X-Git-Url: http://git.megacz.com/?p=anneal.git;a=blobdiff_plain;f=src%2Fedu%2Fberkeley%2Fqfat%2FMesh.java;h=d56e2a0d639a827160e9adbd35611e0d7515c21e;hp=6fd53d3e68d6002dde7ed63cb0a637f73893ec9e;hb=2a2e64829786ee415fd0c0f16957c55e174b793b;hpb=ba475c8edc2d38444381eeed6545ae36e47b093e

diff --git a/src/edu/berkeley/qfat/Mesh.java b/src/edu/berkeley/qfat/Mesh.java
index 6fd53d3..d56e2a0 100644
--- a/src/edu/berkeley/qfat/Mesh.java
+++ b/src/edu/berkeley/qfat/Mesh.java
@@ -6,6 +6,7 @@ import javax.swing.*;
 import javax.media.opengl.*;
 import javax.media.opengl.glu.*;
 import edu.berkeley.qfat.geom.*;
+import edu.berkeley.qfat.geom.HasBindingGroup;
 import edu.wlu.cs.levy.CG.KDTree;
 import edu.berkeley.qfat.geom.Point;
 import com.infomatiq.jsi.IntProcedure;
@@ -18,8 +19,48 @@ 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 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); 
+            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 boolean ignorecollision    = false;
     public Mesh    error_against      = null;
     public double  error              = 0;
 
@@ -45,12 +86,14 @@ public class Mesh implements Iterable<Mesh.T> {
             t.e2().dobind();
             t.e3().dobind();
         }
+        System.out.println("rebound!");
     }
 
     public void transform(Matrix m) {
         ArrayList<Vertex> set = new ArrayList<Vertex>();
         for(Vertex v : vertices) set.add(v);
-        for(Vertex v : set) v.transform(m.times(v.p), true);
+        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();*/ }
@@ -76,22 +119,31 @@ public class Mesh implements Iterable<Mesh.T> {
 
     /** a vertex in the mesh */
     public final class Vertex extends HasQuadric implements Visitor {
-        public Point p, oldp;
+        public Point p, goodp;
+        public Point oldp;
         E e;                // some edge *leaving* this point
 
-        Matrix binding = Matrix.ONE;
-        Vertex bound_to = this;
-        private boolean good;
+        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);
         }
 
+        public void reinsert() {
+            vertices.remove(this);
+            vertices.add(this);
+            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) e.t.reinsert();
+        }
+
         public float olderror = 0;
         public void setError(float nerror) {
             error -= olderror;
@@ -99,6 +151,41 @@ 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;
+            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
+                ret += e.t.area();
+                count++;
+            }
+            return ret/count;
+        }
+        public float averageEdgeLength() {
+            int count = 0;
+            float ret = 0;
+            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next) {
+                ret += e.length();
+                count++;
+            }
+            return ret/count;
+        }
+
         public Matrix _recomputeFundamentalQuadric() {
             Matrix m = Matrix.ZERO;
             int count = 0;
@@ -106,100 +193,179 @@ 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;
             float nerror =
-                quadric_count != 0
-                ? (quadric.preAndPostMultiply(p) * 100) / quadric_count
-                : nearest_in_other_mesh != null
-                ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p) * 100 * 10
-                : error_against != null
-                ? nearest().fundamentalQuadric().preAndPostMultiply(p) * 100 * 10
-                : 0;
+                nearest_in_other_mesh != null
+                ? nearest_in_other_mesh.fundamentalQuadric().preAndPostMultiply(p)
+                : nearest().fundamentalQuadric().preAndPostMultiply(p);
+            if (quadric_count != 0)
+                nerror = (nerror + quadric.preAndPostMultiply(p))/(quadric_count+1);
+
+            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.crossAngle());
+                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) {
+
+            boolean good = true;
+
+            //     t1' = M * t1
+            //     t2' = t2.getMatrix(t1) * t1'
+            //     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);
+            }
+
+            if (bindingGroup != null) {
+                Matrix m2 = null;
+                for(int i=0; i<20 && !m.equals(m2); i++) {
+                    m2 = m.times(getConstraint());
+                    //System.out.println(m.minus(m2));
+                }
+                if (!m.equals(m2)) return true;
+            }
+            ok = false;
+            Point op = this.p;
+            Point pt = m.times(this.p);
+            for(Vertex v : (Iterable<Vertex>)getBoundPeers()) {
+                Point pt2 = v.getBindingMatrix(this).times(pt);
+                /*
+                if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) > 5)
+                    throw new Error(v.p+" "+pt2+"\n"+op+" "+pt+"\n"+v.getBindingMatrix(this));
+                if (Math.abs( v.p.minus(pt2).mag() / pt.minus(op).mag() ) < 1/5) throw new Error();
+                */
+                good &= v.transform(pt2, ignoreProblems, v.getBindingMatrix(this));
+            }
+
+            if (!good && !ignoreProblems) {
+                for(Vertex v : (Iterable<Vertex>)getBoundPeers()) 
+                    v.transform(v.oldp, true, null);
+            }
+
+            for(Vertex v : (Iterable<Vertex>)getBoundPeers())
+                v.recomputeFundamentalQuadricIfNeighborChanged();
+            for(Vertex v : (Iterable<Vertex>)getBoundPeers())
+                v.reComputeErrorAround();
+            ok = true;
+            return good;
+        }
+        public boolean ok = true;
+
         /** does NOT update bound pairs! */
-        public boolean transform(Point newp, boolean ignoreProblems) {
+        private boolean transform(Point newp, boolean ignoreProblems, Matrix yes) {
             this.oldp = this.p;
             if (immutableVertices) throw new Error();
 
             unApplyQuadricToNeighbor();
 
-            if (vertices.get(this.p)==null) throw new Error();
-            vertices.remove(this);
-            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
-                if (e.t != null) e.t.removeFromRTree();
-            this.p = newp;
-            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
-                if (e.t != null) e.t.addToRTree();
-            vertices.add(this);
-
-            applyQuadricToNeighbor();
-
-            good = true;
 
-            if (!ignoreProblems)
-                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;
+            boolean illegalbefore = illegal;
+            illegal = false;
+            /*
+            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();
+            applyQuadricToNeighbor();
 
-            if (!ignorecollision && !ignoreProblems && good)
-                triangles.range(oldp, this.p, (Visitor<T>)this);
+            if (!ignoreProblems) {
+                checkLegality();
+            }
+            for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
+                e.p2.quadricStale = true;
+            return !illegal || (illegalbefore && illegal);
+        } 
 
-            return good;
+        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);
         }
 
         public void reComputeErrorAround() {
             reComputeError();
-            if (nearest_in_other_mesh != null) nearest_in_other_mesh.reComputeError();
+            if (nearest_in_other_mesh != null)
+                nearest_in_other_mesh.reComputeError();
             for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
                 e.p2.reComputeError();
         }
 
         public boolean visit(Object o) {
-            if (o instanceof T) {
-                T t = (T)o;
-                if (!good) return false;
-                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; }
-                    }
+            if (o instanceof Vertex)
+                return ((Vertex)o).e != null && ((Vertex)o).norm().dot(Vertex.this.norm()) >= 0;
+            T t = (T)o;
+            if (illegal) return false;
+            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)) { illegal = true; }
+                if (e.t != null) {
+                    if (!e.t.has(t.e1().p1) && !e.t.has(t.e1().p2) && t.e1().intersects(e.t)) { illegal = true; }
+                    if (!e.t.has(t.e2().p1) && !e.t.has(t.e2().p2) && t.e2().intersects(e.t)) { illegal = true; }
+                    if (!e.t.has(t.e3().p1) && !e.t.has(t.e3().p2) && t.e3().intersects(e.t)) { illegal = true; }
                 }
-                return good;
-            } else {
-                Vertex v = (Vertex)o;
-                if (v.e==null || v.norm().dot(Vertex.this.norm()) < 0)
-                    return false;
-                return true;
             }
+            return !illegal;
         }
 
