 0.1 && !ignoreProblems) {
             /*
+            if (this.p.minus(newp).mag() > 0.1 && !ignoreProblems) {
                 try {
                     throw new Exception(""+this.p.minus(newp).mag()+" "+ignoreProblems+" "+yes);
                 } catch(Exception e) {
                     e.printStackTrace();
                 }
-            */
                 illegal = true;
             }
+            */
 
             this.p = newp;
             reinsert();
@@ -236,15 +423,17 @@ public class Mesh implements Iterable<Mesh.T> {
             }
             for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
                 e.p2.quadricStale = true;
-            return !illegal;
+            return !illegal || (illegalbefore && illegal);
         } 
 
         public void checkLegality() {
+            /*
             for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
                 if (Math.abs(e.dihedralAngle()) > (Math.PI * 0.9) ||
                     Math.abs(e.next.dihedralAngle()) > (Math.PI * 0.9)) illegal = true;
                 if (e.t.aspect() < 0.2) illegal = true;
             }
+            */
             if (!illegal) triangles.range(oldp, this.p, (Visitor<T>)this);
         }
 
@@ -272,6 +461,7 @@ public class Mesh implements Iterable<Mesh.T> {
             return !illegal;
         }
 
+        public E getEdge() { return e; }
         public E getFreeIncident() {
             E ret = getFreeIncident(e, e);
             if (ret != null) return ret;
@@ -293,8 +483,14 @@ public class Mesh implements Iterable<Mesh.T> {
             return getE(v);
         }
         public E getE(Vertex p2) {
-            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
+            if (this.e!=null && this!=this.e.p1 && this!=this.e.p2) throw new RuntimeException();
+            int i=0;
+            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;
+                i++;
+                e.sanity();
+                if (e.destroyed) throw new RuntimeException();
+            }
             return null;
         }
 
@@ -317,6 +513,13 @@ public class Mesh implements Iterable<Mesh.T> {
     /** [UNIQUE] an edge */
     public final class E extends HasBindingGroup implements Comparable<E> {
 
+        public void sanity() {
+            if (destroyed) return;
+            if (pair!=null && (pair.p1!=p2 || pair.p2!=p1)) throw new RuntimeException();
+            if (next!=null && next.p1!=p2) throw new RuntimeException();
+            if (prev!=null && prev.p2!=p1) throw new RuntimeException();
+        }
+
         public final Vertex p1, p2;
         T t;     // triangle to our "left"
         E prev;  // previous half-edge
@@ -326,6 +529,37 @@ public class Mesh implements Iterable<Mesh.T> {
 
         public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
 
+        public Segment getSegment() { return new Segment(p1.getPoint(), p2.getPoint()); }
+
+        public void flip() {
+            // FIXME: coplanarity check needed
+            if (destroyed) return;
+            for (E e : (Iterable<E>)getBoundPeers()) {
+                if (!e.pair.isBoundTo(pair)) throw new RuntimeException("cannot flip!");
+            }
+            Vertex v1 = t.getOtherVertex(this);
+            Vertex v2 = pair.t.getOtherVertex(pair);
+            destroy();
+            pair.destroy();
+            newT(v1, v2, p2).red = true;
+            newT(v2, v1, p1).red = true;
+            for (E e : (Iterable<E>)getBoundPeers()) {
+                if (e.destroyed) continue;
+                Vertex v1e = e.t.getOtherVertex(e);
+                Vertex v2e = e.pair.t.getOtherVertex(e.pair);
+                e.destroy();
+                e.pair.destroy();
+                if (v1e.getE(v2e)!=null) throw new RuntimeException();
+                newT(v1e, v2e, e.p2).red = true;
+                newT(v2e, v1e, e.p1).red = true;
+                makeE(v1.getPoint(),
+                      v2.getPoint()).bindTo(this.getBindingMatrix(e), makeE(v1e.getPoint(), v2e.getPoint()));
+                makeE(v2.getPoint(),
+                      v1.getPoint()).bindTo(pair.getBindingMatrix(e.pair), makeE(v2e.getPoint(), v1e.getPoint()));
+
+            }
+        }
+
         public void bindingGroupChanged(edu.berkeley.qfat.geom.BindingGroup newBindingGroup_) {
 
             edu.berkeley.qfat.geom.BindingGroup<E> newBindingGroup =
@@ -337,11 +571,18 @@ public class Mesh implements Iterable<Mesh.T> {
             for(E eother : nbg) {
                 if (next==null || prev==null) continue;
                 if (eother.next==null || eother.prev==null) continue;
+
                 if (next.isBoundTo(eother.pair.prev.pair) && !prev.isBoundTo(eother.pair.next.pair))
                     prev.bindTo(next.getBindingMatrix(eother.pair.prev.pair), eother.pair.next.pair);
                 if (!next.isBoundTo(eother.pair.prev.pair) && prev.isBoundTo(eother.pair.next.pair))
                     next.bindTo(prev.getBindingMatrix(eother.pair.next.pair), eother.pair.prev.pair);
 
