add items to TODO list
[anneal.git] / src / edu / berkeley / qfat / Mesh.java
index f7143f0..2e68c17 100644 (file)
@@ -1,16 +1,19 @@
 package edu.berkeley.qfat;
 import java.awt.*;
 import java.util.*;
+import java.io.*;
 import java.awt.event.*;
 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.bind.*;
 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;
@@ -23,28 +26,39 @@ public class Mesh implements Iterable<Mesh.T> {
     public boolean option_errorNormals = false;
     public boolean option_selectable   = true;
 
-    public void render(GL gl, Matrix m) {
+    public void render(GL gl, Matrix m) { render(gl, m, false); }
+    public void render(GL gl, Matrix m, boolean noColor) {
         if (option_wireframe) {
             gl.glDisable(GL.GL_LIGHTING);
             gl.glBegin(GL.GL_LINES);
-            gl.glColor3f(1, 1, 1);
+            if (!noColor) 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);
+                // fixme used to be .goodp
+                m.times(t.e1().v1.p).glVertex(gl);
+                m.times(t.e1().v2.p).glVertex(gl);
+                m.times(t.e2().v1.p).glVertex(gl);
+                m.times(t.e2().v2.p).glVertex(gl);
+                m.times(t.e3().v1.p).glVertex(gl);
+                m.times(t.e3().v2.p).glVertex(gl);
             }
             gl.glEnd();
             gl.glEnable(GL.GL_LIGHTING);
             return;
         }
         for(T t : this) {
-            gl.glColor4f((float)(0.25+(0.05*t.color)),
+            if (!noColor)
+                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)(0.75+(0.05*t.color)),
                          (float)0.3); 
+            }
+            */
             t.glTriangle(gl, m);
         }
         if (option_errorNormals)
@@ -52,7 +66,8 @@ public class Mesh implements Iterable<Mesh.T> {
                 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);
+                        if (!noColor)
+                            gl.glColor3f(1, 1, 1);
                         p.p.glVertex(gl);
                         p.p.plus(p.norm().times((float)p.error()*10)).glVertex(gl);
                         gl.glEnd();
@@ -70,6 +85,7 @@ public class Mesh implements Iterable<Mesh.T> {
     public float error() { return (float)error; }
 
     public int size() { return vertices.size(); }
+    public int numTriangles() { return triangles.size(); }
     public Iterable<Vertex> vertices() { return vertices; }
     public Iterator<T> iterator() { return triangles.iterator(); }
 
@@ -116,31 +132,142 @@ public class Mesh implements Iterable<Mesh.T> {
 
 
     public void subdivide() {
-        for (T t : this) t.old = true;
         for (Vertex v : vertices()) v.original = true;
-        OUTER: while(true) {
-            for (T t : this)
-                if (t.old) {
-                    Point p = t.e1.midpoint();
-                    System.out.println("shatter " + t.e1);
-                    t.e1.shatter();
-                    nearest(p).edge = true;
-                    continue OUTER;
+        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.v1.getE(m).next;
+                if (e3.v2.original)
+                    flip.add(e3);
+            }
+        }
+
+        int i=0;
+
+        for(E e : flip) {
+            e.flip();
+            System.out.println("flip!");
+            i++;
+        }
+
+        System.out.println("count="+count);
+
+        rebindPoints();
+        HashSet<Vertex> verts = new HashSet<Vertex>();
+        for(Vertex v : vertices()) verts.add(v);
+        for (Vertex v : verts)
+            v.clearWish();
+        for (Vertex v : verts) {
+            if (v.edge) {
+                for(E e = v.e; e!=null; e=e.pair.next==v.e?null:e.pair.next) {
+                    if (e.v2.original) {
+                        v.wish(e.v2);
+                        v.wish(e.v2);
+                        v.wish(e.v2);
+                        v.wish(e.v2);
+                    }
+                }
+                for(E e = v.e; e!=null; e=e.pair.next==v.e?null:e.pair.next) {
+                    for(E e2 = e.v2.e; e2!=null; e2=e2.pair.next==e.v2.e?null:e2.pair.next) {
+                        if (e2.v2.original) {
+                            v.wish(e.v2);
+                        }
+                    }
+                }
+            }
+        }
+        for (Vertex v : verts)
+            v.grantWish();
+        System.out.println("-------------------------------------------------------------------");
+        /*
+        for (Vertex v : verts) {
+            if (v.original) {
+                int n=0;
+                for(E e = v.e; e!=null; e=e.pair.next==v.e?null:e.pair.next) {
+                    n++;
+                    v.wish(e.midpoint());
+                    v.wish(e.midpoint());
+                    v.wish(e.next.pair.t.centroid());
                 }
-            break;
+                v.avgWish();
+                v.wishes = 3;
+                for(int j=0; j<n-3; j++)
+                    v.wish(v.getPoint());
+            }
         }
+        for (Vertex v : verts)
+            v.avgWish();
+        for (Vertex v : verts)
+            v.grantWish();
+        */
     }
 