-        public boolean move(Vec v) {
-            Matrix m = Matrix.translate(v);
-            boolean good = true;
-            for(Vertex p = this; p != null; p = (p.bound_to==this)?null:p.bound_to)
-                good &= p.transform(m.times(p.p), false);
-            for(Vertex p = this; p != null; p = (p.bound_to==this)?null:p.bound_to)
-                if (good)  p.reComputeErrorAround();
-                else       p.transform(p.oldp, true);
-            return good;
-        }
-
+        public E getEdge() { return e; }
         public E getFreeIncident() {
             E ret = getFreeIncident(e, e);
             if (ret != null) return ret;
@@ -238,112 +404,153 @@ public class Mesh implements Iterable<Mesh.T> {
             return norm.norm();
         }
 
-        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(Vertex p) { bind(p, Matrix.ONE); }
-        public void bind(Vertex p, Matrix binding) {
-            if (isBoundTo(p)) return;
-            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
-            this.bound_to = temp_bound_to;
-            this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
-        }
+        public void bindTo(Vertex p) { bindTo(Matrix.ONE, p); }
     }
 
-    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 */
-    public final class E implements Comparable<E> {
+    public final class E extends HasBindingGroup implements Comparable<E> {
 
         public final Vertex p1, p2;
         T t;     // triangle to our "left"
         E prev;  // previous half-edge
         E next;  // next half-edge
         E pair;  // partner half-edge
-        public BindingGroup bind_peers  = new BindingGroup(this);
-        public BindingGroup bind_to     = bind_peers.other();
         boolean shattered = false;
 
         public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
-        public float comparator() {
+
+        public Segment getSegment() { return new Segment(p1.getPoint(), p2.getPoint()); }
+
+        public void bindingGroupChanged(edu.berkeley.qfat.geom.BindingGroup newBindingGroup_) {
+
+            edu.berkeley.qfat.geom.BindingGroup<E> newBindingGroup =
+                (edu.berkeley.qfat.geom.BindingGroup<E>)newBindingGroup_;
+            if (newBindingGroup==null) return;
+            if (this==newBindingGroup.getMaster()) return;
+            HashSet<E> nbg = new HashSet<E>();
+            for(E eother : (Iterable<E>)newBindingGroup) nbg.add(eother);
+            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))
+                    next.bindTo(prev.getBindingMatrix(eother.prev), eother.next);
+            }
+
+        }
+
+        public float stretchRatio() {
             Vertex nearest = error_against.nearest(midpoint());
-            return (float)Math.max(length(), midpoint().distance(nearest.p));
+            float nearest_distance = midpoint().distance(nearest.p);
+            float other_distance =
+                (p1.p.distance(error_against.nearest(p1.p).p)+
+                 p2.p.distance(error_against.nearest(p2.p).p))/2;
+            return nearest_distance/other_distance;
+        }
+        public float comparator() {
+            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 void bindEdge(E e, Matrix m) {
+            _bindEdge(e, m);
+            pair._bindEdge(e.pair, m);
+        }
+        public void _bindEdge(E e, Matrix m) {
+            e = e.pair;
+            /*
+            //assumes edges are identical length at binding time
+            Vec reflectionPlaneNormal = e.p2.p.minus(e.p1.p).norm();
+            float a = reflectionPlaneNormal.x;
+            float b = reflectionPlaneNormal.y;
+            float c = reflectionPlaneNormal.z;
+            Matrix reflectionMatrix =
+                new Matrix( 1-2*a*a,  -2*a*b,  -2*a*c, 0,
+                            -2*a*b,  1-2*b*b,  -2*b*c, 0,
+                            -2*a*c,   -2*b*c, 1-2*c*c, 0,
+                            0,       0,       0,       1);
+            m = m.times(Matrix.translate(e.midpoint().minus(Point.ORIGIN))
+                        .times(reflectionMatrix)
+                        .times(Matrix.translate(Point.ORIGIN.minus(e.midpoint()))));
+            System.out.println(reflectionPlaneNormal);
+            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);
+        }
+        
+        public void dobind() {
+            for(E e : (Iterable<E>)getBoundPeers()) {
+                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() { return shatter(midpoint(), null, null); }
-        public Point shatter(Point mid, BindingGroup bg1, BindingGroup bg2) {
-            if (shattered || destroyed) return mid;
+        public Point shatter() {
+            if (shattered || destroyed) return null;
             shattered = true;
-
-            Vertex 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);
-            old_bind_to.shatter(bg2.other(), bg1.other());
-            pair.shatter();
-            destroy();
-
-            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;
+            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;
         }
 