+                /*
+                if (next.isBoundTo(eother.prev) && !prev.isBoundTo(eother.next))
+                    prev.bindTo(next.getBindingMatrix(eother.prev), eother.next);
+                if (!next.isBoundTo(eother.prev) && prev.isBoundTo(eother.next))
+                    next.bindTo(prev.getBindingMatrix(eother.next), eother.prev);
+                */
                 if (next.isBoundTo(eother.next) && !prev.isBoundTo(eother.prev))
                     prev.bindTo(next.getBindingMatrix(eother.next), eother.prev);
                 if (!next.isBoundTo(eother.next) && prev.isBoundTo(eother.prev))
@@ -360,7 +601,6 @@ public class Mesh implements Iterable<Mesh.T> {
         }
         public float comparator() {
             return length();
-            //return t==null?0:(1/t.aspect());
         }
         public int compareTo(E e) {
             return e.comparator() > comparator() ? 1 : -1;
@@ -389,8 +629,10 @@ public class Mesh implements Iterable<Mesh.T> {
             System.out.println("  " + p1.p + " " + m.times(e.p1.p));
             System.out.println("  " + p2.p + " " + m.times(e.p2.p));
             */
+            /*
             if (m.times(e.p1.p).minus(p1.p).mag() > EPSILON) throw new Error();
             if (m.times(e.p2.p).minus(p2.p).mag() > EPSILON) throw new Error();
+            */
             this.bindTo(m, e);
         }
         
@@ -399,11 +641,13 @@ public class Mesh implements Iterable<Mesh.T> {
                 if (e==this) continue;
                 p1.bindTo(getBindingMatrix(e), e.p1);
                 p2.bindTo(getBindingMatrix(e), e.p2);
+                e.p1.setConstraint(getConstraint());
+                e.p2.setConstraint(getConstraint());
             }
         }
 
-        public Point shatter() {
-            if (shattered || destroyed) return null;
+        public Vertex shatter() {
+            if (shattered || destroyed) return nearest(midpoint());
             shattered = true;
             E first = null;
             E firste = null;
@@ -439,12 +683,12 @@ public class Mesh implements Iterable<Mesh.T> {
                 e.p1.getE(mid).pair.     bindTo(e.getBindingMatrix(firste), first.pair);
                 e.p2.getE(mid).pair.     bindTo(e.getBindingMatrix(firste), firstq);
                 e.p2.getE(mid).pair.pair.bindTo(e.getBindingMatrix(firste), firstq.pair);
-                first.bindingGroup.setKrank(e.bindingGroup.krank);
-                firstq.bindingGroup.setKrank(e.bindingGroup.krank);
-                first.pair.bindingGroup.setKrank(e.bindingGroup.krank);
-                firstq.pair.bindingGroup.setKrank(e.bindingGroup.krank);
             }
-            return null;
+            /*
+            first.setConstraint(firste.getConstraint());
+            firstq.setConstraint(firste.getConstraint());
+            */
+            return nearest(midpoint());
         }
 
         public boolean destroyed = false;
@@ -469,12 +713,22 @@ public class Mesh implements Iterable<Mesh.T> {
             pair.next.t = null;
             pair.prev.t = null;
 
+            if (next.destroyed) throw new RuntimeException();
+            if (prev.destroyed) throw new RuntimeException();
             pair.prev.next = next;
             next.prev = pair.prev;
             prev.next = pair.next;
             pair.next = prev;
+
             if (p1.e == this) p1.e = prev.next;
             if (pair.p1.e == pair) pair.p1.e = pair.prev.next;
+            if (p2.e == this) throw new RuntimeException();
+            if (pair.p2.e == pair) throw new RuntimeException();
+
+            sanity();
+            next.sanity();
+            prev.sanity();
+            pair.sanity();
         }
 
         private void sync() {
@@ -493,7 +747,12 @@ public class Mesh implements Iterable<Mesh.T> {
         public double dihedralAngle() {
             Vec v1 = t.norm().times(-1);
             Vec v2 = pair.t.norm().times(-1);
-            return Math.acos(v1.norm().dot(v2.norm()));
+            double prod = v1.norm().dot(v2.norm());
+            prod = Math.min(1,prod);
+            prod = Math.max(-1,prod);
+            double ret = Math.acos(prod);
+            if (Double.isNaN(ret)) throw new Error("nan! " + prod);
+            return ret;
         }
 
         /** angle between this half-edge and the next */
@@ -503,10 +762,16 @@ public class Mesh implements Iterable<Mesh.T> {
             return Math.acos(v1.norm().dot(v2.norm()));
         }
 
+        public Vertex getOther(Vertex v) {
+            if (this.p1 == v) return p2;
+            if (this.p2 == v) return p1;
+            throw new Error();
+        }
+
         public void makeAdjacent(E e) {
             if (this.next == e) return;
-            if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex");
-            if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free ");
+            if (p2 != e.p1) throw new Error("cannot make adjacent -- no shared vertex: " + this + " " + e);
+            if (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free " + t + " " + e.t);
 
             E freeIncident = p2.getFreeIncident(e, this);
 
@@ -543,6 +808,7 @@ public class Mesh implements Iterable<Mesh.T> {
             this.p1 = prev.p2;
             this.p2 = p2;
             this.prev = prev;
+            if (prev.destroyed) throw new RuntimeException();
             if (p2.getE(p1) != null) throw new Error();
             if (p2.e==null) {
                 this.next = this.pair = new E(this, this, prev.next);
@@ -562,6 +828,7 @@ public class Mesh implements Iterable<Mesh.T> {
         public E(E prev, E pair, E next) {
             this.p1 = prev.p2;
             this.p2 = next.p1;
+            if (prev.destroyed) throw new RuntimeException();
             this.prev = prev;
             this.next = next;
             this.pair = pair;
@@ -591,6 +858,9 @@ public class Mesh implements Iterable<Mesh.T> {
     private static float round(float f) {
         return Math.round(f*1000)/1000f;
     }
+    public T newT(HasPoint p1, HasPoint p2, HasPoint p3) {
+        return newT(p1.getPoint(), p2.getPoint(), p3.getPoint(), null, 0);
+    }
     public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
         if (coalesce) {
 
@@ -624,12 +894,122 @@ public class Mesh implements Iterable<Mesh.T> {
         return ret;
     }
 
+    private int max_serial = 0;
     /** [UNIQUE] a triangle (face) */
     public final class T extends Triangle {
         public final E e1;
         public final int color;
         public final int colorclass;
 
+        public boolean red = false;
+        public boolean old = false;
+
+        public final int serial = max_serial++;
+        public boolean occluded;
+
+        public Point shatter() {
+            if (destroyed) return null;
+            E e = e1();
+            
+            HashSet<E> forward = new HashSet<E>();
+            HashSet<E> backward = new HashSet<E>();
+            HashSet<E> both = new HashSet<E>();
+
+            for(E eb : (Iterable<E>)e.getBoundPeers()) {
+                if (eb==e) continue;
+                if (eb.next.isBoundTo(e.next) && eb.prev.isBoundTo(e.prev)) {
+                    forward.add(eb);
+                    both.add(eb);
+                }
+                if (eb.pair.next.pair.isBoundTo(e.prev) && eb.pair.prev.pair.isBoundTo(e.next)) {
+                    backward.add(eb.pair);
+                    both.add(eb.pair);
+                }
+            }
+
+            Vertex v1 = e.t.v1();
+            Vertex v2 = e.t.v2();
+            Vertex v3 = e.t.v3();
+            Point c = e.t.centroid();
+            E e_next = e.next;
+            E e_prev = e.prev;
+            e.t.destroy();
+            newT(v1, v2, c);
+            newT(c,  v2, v3);
+            newT(v3, v1, c);
+
+            // FIXME: forward too
+            for(E ex : backward) {
+                Vertex v1x = ex.t.v1();
+                Vertex v2x = ex.t.v2();
+                Vertex v3x = ex.t.v3();
+                Point cx = ex.t.centroid();
+                E ex_next = ex.next;
+                E ex_prev = ex.prev;
+                ex.t.destroy();
+                newT(v1x, v2x, cx);
+                newT(cx,  v2x, v3x);
+                newT(v3x, v1x, cx);
+
+                // FIXME: i have no idea if this is right
+                e.next.bindTo(e.getBindingMatrix(ex.pair), ex.prev);
+                e.prev.bindTo(e.getBindingMatrix(ex.pair), ex.next);
+                e.next.pair.bindTo(e.getBindingMatrix(ex.pair), ex.prev.pair);
+                e.prev.pair.bindTo(e.getBindingMatrix(ex.pair), ex.next.pair);
+
+                e_next.next.bindTo(e_next.getBindingMatrix(ex_prev.pair), ex_prev.prev.pair);
+                e_next.prev.bindTo(e_next.getBindingMatrix(ex_prev.pair), ex_prev.next.pair);
+
+                e_prev.next.bindTo(e_prev.getBindingMatrix(ex_next.pair), ex_next.prev.pair);
+                e_prev.prev.bindTo(e_prev.getBindingMatrix(ex_next.pair), ex_next.next.pair);
+            }
+
+            /*
+
+            E first = null;
+            E firste = null;
+            E firstx = null;
+            E firstq = null;
+            for(E e : (Iterable<E>)getBoundPeers()) {
+                E enext = e.next;
+                E eprev = e.prev;
+                E pnext = e.pair.next;
+                E pprev = e.pair.prev;
+                Point mid = e.midpoint();
+                Vertex r = e.next.p2;
+                Vertex l = e.pair.next.p2;
+                if (!e.destroyed) {
+                    e.destroy();
+                    e.pair.destroy();
+                    newT(r.p, e.p1.p, mid,    null, 0);
+                    newT(r.p, mid,    e.p2.p, null, 0);
+                    newT(l.p, mid,    e.p1.p, null, 0);
+                    newT(l.p, e.p2.p, mid,    null, 0);
+                }
+            }
+            for(E e : (Iterable<E>)getBoundPeers()) {
+                Point mid = e.midpoint();
+                if (first==null) {
+                    first = e.p1.getE(mid);
+                    firste = e;
+                    firstx = e.pair;
+                    firstq = e.p2.getE(mid).pair;
+                    continue;
+                }
+                e.p1.getE(mid).          bindTo(e.getBindingMatrix(firste), first);
+                e.p1.getE(mid).pair.     bindTo(e.getBindingMatrix(firste), first.pair);
+                e.p2.getE(mid).pair.     bindTo(e.getBindingMatrix(firste), firstq);
+                e.p2.getE(mid).pair.pair.bindTo(e.getBindingMatrix(firste), firstq.pair);
+            }
+            */
+            /*
+            first.setConstraint(firste.getConstraint());
+            firstq.setConstraint(firste.getConstraint());
+            */
+            return null;
+        }
+
+
         T(E e1, int colorclass) {
             this.e1 = e1;
             E e2 = e1.next;
@@ -667,11 +1047,30 @@ public class Mesh implements Iterable<Mesh.T> {
         public boolean hasE(E e) { return e1==e || e1.next==e || e1.prev==e; }
         public boolean has(Vertex v) { return v1()==v || v2()==v || v3()==v; }
 
+        public Vertex getOtherVertex(E e) {
+            if (!hasE(e)) throw new RuntimeException();
+            if (!e.has(v1())) return v1();
+            if (!e.has(v2())) return v2();
+            if (!e.has(v3())) return v3();
+            throw new RuntimeException();
+        }
+
         public void removeFromRTree() { triangles.remove(this); }
         public void addToRTree() { triangles.insert(this); }
-        public void destroy() { triangles.remove(this); }
+        public void destroy() {
+            if (e1 != null) {
+                e1.t = null;
+                e1.next.t = null;
+                e1.prev.t = null;
+            }
+            triangles.remove(this);
+            destroyed = true;
+        }
         public void reinsert() { triangles.remove(this); triangles.add(this); }
 
+        private boolean destroyed = false;
+        public boolean destroyed() { return destroyed; }
+
         public boolean shouldBeDrawn() {
 
             if (e1().bindingGroupSize() <= 1) return false;
@@ -681,17 +1080,18 @@ public class Mesh implements Iterable<Mesh.T> {
             return true;
         }
 
+        public void glTriangle(GL gl, Matrix m) {
+            gl.glPushName(serial);
+            gl.glBegin(GL.GL_TRIANGLES);
+            glVertices(gl, m);
+            gl.glEnd();
+            gl.glPopName();
+        }
+
         /** issue gl.glVertex() for each of the triangle's points */
-        public void glVertices(GL gl) {
+        public void glVertices(GL gl, Matrix m) {
             if (!shouldBeDrawn()) return;
-            norm().glNormal(gl);
-            Point p1 = v1().goodp;
-            Point p2 = v2().goodp;
-            Point p3 = v3().goodp;
-            p1.glVertex(gl);
-            p2.glVertex(gl);
-            p3.glVertex(gl);
+            super.glVertices(gl, m);
         }
-
     }
 }