     // Vertexices //////////////////////////////////////////////////////////////////////////////
 
+
     /** a vertex in the mesh */
-    public final class Vertex extends HasQuadric implements Visitor {
+    public final class Vertex extends HasQuadric implements Visitor, HasPoint {
+        public void bindTo(Matrix bindingMatrix, HasBindingGroup other) {
+            bindTo(bindingMatrix, other, EPSILON);
+        }
+        public float getMaxX() { return getPoint().getMaxX(); }
+        public float getMinX() { return getPoint().getMinX(); }
+        public float getMaxY() { return getPoint().getMaxY(); }
+        public float getMinY() { return getPoint().getMinY(); }
+        public float getMaxZ() { return getPoint().getMaxZ(); }
+        public float getMinZ() { return getPoint().getMinZ(); }
+
         public Point p, goodp;
         public Point oldp;
         E e;                // some edge *leaving* this point
 
         public boolean original = false;
         public boolean edge = false;
+        public boolean face = false;
+
+        private int wishes = 0;
+        private Point wish = Point.ZERO;
+        public void clearWish() { wishes = 0; wish = Point.ZERO; }
+        public void wish(HasPoint hp) {
+            Point p = hp.getPoint();
+            wishes++;
+            wish = new Point(wish.x+p.x, wish.y+p.y, wish.z+p.z);
+        }
+        public void grantWish() {
+            for(Vertex v : (Iterable<Vertex>)getBoundPeers()) {
+                if (v==this) continue;
+                if (v.wishes==0) continue;
+                Point p = this.getBindingMatrix(v).times(v.wish.minus(Point.ZERO).div(v.wishes).plus(Point.ZERO));
+                wish = p.minus(Point.ZERO).times(v.wishes).plus(wish);
+                wishes += v.wishes;
+                v.clearWish();
+            }
+            if (wishes==0) return;
+            Vec d = wish.minus(Point.ZERO).div(wishes).plus(Point.ZERO).minus(getPoint());
+            move(d, false);
+            clearWish();
+        }
+        public void avgWish() {
+            if (wishes==0) return;
+            wish = wish.minus(Point.ZERO).div(wishes).plus(Point.ZERO);
+            wishes = 1;
+        }
 
         private boolean illegal = false;
 
@@ -163,6 +290,17 @@ 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;
@@ -222,6 +360,7 @@ public class Mesh implements Iterable<Mesh.T> {
         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)
@@ -241,7 +380,7 @@ public class Mesh implements Iterable<Mesh.T> {
                 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;
+                //nerror += (1-e.t.quality())*0.0001;
                 if (ang > minangle) nerror += (ang - minangle);
 
                 //System.out.println(((ang / Math.PI)*(ang/Math.PI)) * 0.000001);
@@ -276,27 +415,24 @@ public class Mesh implements Iterable<Mesh.T> {
             //     t1 =     t1.getMatrix(t2) * t2
             // M * t1 = M * t1.getMatrix(t2) * t2
 
