Fix short taper bug for spiral_sweep()

Doc fixes

math.scad

@@ -101,7 +101,7 @@ function lerp(a,b,u) =
 // Description:
 //   Returns exactly `n` values, linearly interpolated between `a` and `b`.
 //   If `endpoint` is true, then the last value will exactly equal `b`.
-//   If `endpoint` is false, then the last value will about `a+(b-a)*(1-1/n)`.
+//   If `endpoint` is false, then the last value will be `a+(b-a)*(1-1/n)`.
 // Arguments:
 //   a = First value or vector.
 //   b = Second value or vector.

skin.scad

@@ -1026,6 +1026,8 @@ module rotate_sweep(
 function _taperfunc(x) =
      let(higofs = pow(0.05,2))   // Smallest hig scale is the square root of this value
      sqrt((1-higofs)*x+higofs);
+function _taperfunc(x) =
+     sqrt(1-(1-x)^2);
 function _ss_polygon_r(N,theta) =
         let( alpha = 360/N )
         cos(alpha/2)/(cos(posmod(theta,alpha)-alpha/2));
@@ -1045,7 +1047,7 @@ function spiral_sweep(poly, h, r, turns=1, higbee, center, r1, r2, d, d1, d2, hi
         sides = segs(max(r1,r2)),
         dir = sign(twist),
         ang_step = 360/sides*dir,
-        anglist = [for(ang = [0:ang_step:twist-EPSILON]) ang,
+        orig_anglist = [for(ang = [0:ang_step:twist-EPSILON]) ang,
                         twist],
         higbee1 = first_defined([higbee1, higbee, 0]),
         higbee2 = first_defined([higbee2, higbee, 0]),
@@ -1056,11 +1058,20 @@ function spiral_sweep(poly, h, r, turns=1, higbee, center, r1, r2, d, d1, d2, hi
     assert(higang1 < dir*twist/2,"Higbee1 is more than half the threads")
     assert(higang2 < dir*twist/2,"Higbee2 is more than half the threads")
     let(
+        // This complicated sampling scheme is designed to ensure that there is always a facet boundary
+        // at the $fn specified location, regardless of what kind of subsampling occurs for tapers."
+        anglist = [
+           for(a=orig_anglist) if (a*dir<higang1-EPSILON) a,
+           dir*higang1,
+           for(a=orig_anglist) if (a*dir>higang1+EPSILON && (twist-a)*dir>higang2+EPSILON) a,
+           twist-dir*higang2,
+           for(a=orig_anglist) if ((twist-a)*dir<higang2-EPSILON) a
+        ],
         interp_ang = [
                       for(i=idx(anglist,e=-2))
                           each lerpn(anglist[i],anglist[i+1],
-                                     (higang1>0 && higang1>dir*anglist[i+1]
-                                      || (higang2>0 && higang2>dir*(twist-anglist[i]))) ? ceil((anglist[i+1]-anglist[i])/ang_step*higsample)
+                                         (higang1>0 && dir*anglist[i+1]<=higang1) || (higang2>0 && dir*(twist-anglist[i])<=higang2)
+                                            ? ceil((anglist[i+1]-anglist[i])/ang_step*higsample)
                                             : 1,
                                      endpoint=false),
                       last(anglist)
@@ -1082,7 +1093,7 @@ function spiral_sweep(poly, h, r, turns=1, higbee, center, r1, r2, d, d1, d2, hi
             ) pts
         ],
         vnf = vnf_vertex_array(
-            points, col_wrap=true, caps=true, reverse=dir>0?true:false,
+            points, col_wrap=true, caps=true, reverse=dir>0,
         //    style=higbee1>0 || higbee2>0 ? "quincunx" : "alt"
             style="convex"
         )

vectors.scad

@@ -1,7 +1,7 @@
 //////////////////////////////////////////////////////////////////////
 // LibFile: vectors.scad
 //   This file provides some mathematical operations that apply to each
-//   entry in a vector.  It provides normalizatoin and angle computation, and
+//   entry in a vector.  It provides normalization and angle computation, and
 //   it provides functions for searching lists of vectors for matches to
 //   a given vector.  
 // Includes: