diff --git a/Makefile b/Makefile
index 237bab72..10a07acc 100644
--- a/Makefile
+++ b/Makefile
@@ -21,6 +21,7 @@ SSOBJS   = $(OBJDIR)\solvespace.obj \
            $(OBJDIR)\drawconstraint.obj \
            $(OBJDIR)\file.obj \
            $(OBJDIR)\system.obj \
+           $(OBJDIR)\polygon.obj \
 
 
 LIBS = user32.lib gdi32.lib comctl32.lib advapi32.lib opengl32.lib glu32.lib
diff --git a/drawconstraint.cpp b/drawconstraint.cpp
index 83d5061e..ee879c1d 100644
--- a/drawconstraint.cpp
+++ b/drawconstraint.cpp
@@ -33,7 +33,7 @@ void Constraint::DrawOrGetDistance(Vector *labelPos) {
     Vector gu = SS.GW.projUp;
     Vector gn = gr.Cross(gu);
 
-    glxColor(1, 0.2, 1);
+    glxColor3d(1, 0.2, 1);
     switch(type) {
         case PT_PT_DISTANCE: {
             Vector ap = SS.GetEntity(ptA)->PointGetCoords();
@@ -86,7 +86,7 @@ void Constraint::DrawOrGetDistance(Vector *labelPos) {
                 for(int i = 0; i < 2; i++) {
                     Vector p = SS.GetEntity(i == 0 ? ptA : ptB)->
                                                             PointGetCoords();
-                    glxColor(0.4, 0, 0.4);
+                    glxColor3d(0.4, 0, 0.4);
                     glBegin(GL_QUADS);
                         glxVertex3v(p.Plus (r).Plus (d));
                         glxVertex3v(p.Plus (r).Minus(d));
diff --git a/dsc.h b/dsc.h
index 86d5e3e3..f558ba02 100644
--- a/dsc.h
+++ b/dsc.h
@@ -33,6 +33,7 @@ public:
     
     static Vector MakeFrom(double x, double y, double z);
 
+    bool Equals(Vector v);
     Vector Plus(Vector b);
     Vector Minus(Vector b);
     Vector Negated(void);
diff --git a/entity.cpp b/entity.cpp
index 6e1dbc08..4df3d3e2 100644
--- a/entity.cpp
+++ b/entity.cpp
@@ -211,13 +211,31 @@ void Entity::LineDrawOrGetDistance(Vector a, Vector b) {
     }
 }
 
+void Entity::LineDrawOrGetDistanceOrEdge(Vector a, Vector b) {
+    LineDrawOrGetDistance(a, b);
+    if(dogd.edges) {
+        SEdge edge;
+        edge.a = a; edge.b = b;
+        dogd.edges->l.Add(&edge);
+    }
+}
+
 void Entity::Draw(int order) {
     dogd.drawing = true;
+    dogd.edges = NULL;
     DrawOrGetDistance(order);
 }
 
+void Entity::GenerateEdges(SEdgeList *el) {
+    dogd.drawing = false;
+    dogd.edges = el;
+    DrawOrGetDistance(-1);
+    dogd.edges = NULL;
+}
+
 double Entity::GetDistance(Point2d mp) {
     dogd.drawing = false;
+    dogd.edges = NULL;
     dogd.mp = mp;
     dogd.dmin = 1e12;
 
@@ -227,7 +245,7 @@ double Entity::GetDistance(Point2d mp) {
 }
 
 void Entity::DrawOrGetDistance(int order) {  
-    glxColor(1, 1, 1);
+    glxColor3d(1, 1, 1);
 
     switch(type) {
         case POINT_IN_3D:
@@ -245,7 +263,7 @@ void Entity::DrawOrGetDistance(int order) {
                 Vector r = SS.GW.projRight.ScaledBy(s/SS.GW.scale);
                 Vector d = SS.GW.projUp.ScaledBy(s/SS.GW.scale);
 
-                glxColor(0, 0.8, 0);
+                glxColor3d(0, 0.8, 0);
                 glBegin(GL_QUADS);
                     glxVertex3v(v.Plus (r).Plus (d));
                     glxVertex3v(v.Plus (r).Minus(d));
@@ -279,7 +297,7 @@ void Entity::DrawOrGetDistance(int order) {
             Vector mm = p.Minus(us).Minus(vs);
             Vector mp = p.Minus(us).Plus (vs);
 
