diff --git a/affine.scad b/affine.scad
index b1a328a..07c662c 100644
--- a/affine.scad
+++ b/affine.scad
@@ -50,7 +50,7 @@ function ident(n) = [
 // Arguments:
 //   x = The value to test for being an affine matrix.
 //   dim = The number of dimensions the given affine is required to be for.  Generally 2 for 2D or 3 for 3D.  If given as a list of integers, allows any of the given dimensions.  Default: `[2,3]`
-// Examples:
+// Example:
 //   bool = is_affine(affine2d_scale([2,3]));  // Returns true
 //   bool = is_affine(affine3d_scale([2,3,4]));  // Returns true
 //   bool = is_affine(affine3d_scale([2,3,4]),2);  // Returns false
@@ -74,7 +74,7 @@ function is_affine(x,dim=[2,3]) =
 //   for a simple scaling of z.  Note that an input which is only a zscale returns false.
 // Arguments:
 //   t = The transformation matrix to check.
-// Examples:
+// Example:
 //   b = is_2d_transform(zrot(45));  // Returns: true
 //   b = is_2d_transform(yrot(45));  // Returns: false
 //   b = is_2d_transform(xrot(45));  // Returns: false
diff --git a/fnliterals.scad b/fnliterals.scad
index f5f5951..c0cde8b 100644
--- a/fnliterals.scad
+++ b/fnliterals.scad
@@ -141,12 +141,10 @@ function reduce(func, list, init=0) =
 //   list = The input list.
 //   init = The starting value for the accumulator.  Default: 0
 // See Also: map(), filter(), reduce(), while(), for_n()
-// Examples: Reimplement cumsum()
-//   echo(accumulate(function (a,b) a+b, [3,4,5],0));
-//   // ECHO: [3,7,12]
-// Examples: Reimplement cumprod()
-//   echo(accumulate(f_mul(),[3,4,5],1));
-//   // ECHO: [3,12,60,360]
+// Example: Reimplement cumsum()
+//   echo(accumulate(function (a,b) a+b, [3,4,5],0));  // ECHO: [3,7,12]
+// Example: Reimplement cumprod()
+//   echo(accumulate(f_mul(),[3,4,5],1)); // ECHO: [3,12,60,360]
 function accumulate(func, list, init=0) =
     assert(is_function(func))
     assert(is_list(list))
@@ -313,7 +311,7 @@ function binsearch(key, list, idx, cmp=f_cmp()) =
 // Arguments:
 //   x = The value to get the simple hash value  of.
 // See Also: hashmap()
-// Examples:
+// Example:
 //   x = simple_hash("Foobar");
 //   x = simple_hash([[10,20],[-5,3]]);
 function simple_hash(x) =
diff --git a/gears.scad b/gears.scad
index f44acd7..58a9122 100644
--- a/gears.scad
+++ b/gears.scad
@@ -37,7 +37,7 @@
 // Arguments:
 //   pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
 //   mod = The metric module/modulus of the gear.
-// Examples:
+// Example:
 //   circp = circular_pitch(pitch=5);
 //   circp = circular_pitch(mod=2);
 function circular_pitch(pitch=5, mod) =
@@ -54,7 +54,7 @@ function circular_pitch(pitch=5, mod) =
 // Arguments:
 //   pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
 //   mod = The metric module/modulus of the gear.
-// Examples:
+// Example:
 //   dp = diametral_pitch(pitch=5);
 //   dp = diametral_pitch(mod=2);
 function diametral_pitch(pitch=5, mod) =
@@ -96,7 +96,7 @@ function module_value(pitch=5) = pitch / PI;
 // Arguments:
 //   pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
 //   mod = The metric module/modulus of the gear.
-// Examples:
+// Example:
 //   ad = adendum(pitch=5);
 //   ad = adendum(mod=2);
 // Example(2D):
@@ -123,7 +123,7 @@ function adendum(pitch=5, mod) =
 //   pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
 //   clearance = If given, sets the clearance between meshing teeth.
 //   mod = The metric module/modulus of the gear.
-// Examples:
+// Example:
 //   ddn = dedendum(pitch=5);
 //   ddn = dedendum(mod=2);
 // Example(2D):
@@ -152,7 +152,7 @@ function dedendum(pitch=5, clearance, mod) =
 //   pitch = The circular pitch, or distance between teeth around the pitch circle, in mm.
 //   teeth = The number of teeth on the gear.
 //   mod = The metric module/modulus of the gear.
-// Examples:
+// Example:
 //   pr = pitch_radius(pitch=5, teeth=11);
 //   pr = pitch_radius(mod=2, teeth=20);
 // Example(2D):
@@ -177,7 +177,7 @@ function pitch_radius(pitch=5, teeth=11, mod) =
 //   clearance = If given, sets the clearance between meshing teeth.
 //   interior = If true, calculate for an interior gear.
 //   mod = The metric module/modulus of the gear.
-// Examples:
+// Example:
 //   or = outer_radius(pitch=5, teeth=20);
 //   or = outer_radius(mod=2, teeth=16);
 // Example(2D):
@@ -203,7 +203,7 @@ function outer_radius(pitch=5, teeth=11, clearance, interior=false, mod) =
 //   clearance = If given, sets the clearance between meshing teeth.
 //   interior = If true, calculate for an interior gear.
 //   mod = The metric module/modulus of the gear.
-// Examples:
+// Example:
 //   rr = root_radius(pitch=5, teeth=11);
 //   rr = root_radius(mod=2, teeth=16);
 // Example(2D):
@@ -228,7 +228,7 @@ function root_radius(pitch=5, teeth=11, clearance, interior=false, mod) =
 //   teeth = The number of teeth on the gear.
 //   pressure_angle = Pressure angle in degrees.  Controls how straight or bulged the tooth sides are.
 //   mod = The metric module/modulus of the gear.
-// Examples:
+// Example:
 //   br = base_radius(pitch=5, teeth=20, pressure_angle=20);
 //   br = base_radius(mod=2, teeth=18, pressure_angle=20);
 // Example(2D):
@@ -253,7 +253,7 @@ function base_radius(pitch=5, teeth=11, pressure_angle=28, mod) =
 //   teeth = Number of teeth that this gear has.
 //   mate_teeth = Number of teeth that the matching gear has.
 //   drive_angle = Angle between the drive shafts of each gear.  Default: 90º.
-// Examples:
+// Example:
 //   ang = bevel_pitch_angle(teeth=18, mate_teeth=30);
 // Example(2D):
 //   t1 = 13; t2 = 19; pitch=5;
@@ -287,7 +287,7 @@ function bevel_pitch_angle(teeth, mate_teeth, drive_angle=90) =
 //   crowning = The amount to oversize the virtual hobbing cutter used to make the teeth, to add a slight crowning to the teeth to make them fir the work easier.  Default: 1
 //   clearance = Clearance gap at the bottom of the inter-tooth valleys.
 //   mod = The metric module/modulus of the gear.
-// Examples:
+// Example:
 //   thick = worm_gear_thickness(pitch=5, teeth=36, worm_diam=30);
 //   thick = worm_gear_thickness(mod=2, teeth=28, worm_diam=25);
 // Example(2D):
diff --git a/mutators.scad b/mutators.scad
index 0f51e73..fc5c026 100644
--- a/mutators.scad
+++ b/mutators.scad
@@ -1049,7 +1049,7 @@ module rainbow(list, stride=1)
 {
     ll = len(list);
     huestep = 360 / ll;
-    hues = [for (i=[0:1:ll-1]) posmod(i*huestep+i*360/stride,360)];
+    hues = shuffle([for (i=[0:1:ll-1]) posmod(i*huestep+i*360/stride,360)]);
     for($idx=idx(list)) {
         $item = list[$idx];
         HSV(h=hues[$idx]) children();
diff --git a/paths.scad b/paths.scad
index 83b301b..dfce2c3 100644
--- a/paths.scad
+++ b/paths.scad
@@ -109,17 +109,18 @@ function _path_select(path, s1, u1, s2, u2, closed=false) =
 //   path_merge_collinear(path, [eps])
 // Arguments:
 //   path = A list of path points of any dimension.
+//   closed = treat as closed polygon.  Default: false
 //   eps = Largest positional variance allowed.  Default: `EPSILON` (1-e9)
-function path_merge_collinear(path, eps=EPSILON) =
+function path_merge_collinear(path, closed=false, eps=EPSILON) =
     assert( is_path(path), "Invalid path." )
     assert( is_undef(eps) || (is_finite(eps) && (eps>=0) ), "Invalid tolerance." )    
     len(path)<=2 ? path :
     let(
         indices = [
             0,
-            for (i=[1:1:len(path)-2]) 
-                if (!is_collinear(path[i-1], path[i], path[i+1], eps=eps)) i, 
-            len(path)-1 
+            for (i=[1:1:len(path)-(closed?1:2)]) 
+                if (!is_collinear(path[i-1], path[i], select(path,i+1), eps=eps)) i, 
+            if (!closed) len(path)-1 
         ]
     ) [for (i=indices) path[i]];
 
@@ -156,6 +157,27 @@ function path_segment_lengths(path, closed=false) =
     ]; 
 
 
+// Function: path_length_fractions()
+// Usage:
+//   fracs = path_length_fractions(path, [closed]);
+// Description:
+//    Returns the distance fraction of each point in the path along the path, so the first
+//    point is zero and the final point is 1.  If the path is closed the length of the output
+//    will have one extra point because of the final connecting segment that connects the last
+//    point of the path to the first point.
+function path_length_fractions(path, closed=false) =
+    assert(is_path(path))
+    assert(is_bool(closed))
+    let(
+        lengths = [
+            0,
+            for (i=[0:1:len(path)-(closed?1:2)])
+                norm(select(path,i+1)-path[i])
+        ],
+        partial_len = cumsum(lengths),
+        total_len = last(partial_len)
+    ) partial_len / total_len;
+
 
 // Function: path_closest_point()
 // Usage:
@@ -181,6 +203,8 @@ function path_closest_point(path, pt) =
     ) [min_seg, pts[min_seg]];
 
 
+// Section: Geometric Properties of Paths
+
 // Function: path_tangents()
 // Usage:
 //   tangs = path_tangents(path, [closed], [uniform]);
@@ -574,7 +598,7 @@ function split_path_at_self_crossings(path, closed=true, eps=EPSILON) =
     ];
 
 
-function _tag_self_crossing_subpaths(path, closed=true, eps=EPSILON) =
+function _tag_self_crossing_subpaths(path, nonzero, closed=true, eps=EPSILON) =
     let(
         subpaths = split_path_at_self_crossings(
             path, closed=closed, eps=eps
@@ -586,8 +610,8 @@ function _tag_self_crossing_subpaths(path, closed=true, eps=EPSILON) =
             n = line_normal(seg) / 2048,
             p1 = mp + n,
             p2 = mp - n,
-            p1in = point_in_polygon(p1, path) >= 0,
-            p2in = point_in_polygon(p2, path) >= 0,
+            p1in = point_in_polygon(p1, path, nonzero=nonzero) >= 0,
+            p2in = point_in_polygon(p2, path, nonzero=nonzero) >= 0,
             tag = (p1in && p2in)? "I" : "O"
         ) [tag, subpath]
     ];
@@ -595,7 +619,7 @@ function _tag_self_crossing_subpaths(path, closed=true, eps=EPSILON) =
 
 // Function: decompose_path()
 // Usage:
-//   splitpaths = decompose_path(path, [closed], [eps]);
+//   splitpaths = decompose_path(path, [nonzero], [closed], [eps]);
 // Description:
 //   Given a possibly self-crossing path, decompose it into non-crossing paths that are on the perimeter
 //   of the areas bounded by that path.
@@ -609,10 +633,10 @@ function _tag_self_crossing_subpaths(path, closed=true, eps=EPSILON) =
 //   ];
 //   splitpaths = decompose_path(path, closed=true);
 //   rainbow(splitpaths) stroke($item, closed=true, width=3);
-function decompose_path(path, closed=true, eps=EPSILON) =
+function decompose_path(path, nonzero, closed=true, eps=EPSILON) =
     let(
         path = cleanup_path(path, eps=eps),
-        tagged = _tag_self_crossing_subpaths(path, closed=closed, eps=eps),
+        tagged = _tag_self_crossing_subpaths(path, nonzero=nonzero, closed=closed, eps=eps),
         kept = [for (sub = tagged) if(sub[0] == "O") sub[1]],
         outregion = _assemble_path_fragments(kept, eps=eps)
     ) outregion;
@@ -867,6 +891,7 @@ function _path_cuts_dir(path, cuts, closed=false, eps=1e-2) =
 
 // Function: path_cut()
 // Topics: Paths
+// See Also: split_path_at_self_crossings()
 // Usage:
 //    path_list = path_cut(path, cutdist, [closed=]);
 // Description:
@@ -956,6 +981,8 @@ function _sum_preserving_round(data, index=0) =
     );
 
 
+// Section: Changing sampling of paths
+
 // Function: subdivide_path()
 // Usage:
 //   newpath = subdivide_path(path, [N|refine], method);
@@ -1052,27 +1079,6 @@ function subdivide_path(path, N, refine, closed=true, exact=true, method="length
     );
 
 
-// Function: path_length_fractions()
-// Usage:
-//   fracs = path_length_fractions(path, [closed]);
-// Description:
-//    Returns the distance fraction of each point in the path along the path, so the first
-//    point is zero and the final point is 1.  If the path is closed the length of the output
-//    will have one extra point because of the final connecting segment that connects the last
-//    point of the path to the first point.
-function path_length_fractions(path, closed=false) =
-    assert(is_path(path))
-    assert(is_bool(closed))
-    let(
-        lengths = [
-            0,
-            for (i=[0:1:len(path)-(closed?1:2)])
-                norm(select(path,i+1)-path[i])
-        ],
-        partial_len = cumsum(lengths),
-        total_len = last(partial_len)
-    ) partial_len / total_len;
-
 
 // Function: resample_path()
 // Usage:
diff --git a/regions.scad b/regions.scad
index c7d771d..e839fe0 100644
--- a/regions.scad
+++ b/regions.scad
@@ -489,7 +489,7 @@ function _shift_segment(segment, d) =
 // Extend to segments to their intersection point.  First check if the segments already have a point in common,
 // which can happen if two colinear segments are input to the path variant of `offset()`
 function _segment_extension(s1,s2) =
-    norm(s1[1]-s2[0])<1e-6 ? s1[1] : line_intersection(s1,s2);
+    norm(s1[1]-s2[0])<1e-6 ? s1[1] : line_intersection(s1,s2,LINE,LINE);
 
 
 function _makefaces(direction, startind, good, pointcount, closed) =
@@ -745,7 +745,11 @@ function offset(
         quality = max(0,round(quality)),
         flip_dir = closed && !is_polygon_clockwise(path)? -1 : 1,
         d = flip_dir * (is_def(r) ? r : delta),
-        shiftsegs = [for(i=[0:len(path)-1]) _shift_segment(select(path,i,i+1), d)],
+//        shiftsegs = [for(i=[0:len(path)-1]) _shift_segment(select(path,i,i+1), d)],
+        shiftsegs = [for(i=[0:len(path)-2]) _shift_segment([path[i],path[i+1]], d),
+                     if (closed) _shift_segment([last(path),path[0]],d)
+                     else [path[0],path[1]]  // dummy segment, not used
+                    ],
         // good segments are ones where no point on the segment is less than distance d from any point on the path
         good = check_valid ? _good_segments(path, abs(d), shiftsegs, closed, quality) : repeat(true,len(shiftsegs)),
         goodsegs = bselect(shiftsegs, good),
diff --git a/shapes3d.scad b/shapes3d.scad
index 1a135f4..ab01138 100644
--- a/shapes3d.scad
+++ b/shapes3d.scad
@@ -1,6 +1,10 @@
 //////////////////////////////////////////////////////////////////////
 // LibFile: shapes3d.scad
-//   Common useful shapes and structured objects.
+//   Some standard modules for making 3d shapes with attachment support, and function forms
+//   that produce a VNF.  Also included are shortcuts cylinders in each orientation and extended versions of
+//   the standard modules that provide roundovers and chamfers.  The sphereoid() module provides
+//   several different ways to make a sphere, and the text modules let you write text on a path
+//   so you can place it on a curved object.  
 // Includes:
 //   include <BOSL2/std.scad>
 //////////////////////////////////////////////////////////////////////
@@ -1396,6 +1400,61 @@ module tube(
 
 
 
+// Module: pie_slice()
+//
+// Description:
+//   Creates a pie slice shape.
+//
+// Usage: Typical
+//   pie_slice(l|h, r, ang, [center]);
+//   pie_slice(l|h, d=, ang=, ...);
+//   pie_slice(l|h, r1=|d1=, r2=|d2=, ang=, ...);
+// Usage: Attaching Children
+//   pie_slice(l|h, r, ang, ...) [attachments];
+//
+// Arguments:
+//   h / l = height of pie slice.
+//   r = radius of pie slice.
+//   ang = pie slice angle in degrees.
+//   center = If given, overrides `anchor`.  A true value sets `anchor=CENTER`, false sets `anchor=UP`.
+//   ---
+//   r1 = bottom radius of pie slice.
+//   r2 = top radius of pie slice.
+//   d = diameter of pie slice.
+//   d1 = bottom diameter of pie slice.
+//   d2 = top diameter of pie slice.
+//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#anchor).  Default: `CENTER`
+//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#spin).  Default: `0`
+//   orient = Vector to rotate top towards, after spin.  See [orient](attachments.scad#orient).  Default: `UP`
+//
+// Example: Cylindrical Pie Slice
+//   pie_slice(ang=45, l=20, r=30);
+// Example: Conical Pie Slice
+//   pie_slice(ang=60, l=20, d1=50, d2=70);
+module pie_slice(
+    h, r, ang=30, center,
+    r1, r2, d, d1, d2, l,
+    anchor, spin=0, orient=UP
+) {
+    l = first_defined([l, h, 1]);
+    r1 = get_radius(r1=r1, r=r, d1=d1, d=d, dflt=10);
+    r2 = get_radius(r1=r2, r=r, d1=d2, d=d, dflt=10);
+    maxd = max(r1,r2)+0.1;
+    anchor = get_anchor(anchor, center, BOT, BOT);
+    attachable(anchor,spin,orient, r1=r1, r2=r2, l=l) {
+        difference() {
+            cyl(r1=r1, r2=r2, h=l);
+            if (ang<180) rotate(ang) back(maxd/2) cube([2*maxd, maxd, l+0.1], center=true);
+            difference() {
+                fwd(maxd/2) cube([2*maxd, maxd, l+0.2], center=true);
+                if (ang>180) rotate(ang-180) back(maxd/2) cube([2*maxd, maxd, l+0.1], center=true);
+            }
+        }
+        children();
+    }
+}
+
+
 
 // Section: Other Round Objects
 
@@ -2204,59 +2263,6 @@ module nil() union(){}
 module noop(spin=0, orient=UP) attachable(CENTER,spin,orient, d=0.01) {nil(); children();}
 
 
-// Module: pie_slice()
-//
-// Description:
-//   Creates a pie slice shape.
-//
-// Usage: Typical
-//   pie_slice(l|h, r, ang, [center]);
-//   pie_slice(l|h, d=, ang=, ...);
-//   pie_slice(l|h, r1=|d1=, r2=|d2=, ang=, ...);
-// Usage: Attaching Children
-//   pie_slice(l|h, r, ang, ...) [attachments];
-//
-// Arguments:
-//   h / l = height of pie slice.
-//   r = radius of pie slice.
-//   ang = pie slice angle in degrees.
-//   center = If given, overrides `anchor`.  A true value sets `anchor=CENTER`, false sets `anchor=UP`.
-//   ---
-//   r1 = bottom radius of pie slice.
-//   r2 = top radius of pie slice.
-//   d = diameter of pie slice.
-//   d1 = bottom diameter of pie slice.
-//   d2 = top diameter of pie slice.
-//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#anchor).  Default: `CENTER`
-//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#spin).  Default: `0`
-//   orient = Vector to rotate top towards, after spin.  See [orient](attachments.scad#orient).  Default: `UP`
-//
-// Example: Cylindrical Pie Slice
-//   pie_slice(ang=45, l=20, r=30);
-// Example: Conical Pie Slice
-//   pie_slice(ang=60, l=20, d1=50, d2=70);
-module pie_slice(
-    h, r, ang=30, center,
-    r1, r2, d, d1, d2, l,
-    anchor, spin=0, orient=UP
-) {
-    l = first_defined([l, h, 1]);
-    r1 = get_radius(r1=r1, r=r, d1=d1, d=d, dflt=10);
-    r2 = get_radius(r1=r2, r=r, d1=d2, d=d, dflt=10);
-    maxd = max(r1,r2)+0.1;
-    anchor = get_anchor(anchor, center, BOT, BOT);
-    attachable(anchor,spin,orient, r1=r1, r2=r2, l=l) {
-        difference() {
-            cyl(r1=r1, r2=r2, h=l);
-            if (ang<180) rotate(ang) back(maxd/2) cube([2*maxd, maxd, l+0.1], center=true);
-            difference() {
-                fwd(maxd/2) cube([2*maxd, maxd, l+0.2], center=true);
-                if (ang>180) rotate(ang-180) back(maxd/2) cube([2*maxd, maxd, l+0.1], center=true);
-            }
-        }
-        children();
-    }
-}
 
 
 // Module: interior_fillet()
diff --git a/skin.scad b/skin.scad
index 4640086..5deceaa 100644
--- a/skin.scad
+++ b/skin.scad
@@ -832,8 +832,13 @@ function path_sweep(shape, path, method="incremental", normal, closed=false, twi
     caps = is_def(caps) ? caps :
            closed ? false : true,
     capsOK = is_bool(caps) || (is_list(caps) && len(caps)==2 && is_bool(caps[0]) && is_bool(caps[1])),
-    fullcaps = is_bool(caps) ? [caps,caps] : caps
+    fullcaps = is_bool(caps) ? [caps,caps] : caps,
+    normalOK = is_undef(normal) || (method!="natural" && is_vector(normal,3))
+                                || (method=="manual" && same_shape(normal,path))
   )
+  assert(normalOK,  method=="natural" ? "Cannot specify normal with the \"natural\" method"
+                  : method=="incremental" ? "Normal with \"incremental\" method must be a 3-vector"
+                  : str("Incompatible normal given.  Must be a 3-vector or a list of ",len(path)," 3-vectors"))
   assert(capsOK, "caps must be boolean or a list of two booleans")
   assert(!closed || !caps, "Cannot make closed shape with caps")
   assert(is_undef(normal) || (is_vector(normal) && len(normal)==3) || (is_path(normal) && len(normal)==len(path) && len(normal[0])==3), "Invalid normal specified")
diff --git a/vnf.scad b/vnf.scad
index 0cfe001..3ea55d3 100644
--- a/vnf.scad
+++ b/vnf.scad
@@ -9,9 +9,8 @@
 //////////////////////////////////////////////////////////////////////
 
 
-// Creating Polyhedrons with VNF Structures
+// Section: Creating Polyhedrons with VNF Structures
 
-// Section: VNF Testing and Access
 //   VNF stands for "Vertices'N'Faces".  VNF structures are 2-item lists, `[VERTICES,FACES]` where the
 //   first item is a list of vertex points, and the second is a list of face indices into the vertex
 //   list.  Each VNF is self contained, with face indices referring only to its own vertex list.
@@ -21,8 +20,6 @@
 EMPTY_VNF = [[],[]];  // The standard empty VNF with no vertices or faces.
 
 
-// Section: Constructing VNFs
-
 // Function: vnf_vertex_array()
 // Usage:
 //   vnf = vnf_vertex_array(points, [caps], [cap1], [cap2], [style], [reverse], [col_wrap], [row_wrap], [vnf]);
@@ -207,12 +204,12 @@ function vnf_vertex_array(
 //   points = List of point lists for each row
 //   row_wrap = If true then add faces connecting the first row and last row.  These rows must differ by at most 2 in length.
 //   reverse = Set this to reverse the direction of the faces
-// Examples:  Each row has one more point than the preceeding one.
+// Example:  Each row has one more point than the preceeding one.
 //   pts = [for(y=[1:1:10]) [for(x=[0:y-1]) [x,y,y]]];
 //   vnf = vnf_tri_array(pts);
 //   vnf_wireframe(vnf,d=.1);
 //   color("red")move_copies(flatten(pts)) sphere(r=.15,$fn=9);
-// Examples:  Each row has one more point than the preceeding one.
+// Example:  Each row has one more point than the preceeding one.
 //   pts = [for(y=[0:2:10]) [for(x=[-y/2:y/2]) [x,y,y]]];
 //   vnf = vnf_tri_array(pts);
 //   vnf_wireframe(vnf,d=.1);
@@ -277,58 +274,6 @@ function vnf_tri_array(points, row_wrap=false, reverse=false, vnf=EMPTY_VNF) =
     vnf_merge(cleanup=true, [vnf, [flatten(points), faces]]);
 