         public boolean destroyed = false;
@@ -368,10 +575,6 @@ public class Mesh implements Iterable<Mesh.T> {
             pair.next.t = null;
             pair.prev.t = 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;
@@ -384,7 +587,6 @@ 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;
@@ -394,10 +596,15 @@ public class Mesh implements Iterable<Mesh.T> {
 
         public T makeT(int colorclass) { return t==null ? (t = new T(this, colorclass)) : t; }
 
-        public double crossAngle() {
+        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 */
@@ -407,10 +614,16 @@ 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 (t != null || e.t != null) throw new Error("cannot make adjacent -- edges not both free ");
 
             E freeIncident = p2.getFreeIncident(e, this);
 
@@ -491,7 +704,22 @@ public class Mesh implements Iterable<Mesh.T> {
         if (v2 != null) return new E(v2.getFreeIncident(), p1).pair;
         return new E(p1, p2);
     }
+    public boolean coalesce = false;
+    private static float round(float f) {
+        return Math.round(f*1000)/1000f;
+    }
     public T newT(Point p1, Point p2, Point p3, Vec norm, int colorclass) {
+        if (coalesce) {
+
+            for(Vertex v : vertices) { if (p1.distance(v.p) < EPSILON) { p1 = v.p; break; } }
+            for(Vertex v : vertices) { if (p2.distance(v.p) < EPSILON) { p2 = v.p; break; } }
+            for(Vertex v : vertices) { if (p3.distance(v.p) < EPSILON) { p3 = v.p; break; } }
+            /*
+            p1 = new Point(round(p1.x), round(p1.y), round(p1.z));
+            p2 = new Point(round(p2.x), round(p2.y), round(p2.z));
+            p3 = new Point(round(p3.x), round(p3.y), round(p3.z));
+            */
+        }
         if (norm != null) {
             Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
             float dot = norm.dot(norm2);
@@ -513,17 +741,15 @@ 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 void removeFromRTree() { triangles.remove(this); }
-        public void addToRTree() { triangles.insert(this); }
-
-        public void destroy() { triangles.remove(this); }
+        public final int serial = max_serial++;
+        public boolean occluded;
 
         T(E e1, int colorclass) {
             this.e1 = e1;
@@ -562,12 +788,32 @@ 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 void removeFromRTree() { triangles.remove(this); }
+        public void addToRTree() { triangles.insert(this); }
+        public void destroy() { triangles.remove(this); }
+        public void reinsert() { triangles.remove(this); triangles.add(this); }
+
         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;
+
+            if (e1().bindingGroupSize() <= 1) return false;
+            if (e2().bindingGroupSize() <= 1) return false;
+            if (e3().bindingGroupSize() <= 1) return false;
+
             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, Matrix m) {
+            if (!shouldBeDrawn()) return;
+            super.glVertices(gl, m);
+        }
     }
 }