-            glxColor(0, 0.4, 0.4);
+            glxColor3d(0, 0.4, 0.4);
             LineDrawOrGetDistance(pp, pm);
             LineDrawOrGetDistance(pm, mm);
             LineDrawOrGetDistance(mm, mp);
@@ -299,7 +317,7 @@ void Entity::DrawOrGetDistance(int order) {
             if(order >= 0 && order != 1) break;
             Vector a = SS.GetEntity(assoc[0])->PointGetCoords();
             Vector b = SS.GetEntity(assoc[1])->PointGetCoords();
-            LineDrawOrGetDistance(a, b);
+            LineDrawOrGetDistanceOrEdge(a, b);
             break;
         }
 
diff --git a/glhelper.cpp b/glhelper.cpp
index 2f2ff444..57fd5684 100644
--- a/glhelper.cpp
+++ b/glhelper.cpp
@@ -60,7 +60,7 @@ void glxOntoCsys(Vector u, Vector v)
 void glxLockColorTo(double r, double g, double b)
 {
     ColorLocked = false;    
-    glxColor(r, g, b);
+    glxColor3d(r, g, b);
     ColorLocked = true;
 }
 
@@ -69,9 +69,45 @@ void glxUnlockColor(void)
     ColorLocked = false;    
 }
 
-void glxColor(double r, double g, double b)
+void glxColor3d(double r, double g, double b)
 {
-    if(!ColorLocked) {
-        glColor3f((GLfloat)r, (GLfloat)g, (GLfloat)b);
-    }
+    if(!ColorLocked) glColor3d(r, g, b);
 }
+
+void glxColor4d(double r, double g, double b, double a)
+{
+    if(!ColorLocked) glColor4d(r, g, b, a);
+}
+
+static void __stdcall Vertex(Vector *p) {
+    glxVertex3v(*p);
+}
+void glxFillPolygon(SPolygon *p)
+{
+    int i, j;
+
+    GLUtesselator *gt = gluNewTess();
+    typedef void __stdcall cf(void);
+    gluTessCallback(gt, GLU_TESS_BEGIN, (cf *)glBegin);
+    gluTessCallback(gt, GLU_TESS_END, (cf *)glEnd);
+    gluTessCallback(gt, GLU_TESS_VERTEX, (cf *)Vertex);
+    gluTessProperty(gt, GLU_TESS_WINDING_RULE, GLU_TESS_WINDING_ODD);
+
+    gluTessBeginPolygon(gt, NULL);
+    for(i = 0; i < p->l.n; i++) {
+        SContour *sc = &(p->l.elem[i]);
+        gluTessBeginContour(gt);
+        for(j = 0; j < (sc->l.n-1); j++) {
+            SPoint *sp = &(sc->l.elem[j]);
+            double ap[3];
+            ap[0] = sp->p.x;
+            ap[1] = sp->p.y;
+            ap[2] = sp->p.z;
+            gluTessVertex(gt, ap, &(sp->p));
+        }
+        gluTessEndContour(gt);
+    }
+    gluTessEndPolygon(gt);
+    gluDeleteTess(gt);
+}
+
diff --git a/graphicswin.cpp b/graphicswin.cpp
index 4633ef87..1b58a952 100644
--- a/graphicswin.cpp
+++ b/graphicswin.cpp
@@ -280,7 +280,21 @@ void GraphicsWindow::MenuEdit(int id) {
                 if(s->entity.v) {
                     r = s->entity.request();
                 }
-                if(r.v && !r.IsFromReferences()) SS.request.Tag(r, 1);
+                if(r.v && !r.IsFromReferences()) {
+                    SS.request.Tag(r, 1);
+                    int j;
+                    for(j = 0; j < SS.constraint.n; j++) {
+                        Constraint *c = &(SS.constraint.elem[j]);
+                        if(((c->ptA).request().v == r.v) ||
+                           ((c->ptB).request().v == r.v) ||
+                           ((c->ptC).request().v == r.v) ||
+                           ((c->entityA).request().v == r.v) ||
+                           ((c->entityB).request().v == r.v))
+                        {
+                            SS.constraint.Tag(c->h, 1);
+                        }
+                    }
+                }
                 if(s->constraint.v) {
                     SS.constraint.Tag(s->constraint, 1);
                 }
@@ -561,19 +575,22 @@ void GraphicsWindow::MouseLeftDown(double mx, double my) {
     hRequest hr;
     switch(pendingOperation) {
         case MNU_DATUM_POINT:
-            ClearSelection(); hover.Clear();
-
             hr = AddRequest(Request::DATUM_POINT);
             SS.GetEntity(hr.entity(0))->PointForceTo(v);
 
+            ClearSelection(); hover.Clear();
+
             pendingOperation = 0;
             break;
 
         case MNU_LINE_SEGMENT:
-            ClearSelection(); hover.Clear();
-
             hr = AddRequest(Request::LINE_SEGMENT);
             SS.GetEntity(hr.entity(1))->PointForceTo(v);
+            if(hover.entity.v && SS.GetEntity(hover.entity)->IsPoint()) {
+                Constraint::ConstrainCoincident(hover.entity, hr.entity(1));
+            }
+
+            ClearSelection(); hover.Clear();
 
             pendingOperation = DRAGGING_NEW_LINE_POINT;
             pendingPoint = hr.entity(2);
@@ -776,6 +793,11 @@ void GraphicsWindow::Paint(int w, int h) {
         SS.constraint.elem[i].Draw();
     }
 