 
-// Function: vnf_add_face()
-// Usage:
-//   vnf_add_face(vnf, pts);
-// Description:
-//   Given a VNF structure and a list of face vertex points, adds the face to the VNF structure.
-//   Returns the modified VNF structure `[VERTICES, FACES]`.  It is up to the caller to make
-//   sure that the points are in the correct order to make the face normal point outwards.
-// Arguments:
-//   vnf = The VNF structure to add a face to.
-//   pts = The vertex points for the face.
-function vnf_add_face(vnf=EMPTY_VNF, pts) =
-    assert(is_vnf(vnf))
-    assert(is_path(pts))
-    let(
-        res = set_union(vnf[0], pts, get_indices=true),
-        face = deduplicate(res[0], closed=true)
-    ) [
-        res[1],
-        concat(vnf[1], len(face)>2? [face] : [])
-    ];
-
-
-// Function: vnf_add_faces()
-// Usage:
-//   vnf_add_faces(vnf, faces);
-// Description:
-//   Given a VNF structure and a list of faces, where each face is given as a list of vertex points,
-//   adds the faces to the VNF structure.  Returns the modified VNF structure `[VERTICES, FACES]`.
-//   It is up to the caller to make sure that the points are in the correct order to make the face
-//   normals point outwards.
-// Arguments:
-//   vnf = The VNF structure to add a face to.
-//   faces = The list of faces, where each face is given as a list of vertex points.
-function vnf_add_faces(vnf=EMPTY_VNF, faces) =
-    assert(is_vnf(vnf))
-    assert(is_list(faces))
-    let(
-        res = set_union(vnf[0], flatten(faces), get_indices=true),
-        idxs = res[0],
-        nverts = res[1],
-        offs = cumsum([0, for (face=faces) len(face)]),
-        ifaces = [
-            for (i=idx(faces)) [
-                for (j=idx(faces[i]))
-                idxs[offs[i]+j]
-            ]
-        ]
-    ) [
-        nverts,
-        concat(vnf[1],ifaces)
-    ];
-
 
 // Function: vnf_merge()
 // Usage:
@@ -381,6 +326,64 @@ function vnf_merge(vnfs, cleanup=false, eps=EPSILON) =
     [nverts, nfaces];
 
 
+
+// Function: vnf_add_face()
+// Usage:
+//   vnf_add_face(vnf, pts);
+// Description:
+//   Given a VNF structure and a list of face vertex points, adds the face to the VNF structure.
+//   Returns the modified VNF structure `[VERTICES, FACES]`.  It is up to the caller to make
+//   sure that the points are in the correct order to make the face normal point outwards.
+// Arguments:
+//   vnf = The VNF structure to add a face to.
+//   pts = The vertex points for the face.
+function vnf_add_face(vnf=EMPTY_VNF, pts) =
+    assert(is_vnf(vnf))
+    assert(is_path(pts))
+    let(
+        res = set_union(vnf[0], pts, get_indices=true),
+        face = deduplicate(res[0], closed=true)
+    ) [
+        res[1],
+        concat(vnf[1], len(face)>2? [face] : [])
+    ];
+
+
+
+// Function: vnf_add_faces()
+// Usage:
+//   vnf_add_faces(vnf, faces);
+// Description:
+//   Given a VNF structure and a list of faces, where each face is given as a list of vertex points,
+//   adds the faces to the VNF structure.  Returns the modified VNF structure `[VERTICES, FACES]`.
+//   It is up to the caller to make sure that the points are in the correct order to make the face
+//   normals point outwards.
+// Arguments:
+//   vnf = The VNF structure to add a face to.
+//   faces = The list of faces, where each face is given as a list of vertex points.
+function vnf_add_faces(vnf=EMPTY_VNF, faces) =
+    assert(is_vnf(vnf))
+    assert(is_list(faces))
+    let(
+        res = set_union(vnf[0], flatten(faces), get_indices=true),
+        idxs = res[0],
+        nverts = res[1],
+        offs = cumsum([0, for (face=faces) len(face)]),
+        ifaces = [
+            for (i=idx(faces)) [
+                for (j=idx(faces[i]))
+                idxs[offs[i]+j]
+            ]
+        ]
+    ) [
+        nverts,
+        concat(vnf[1],ifaces)
+    ];
+
+
+// Section: VNF Testing and Access
+
+
 // Function: is_vnf()
 // Usage:
 //   bool = is_vnf(x);