+            /*
             if (bindingGroup!=null && this != bindingGroup.getMaster()) {
                 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) {
-                /*
-                for(int i=0; i<20 ; i++) {
-                    Point p2 = getConstraint().times(pp);
-                    pp = pp.midpoint(p2);
-                    //System.out.println(m.minus(m2));
-                }
-            */
-                    pp = getConstraint().times(pp);
+            Point pt = vv.plus(getPoint());
+            Point pp = pt;
+            pt = getBindingConstraint().getProjection(pp);
+            if (pt==null) {
+                System.out.println("constraint violation: " + getBindingConstraint());
+                return false;
             }
-            pp = pp.minus(op).norm().times(vv.mag()).plus(op);
-            ok = false;
-            Point pt = pp;
+            System.out.println(pt.minus(pp).mag() + " " + getBindingConstraint());
+
             for(Vertex v : (Iterable<Vertex>)getBoundPeers()) {
                 Point pt2 = v.getBindingMatrix(this).times(pt);
                 /*
@@ -349,7 +485,7 @@ public class Mesh implements Iterable<Mesh.T> {
                 checkLegality();
             }
             for(E e = this.e; e!=null; e=e.pair.next==this.e?null:e.pair.next)
-                e.p2.quadricStale = true;
+                e.v2.quadricStale = true;
             return !illegal || (illegalbefore && illegal);
         } 
 
@@ -369,7 +505,7 @@ public class Mesh implements Iterable<Mesh.T> {
             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();
+                e.v2.reComputeError();
         }
 
         public boolean visit(Object o) {
@@ -378,11 +514,11 @@ public class Mesh implements Iterable<Mesh.T> {
             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 (!t.has(e.v1) && !t.has(e.v2) && 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; }
+                    if (!e.t.has(t.e1().v1) && !e.t.has(t.e1().v2) && t.e1().intersects(e.t)) { illegal = true; }
+                    if (!e.t.has(t.e2().v1) && !e.t.has(t.e2().v2) && t.e2().intersects(e.t)) { illegal = true; }
+                    if (!e.t.has(t.e3().v1) && !e.t.has(t.e3().v2) && t.e3().intersects(e.t)) { illegal = true; }
                 }
             }
             return !illegal;
@@ -399,19 +535,25 @@ public class Mesh implements Iterable<Mesh.T> {
 
         public E getFreeIncident(E start, 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)
+                if (e.pair.v2 == this && e.pair.t == null && e.pair.next.t == null)
                     return e.pair;
             return null;
         }
 
-        public E getE(Point p2) {
-            Vertex v = vertices.get(p2);
+        public E getE(Point v2) {
+            Vertex v = vertices.get(v2);
             if (v==null) return null;
             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 (e.p1 == this && e.p2 == p2) return e;
+        public E getE(Vertex v2) {
+            if (this.e!=null && this!=this.e.v1 && this!=this.e.v2) 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.v1 == this && e.v2 == v2) return e;
+                i++;
+                e.sanity();
+                if (e.destroyed) throw new RuntimeException("fark " + i + " " + e.prev + " " + (e.prev.next==e) + " " + e.prev.destroyed);
+            }
             return null;
         }
 
@@ -434,44 +576,122 @@ public class Mesh implements Iterable<Mesh.T> {
     /** [UNIQUE] an edge */
     public final class E extends HasBindingGroup implements Comparable<E> {
 
-        public final Vertex p1, p2;
+        public void bindTo(Matrix bindingMatrix, HasBindingGroup other) {
+            bindTo(bindingMatrix, other, EPSILON);
+        }
+
+        public void sanity() {
+            if (destroyed) return;
+            if (pair!=null && (pair.v1!=v2 || pair.v2!=v1)) throw new RuntimeException();
+            if (next!=null && next.v1!=v2) throw new RuntimeException();
+            if (prev!=null && prev.v2!=v1) throw new RuntimeException();
+        }
+
+        public final Vertex v1, v2;
         T t;     // triangle to our "left"
         E prev;  // previous half-edge
         E next;  // next half-edge
         E pair;  // partner half-edge
         boolean shattered = false;
 
-        public boolean intersects(T t) { return t.intersects(p1.p, p2.p); }
 
-        public Segment getSegment() { return new Segment(p1.getPoint(), p2.getPoint()); }
+        /** the "edge normal" -- average of the normals of the adjacent faces */
+        public Vec norm() {
+            return
+                (t==null || pair==null || pair.t==null)
+                ? null
+                : t.norm().plus(pair.t.norm()).norm();
+        }
+
+        public void glVertices(GL gl) {
+            Point p1 = v1.p;
+            Point p2 = v2.p;
+            if (t != null) {
+                p1 = p1.plus(t.centroid().minus(p1).times(0.1f));
+                p2 = p2.plus(t.centroid().minus(p2).times(0.1f));
+                p1 = p1.plus(norm().times(length() * 0.01f));
+                p2 = p2.plus(norm().times(length() * 0.01f));
+            }
+            p1.glVertex(gl);
+            p2.glVertex(gl);
+            if (t==null || pair.t==null) return;
+
+            Point atip = p2.minus(Point.ZERO).times(4).plus(p1.minus(Point.ZERO)).div(5).plus(Point.ZERO);
+            atip = (t.norm().plus(pair.t.norm())).norm().times(getSegment().length() / 5).plus(atip);
+            p2.glVertex(gl);
+            atip.glVertex(gl);
+        }
 
-        public void bindingGroupChanged(edu.berkeley.qfat.geom.BindingGroup newBindingGroup_) {
+        public boolean intersects(T t) { return t.intersects(v1.p, v2.p); }
 
-            edu.berkeley.qfat.geom.BindingGroup<E> newBindingGroup =
-                (edu.berkeley.qfat.geom.BindingGroup<E>)newBindingGroup_;
-            if (newBindingGroup==null) return;
-            if (this==newBindingGroup.getMaster()) return;
+        public Segment getSegment() { return new Segment(v1.getPoint(), v2.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();
+            T t1 = newT(v1, v2, this.v2);
+            T t2 = newT(v2, v1, this.v1);
+            t1.e1().sanity();
+            t1.e2().sanity();
+            t1.e3().sanity();
+            t2.e1().sanity();
+            t2.e2().sanity();
+            t2.e3().sanity();
+
+            for (E e : (Iterable<E>)getBoundPeers()) {
+                if (e==this) continue;
+                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.v2).red = true;
+                newT(v2e, v1e, e.v1).red = true;
+                v2e.getE(v1e).bindTo(e.getBindingMatrix(this), v1.getE(v2));
+                v1e.getE(v2e).bindTo(e.pair.getBindingMatrix(this.pair), v2.getE(v1));
+            }
+
+        }
+
+        public void bindingGroupChanged() {
             HashSet<E> nbg = new HashSet<E>();
-            for(E eother : (Iterable<E>)newBindingGroup) nbg.add(eother);
+            for(E eother : (Iterable<E>)getBoundPeers()) 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);
+                Matrix m = getBindingMatrix(eother);
+                if (next.isBoundTo(eother.pair.prev.pair) &&
+                    !prev.isBoundTo(eother.pair.next.pair) &&
+                    m.equalsModuloEpsilon(next.getBindingMatrix(eother.pair.prev.pair), EPSILON))
+                    prev.bindEdge(next.getBindingMatrix(eother.pair.prev.pair), eother.pair.next.pair);
+                if (!next.isBoundTo(eother.pair.prev.pair) &&
+                    prev.isBoundTo(eother.pair.next.pair)  &&
+                    m.equalsModuloEpsilon(prev.getBindingMatrix(eother.pair.next.pair), EPSILON))
+                    next.bindEdge(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) &&
+                    m.equalsModuloEpsilon(next.getBindingMatrix(eother.next), EPSILON))
+                    prev.bindEdge(next.getBindingMatrix(eother.next), eother.prev);
+                if (!next.isBoundTo(eother.next) &&
+                    prev.isBoundTo(eother.prev) &&
+                    m.equalsModuloEpsilon(prev.getBindingMatrix(eother.prev), EPSILON))
+                    next.bindEdge(prev.getBindingMatrix(eother.prev), eother.next);
 