+    // Draw the groups; this fills the polygons, if requested.
+    for(i = 0; i < SS.group.n; i++) {
+        SS.group.elem[i].Draw();
+    }
+
     // Then redraw whatever the mouse is hovering over, highlighted.
     glDisable(GL_DEPTH_TEST); 
     glxLockColorTo(1, 1, 0);
diff --git a/polygon.cpp b/polygon.cpp
new file mode 100644
index 00000000..66144f7a
--- /dev/null
+++ b/polygon.cpp
@@ -0,0 +1,78 @@
+#include "solvespace.h"
+
+bool SEdgeList::AssemblePolygon(SPolygon *dest, SEdge *errorAt) {
+    dest->Clear();
+    l.ClearTags();
+
+    for(;;) {
+        Vector first, last;
+        int i;
+        for(i = 0; i < l.n; i++) {
+            if(!l.elem[i].tag) {
+                first = l.elem[i].a;
+                last = l.elem[i].b;
+                l.elem[i].tag = 1;
+                break;
+            }
+        }
+        if(i >= l.n) {
+            return true;
+        }
+
+        dest->AddEmptyContour();
+        dest->AddPoint(first);
+        dest->AddPoint(last);
+        do {
+            for(i = 0; i < l.n; i++) {
+                SEdge *se = &(l.elem[i]);
+                if(se->tag) continue;
+
+                if(se->a.Equals(last)) {
+                    dest->AddPoint(se->b);
+                    last = se->b;
+                    se->tag = 1;
+                    break;
+                }
+                if(se->b.Equals(last)) {
+                    dest->AddPoint(se->a);
+                    last = se->a;
+                    se->tag = 1;
+                    break;
+                }
+            }
+            if(i >= l.n) {
+                // Couldn't assemble a closed contour; mark where.
+                errorAt->a = first;
+                errorAt->b = last;
+                return false;
+            }
+
+        } while(!last.Equals(first));
+    }
+}
+
+void SPolygon::Clear(void) {
+    int i;
+    for(i = 0; i < l.n; i++) {
+        (l.elem[i]).l.Clear();
+    }
+    l.Clear();
+}
+
+void SPolygon::AddEmptyContour(void) {
+    SContour c;
+    memset(&c, 0, sizeof(c));
+    l.Add(&c);
+}
+
+void SPolygon::AddPoint(Vector p) {
+    if(l.n < 1) oops();
+
+    SPoint sp;
+    sp.tag = 0;
+    sp.p = p;
+
+    // Add to the last contour in the list
+    (l.elem[l.n-1]).l.Add(&sp);
+}
+
diff --git a/polygon.h b/polygon.h
index c1355724..61eb740a 100644
--- a/polygon.h
+++ b/polygon.h
@@ -2,16 +2,40 @@
 #ifndef __POLYGON_H
 #define __POLYGON_H
 
+class SPolygon;
+
 template <class T>
 class SList {
 public:
     T   *elem;
     int  n;
     int  elemsAllocated;
+
+    void Add(T *t) {
+        if(n >= elemsAllocated) {
+            elemsAllocated = (elemsAllocated + 32)*2;
+            elem = (T *)MemRealloc(elem, elemsAllocated*sizeof(elem[0]));
+        }
+        elem[n++] = *t;
+    }
+
+    void ClearTags(void) {
+        int i;
+        for(i = 0; i < n; i++) {
+            elem[i].tag = 0;
+        }
+    }
+
+    void Clear(void) {
+        if(elem) MemFree(elem);
+        elem = NULL;
+        n = elemsAllocated = 0;
+    }
 };
 
 class SEdge {
 public:
+    int    tag;
     Vector a, b;
 };
 
@@ -19,16 +43,27 @@ class SEdgeList {
 public:
     SList<SEdge>    l;
 
+    bool AssemblePolygon(SPolygon *dest, SEdge *errorAt);
+};
+
+class SPoint {
+public:
+    int     tag;
+    Vector  p;
 };
 
 class SContour {
 public:
-    SList<Vector>   l;
+    SList<SPoint>   l;
 };
 
 class SPolygon {
 public:
     SList<SContour> l;
+
+    void AddEmptyContour(void);
+    void AddPoint(Vector p);
+    void Clear(void);
 };
 
 class SPolyhedron {
diff --git a/sketch.cpp b/sketch.cpp
index 89b7f6f9..ff5077f7 100644
--- a/sketch.cpp
+++ b/sketch.cpp
@@ -17,6 +17,34 @@ char *Group::DescriptionString(void) {
     return ret;
 }
 
+void Group::Draw(void) {
+    edges.l.Clear();
+    int i;
+    for(i = 0; i < SS.entity.n; i++) {
+        Entity *e = &(SS.entity.elem[i]);
+        hRequest hr = e->h.request();
+        if(SS.GetRequest(hr)->group.v != h.v) continue;
+
+        e->GenerateEdges(&edges);
+    }
+    SPolygon poly;
+    memset(&poly, 0, sizeof(poly));
+    SEdge error;
+    if(edges.AssemblePolygon(&poly, &error)) {
+        glxColor4d(0, 0, 1, 0.15);
+        glxFillPolygon(&poly);
+    } else {
+        glxColor4d(1, 0, 0, 0.3);
+        glLineWidth(10);
+        glBegin(GL_LINES);
+            glxVertex3v(error.a);
+            glxVertex3v(error.b);
+        glEnd();
+        glLineWidth(1);
+    }
+    poly.Clear();
+}
+
 hParam Request::AddParam(IdList<Param,hParam> *param, hParam hp) {
     Param pa;
     memset(&pa, 0, sizeof(pa));
diff --git a/sketch.h b/sketch.h
index a7453979..a474e3ca 100644
--- a/sketch.h
+++ b/sketch.h
@@ -65,10 +65,15 @@ public:
 
     bool        visible;
 
+    SEdgeList   edges;
+    SPolygon    poly;
+
     NameStr     name;
 
     char *DescriptionString(void);
 
+    void Draw(void);
+
     SPolygon GetPolygon(void);
 };
 
@@ -170,14 +175,18 @@ public:
     // Routines to draw and hit-test the representation of the entity
     // on-screen.
     struct {
-        bool    drawing;
-        Point2d mp;
-        double  dmin;
-    } dogd;
+        bool        drawing;
+        Point2d     mp;
+        double      dmin;
+        SEdgeList   *edges;
+    } dogd; // state for drawing or getting distance (for hit testing)
     void LineDrawOrGetDistance(Vector a, Vector b);
+    void LineDrawOrGetDistanceOrEdge(Vector a, Vector b);
     void DrawOrGetDistance(int order);
+
     void Draw(int order);
     double GetDistance(Point2d mp);
+    void GenerateEdges(SEdgeList *el);
 
     char *DescriptionString(void);
 };
@@ -253,9 +262,9 @@ public:
     static void MenuConstrain(int id);
     
     struct {
-        bool    drawing;
-        Point2d mp;
-        double  dmin;
+        bool        drawing;
+        Point2d     mp;
+        double      dmin;
     } dogd; // state for drawing or getting distance (for hit testing)
     void LineDrawOrGetDistance(Vector a, Vector b);
     void DrawOrGetDistance(Vector *labelPos);
diff --git a/solvespace.cpp b/solvespace.cpp
index 0cb48228..ac696171 100644
--- a/solvespace.cpp
+++ b/solvespace.cpp
@@ -156,6 +156,8 @@ void SolveSpace::MenuFile(int id) {
         case GraphicsWindow::MNU_NEW:
             SS.NewFile();
             SS.GenerateAll();
+            SS.GW.Init();
+            SS.TW.Init();
             break;
 
         case GraphicsWindow::MNU_OPEN:
diff --git a/solvespace.h b/solvespace.h
index 410ffbd0..cd3f0d3f 100644
--- a/solvespace.h
+++ b/solvespace.h
@@ -64,12 +64,14 @@ void MemFree(void *p);
 
 // Utility functions that are provided in the platform-independent code.
 void glxVertex3v(Vector u);
+void glxFillPolygon(SPolygon *p);
 void glxWriteText(char *str);
 void glxTranslatev(Vector u);
 void glxOntoCsys(Vector u, Vector v);
 void glxLockColorTo(double r, double g, double b);
 void glxUnlockColor(void);
-void glxColor(double r, double g, double b);
+void glxColor3d(double r, double g, double b);
+void glxColor4d(double r, double g, double b, double a);
 
 
 #define arraylen(x) (sizeof((x))/sizeof((x)[0]))
diff --git a/util.cpp b/util.cpp
index 8cc4f614..8c5f7747 100644
--- a/util.cpp
+++ b/util.cpp
@@ -102,6 +102,13 @@ Vector Vector::MakeFrom(double x, double y, double z) {
     return v;
 }
 
+bool Vector::Equals(Vector v) {
+    double tol = 0.1;
+    if(fabs(x - v.x) > tol) return false;
+    if(fabs(y - v.y) > tol) return false;
+    if(fabs(z - v.z) > tol) return false;
+    return true;
+}
 
 Vector Vector::Plus(Vector b) {
     Vector r;