-                /*
-                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);
             }
 
         }
@@ -480,8 +700,8 @@ public class Mesh implements Iterable<Mesh.T> {
             Vertex nearest = error_against.nearest(midpoint());
             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;
+                (v1.p.distance(error_against.nearest(v1.p).p)+
+                 v2.p.distance(error_against.nearest(v2.p).p))/2;
             return nearest_distance/other_distance;
         }
         public float comparator() {
@@ -490,49 +710,36 @@ public class Mesh implements Iterable<Mesh.T> {
         public int compareTo(E e) {
             return e.comparator() > comparator() ? 1 : -1;
         }
-        public void bindEdge(E e, Matrix m) {
-            _bindEdge(e, m);
-            pair._bindEdge(e.pair, m);
+        public void bindEdge(Matrix m, E e) {
+            bindEdge(e, 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));
-            */
+        public void bindEdge(E e, Matrix m) {
             /*
-            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();
+            for(E e_ : (Iterable<E>)e.getBoundPeers()) {
+                if (e.v1.getPoint().distance((e.getBindingMatrix(e_).times(e_.v1.getPoint()))) > 0.01f)
+                    throw new RuntimeException("blah! " + e.v1.getPoint() + " " + e.getBindingMatrix(e_).times(e_.v1.getPoint()));
+                if (e.v2.getPoint().distance((e.getBindingMatrix(e_).times(e_.v2.getPoint()))) > 0.01f)
+                    throw new RuntimeException("blah! " + e.v2.getPoint() + " " + e.getBindingMatrix(e_).times(e_.v2.getPoint()));
+                if (v1.getPoint().distance(m.times(e.getBindingMatrix(e_).times(e_.v1.getPoint()))) > 0.01f)
+                    throw new RuntimeException("blah! " + v1.getPoint() + " " + m.times(e_.v1.getPoint()));
+                if (v2.getPoint().distance(m.times(e.getBindingMatrix(e_).times(e_.v2.getPoint()))) > 0.01f)
+                    throw new RuntimeException("blah! " + v2.getPoint() + " " + m.times(e_.v2.getPoint()));
+            }
             */
-            this.bindTo(m, e);
+            this.bindTo(m, e,      EPSILON);
+            this.pair.bindTo(m, e.pair, EPSILON);
         }
         
         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());
+                v1.bindTo(getBindingMatrix(e), e.v1);
+                v2.bindTo(getBindingMatrix(e), e.v2);
             }
         }
 
-        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;
@@ -544,36 +751,36 @@ public class Mesh implements Iterable<Mesh.T> {
                 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;
+                Vertex r = e.next.v2;
+                Vertex l = e.pair.next.v2;
                 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);
+                    newT(r.p, e.v1.p, mid,    null, 0);
+                    newT(r.p, mid,    e.v2.p, null, 0);
+                    newT(l.p, mid,    e.v1.p, null, 0);
+                    newT(l.p, e.v2.p, mid,    null, 0);
                 }
             }
             for(E e : (Iterable<E>)getBoundPeers()) {
                 Point mid = e.midpoint();
                 if (first==null) {
-                    first = e.p1.getE(mid);
+                    first = e.v1.getE(mid);
                     firste = e;
                     firstx = e.pair;
-                    firstq = e.p2.getE(mid).pair;
+                    firstq = e.v2.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);
+                e.v1.getE(mid).          bindTo(e.getBindingMatrix(firste), first);
+                e.v1.getE(mid).pair.     bindTo(e.getBindingMatrix(firste), first.pair);
+                e.v2.getE(mid).pair.     bindTo(e.getBindingMatrix(firste), firstq);
+                e.v2.getE(mid).pair.pair.bindTo(e.getBindingMatrix(firste), firstq.pair);
             }
             /*
-            first.setConstraint(firste.getConstraint());
-            firstq.setConstraint(firste.getConstraint());
+            first.setConstraint(firste.getAffineConstraint());
+            firstq.setConstraint(firste.getAffineConstraint());
             */
-            return null;
+            return nearest(midpoint());
         }
 
         public boolean destroyed = false;
@@ -601,18 +808,43 @@ public class Mesh implements Iterable<Mesh.T> {
             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;
+            pair.next.prev = prev;
+
+            if (v1.e == this) v1.e = pair.next;
+            if (pair.v1.e == pair) pair.v1.e = next;
+
+            if (v2.e == this) throw new RuntimeException();
+            if (pair.v2.e == pair) throw new RuntimeException();
+
+            /*
+            next = pair;
+            prev = pair;
+            pair.next = this;
+            pair.prev = this;
+            */
+
+            /*
+            pair.prev = null;
+            pair.next = null;
+            next = null;
+            prev = null;
+            */
+
+            /*
+            sanity();
+            next.sanity();
+            prev.sanity();
+            pair.sanity();
+            */
         }
 
         private void sync() {
             this.prev.next = this;
             this.next.prev = this;
             this.pair.pair = 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;
+            if (this.next.v1 != v2) throw new Error();
+            if (this.prev.v2 != v1) throw new Error();
+            if (this.v1.e == null) this.v1.e = this;
             if (!added) added = true;
         }
         private boolean added = false;
@@ -632,23 +864,23 @@ public class Mesh implements Iterable<Mesh.T> {
 
         /** angle between this half-edge and the next */
         public double angle() {
-            Vec v1 = next.p2.p.minus(p2.p);
-            Vec v2 = this.p1.p.minus(p2.p);
+            Vec v1 = next.v2.p.minus(this.v2.p);
+            Vec v2 = this.v1.p.minus(this.v2.p);
             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;
+            if (this.v1 == v) return v2;
+            if (this.v2 == v) return v1;
             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 (v2 != e.v1) 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);
+            E freeIncident = v2.getFreeIncident(e, this);
 
             e.prev.next = freeIncident.next;
             freeIncident.next.prev = e.prev;
@@ -664,53 +896,56 @@ public class Mesh implements Iterable<Mesh.T> {
         }
 
         /** creates an isolated edge out in the middle of space */
-        public E(Point p1, Point 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);
+        public E(Point v1, Point v2) {
+            if (vertices.get(v1) != null) throw new Error();
+            if (vertices.get(v2) != null) throw new Error();
+            if (v1.equals(v2)) throw new Error("attempt to create a zero-length edge!");
+            this.v1 = new Vertex(v1);
+            this.v2 = new Vertex(v2);
             this.prev = this.next = this.pair = new E(this, this, this);
-            this.p1.e = this;
-            this.p2.e = this.pair;
+            this.v1.e = this;
+            this.v2.e = this.pair;
             sync();
         }
 
-        /** adds a new half-edge from prev.p2 to p2 */
+        /** adds a new half-edge from prev.v2 to v2 */
         public E(E prev, Point p) {
-            Vertex p2;
-            p2 = vertices.get(p);
-            if (p2 == null) p2 = new Vertex(p);
-            this.p1 = prev.p2;
-            this.p2 = p2;
+            Vertex v2;
+            v2 = vertices.get(p);
+            if (v2 == null) v2 = new Vertex(p);
+            this.v1 = prev.v2;
+            this.v2 = v2;
             this.prev = prev;
-            if (p2.getE(p1) != null) throw new Error();
-            if (p2.e==null) {
+            if (prev.destroyed) throw new RuntimeException();
+            if (v2.getE(v1) != null) throw new Error();
+            if (v2.e==null) {
                 this.next = this.pair = new E(this, this, prev.next);
             } else {
-                E q = p2.getFreeIncident();
+                E q = v2.getFreeIncident();
                 this.next = q.next;
                 this.next.prev = this;
                 E z = prev.next;
                 this.prev.next = this;
                 this.pair = new E(q, this, z);
             }
-            if (p2.e==null) p2.e = this.pair;
+            if (v2.e==null) v2.e = this.pair;
             sync();
         }
 
         /** adds a new half-edge to the mesh with a given predecessor, successor, and pair */
         public E(E prev, E pair, E next) {
-            this.p1 = prev.p2;
-            this.p2 = next.p1;
+            this.v1 = prev.v2;
+            this.v2 = next.v1;
+            if (prev.destroyed) throw new RuntimeException();
             this.prev = prev;
             this.next = next;
             this.pair = pair;
             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(Vertex v) { return v==p1 || v==p2; }
-        public float length() { return p1.p.minus(p2.p).mag(); }
-        public String toString() { return p1+"->"+p2; }
+        public Point midpoint() { return new Point((v1.p.x+v2.p.x)/2, (v1.p.y+v2.p.y)/2, (v1.p.z+v2.p.z)/2); }
+        public boolean has(Vertex v) { return v==v1 || v==v2; }
+        public float length() { return v1.p.minus(v2.p).mag(); }
+        public String toString() { return v1+"->"+v2; }
 
     }
 
@@ -731,27 +966,40 @@ public class Mesh implements Iterable<Mesh.T> {
     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) {
+    public T newT(HasPoint v1, HasPoint v2, HasPoint v3) {
+        return newT(v1.getPoint(), v2.getPoint(), v3.getPoint(), null, 0);
+    }
+    public T newT(Point v1, Point v2, Point v3, Vec norm) { return newT(v1, v2, v3, norm, 1); }
+    public T newT(Point v1, Point v2, Point v3, Vec norm, int colorclass) {
+        if (v1.equals(v2)
+            || v2.equals(v3)
+            || v3.equals(v1))
+            throw new Error("attempt to make a triangle with a length-zero side");
         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; } }
+            for(Vertex v : vertices) { if (v1.distance(v.p) < EPSILON) { v1 = v.p; break; } }
+            for(Vertex v : vertices) { if (v2.distance(v.p) < EPSILON) { v2 = v.p; break; } }
+            for(Vertex v : vertices) { if (v3.distance(v.p) < EPSILON) { v3 = 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));
+            v1 = new Point(round(v1.x), round(v1.y), round(v1.z));
+            v2 = new Point(round(v2.x), round(v2.y), round(v2.z));
+            v3 = new Point(round(v3.x), round(v3.y), round(v3.z));
+            */
+            /*
+            // triangle's vertices got merged
+            if (v1.equals(v2) || v2.equals(v3) || v3.equals(v1))
+                return null;
             */
         }
         if (norm != null) {
-            Vec norm2 = p3.minus(p1).cross(p2.minus(p1));
+            Vec norm2 = v3.minus(v1).cross(v2.minus(v1));
             float dot = norm.dot(norm2);
             //if (Math.abs(dot) < EPointSILON) throw new Error("dot products within evertsilon of each other: "+norm+" "+norm2);
-            if (dot < 0) { Point p = p1; p1=p2; p2 = p; }
+            if (dot < 0) { Point p = v1; v1=v2; v2 = p; }
         }
-        E e12 = makeE(p1, p2);
-        E e23 = makeE(p2, p3);
-        E e31 = makeE(p3, p1);
+        E e12 = makeE(v1, v2);
+        E e23 = makeE(v2, v3);
+        E e31 = makeE(v3, v1);
+        if (e12==e23 || e23==e31 || e12==e31) throw new Error();
         while(e12.next != e23 || e23.next != e31 || e31.next != e12) {
             e12.makeAdjacent(e23);
             e23.makeAdjacent(e31);
@@ -771,11 +1019,115 @@ public class Mesh implements Iterable<Mesh.T> {
         public final int color;
         public final int colorclass;
 
-        public boolean old;
+        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.v2;
+                Vertex l = e.pair.next.v2;
+                if (!e.destroyed) {
+                    e.destroy();
+                    e.pair.destroy();
+                    newT(r.p, e.v1.p, mid,    null, 0);
+                    newT(r.p, mid,    e.v2.p, null, 0);
+                    newT(l.p, mid,    e.v1.p, null, 0);
+                    newT(l.p, e.v2.p, mid,    null, 0);
+                }
+            }
+            for(E e : (Iterable<E>)getBoundPeers()) {
+                Point mid = e.midpoint();
+                if (first==null) {
+                    first = e.v1.getE(mid);
+                    firste = e;
+                    firstx = e.pair;
+                    firstq = e.v2.getE(mid).pair;
+                    continue;
+                }
+                e.v1.getE(mid).          bindTo(e.getBindingMatrix(firste), first);
+                e.v1.getE(mid).pair.     bindTo(e.getBindingMatrix(firste), first.pair);
+                e.v2.getE(mid).pair.     bindTo(e.getBindingMatrix(firste), firstq);
+                e.v2.getE(mid).pair.pair.bindTo(e.getBindingMatrix(firste), firstq.pair);
+            }
+            */
+            /*
+            first.setConstraint(firste.getAffineConstraint());
+            firstq.setConstraint(firste.getAffineConstraint());
+            */
+            return null;
+        }
+
+
         T(E e1, int colorclass) {
             this.e1 = e1;
             E e2 = e1.next;
@@ -804,26 +1156,43 @@ public class Mesh implements Iterable<Mesh.T> {
         public E e1() { return e1; }
         public E e2() { return e1.next; }
         public E e3() { return e1.prev; }
-        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 Vertex v1() { return e1.v1; }
+        public Vertex v2() { return e1.v2; }
+        public Vertex v3() { return e1.next.v2; }
+        public Point p1() { return e1.v1.p; }
+        public Point p2() { return e1.v2.p; }
+        public Point p3() { return e1.next.v2.p; }
         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); }
 
-        public boolean shouldBeDrawn() {
-
-            if (e1().bindingGroupSize() <= 1) return false;
-            if (e2().bindingGroupSize() <= 1) return false;
-            if (e3().bindingGroupSize() <= 1) return false;
+        private boolean destroyed = false;
+        public boolean destroyed() { return destroyed; }
 
+        public boolean shouldBeDrawn() {
+            if (e1().bindingGroupUnconstrained()) return false;
+            if (e2().bindingGroupUnconstrained()) return false;
+            if (e3().bindingGroupUnconstrained()) return false;
             return true;
         }
 
@@ -841,4 +1210,24 @@ public class Mesh implements Iterable<Mesh.T> {
             super.glVertices(gl, m);
         }
     }
+
+    // Dump /////////////////////////////////////////////////////////////////////////////
+
+    public void dump(OutputStream os) throws IOException {
+        PrintWriter pw = new PrintWriter(new OutputStreamWriter(os));
+        pw.println("solid dump");
+        for(Mesh.T t : this) {
+            Vec normal = t.norm();
+            pw.println("facet normal " + normal.x + " " + normal.y + " " + normal.z);
+            pw.println("  outer loop");
+            for(Mesh.Vertex v : new Mesh.Vertex[] { t.v1(), t.v2(), t.v3() }) {
+                pw.println("    vertex " + v.p.x + " " + v.p.y + " " + v.p.z);
+            }
+            pw.println("  endloop");
+            pw.println("endfacet");
+        }
+        pw.println("endsolid dump");
+        pw.flush();
+    }
+
 }