Cleanup of path_resample, add tests for round_corners, fix

bezier_curve and arc to always return n points for either endpoint
setting.

beziers.scad

@@ -435,9 +435,11 @@ function bezier_curvature(curve, u) =
 //   bez = [[0,0], [5,15], [40,20], [60,-15], [80,0]];
 //   move_copies(bezier_curve(bez, 8)) sphere(r=1.5, $fn=12);
 //   trace_bezier(bez, N=len(bez)-1);
-function bezier_curve(curve,n,endpoint) = [each bezier_points(curve, [0:1/n:(n-0.5)/n]),
-                                           if (endpoint) curve[len(curve)-1]
-                                          ];
+function bezier_curve(curve,n,endpoint=true) =
+      [
+         each bezier_points(curve, rangex(endpoint?n-1:n,0,1)),
+         if (endpoint) last(curve)
+      ];
 
 // Function: bezier_segment_closest_point()
 // Usage:

paths.scad

@@ -1238,15 +1238,17 @@ module path_extrude(path, convexity=10, clipsize=100) {
 module path_spread(path, n, spacing, sp=undef, rotate_children=true, closed=false)
 {
     length = path_length(path,closed);
-    distances = is_def(sp)? (
-        is_def(n) && is_def(spacing)? range(s=sp, step=spacing, n=n) :
-        is_def(n)? range(s=sp, e=length, n=n) :
-        range(s=sp, step=spacing, e=length)
-    ) : is_def(n) && is_undef(spacing)? (
-        closed?
-            let(range=range(s=0,e=length, n=n+1)) list_head(range) :
-            range(s=0, e=length, n=n)
-    ) : (
+    distances =
+        is_def(sp)? (   // Start point given
+            is_def(n) && is_def(spacing)? range(s=sp, step=spacing, n=n) :
+            is_def(n)? range(s=sp, e=length, n=n) :
+            range(s=sp, step=spacing, e=length)
+        )
+      : is_def(n) && is_undef(spacing)? ( let(a=echo(n=n))  // N alone given
+            closed ? rangex(s=0, e=length, n=n)
+                   : range(s=0, e=length, n=n)
+        )
+      : (      // No start point and spacing is given, N maybe given
         let(
             n = is_def(n)? n : floor(length/spacing)+(closed?0:1),
             ptlist = range(s=0,step=spacing,n=n),
@@ -1600,13 +1602,17 @@ function resample_path(path, N, spacing, closed=false) =
    assert(num_defined([N,spacing])==1,"Must define exactly one of N and spacing")
    assert(is_bool(closed))
    let(
-    length = path_length(path,closed),
-    N = is_def(N) ? N : round(length/spacing) + (closed?0:1), 
-        spacing = length/(closed?N:N-1),     // Note: worried about round-off error, so don't include 
-        distlist = range(closed?N:N-1,step=spacing),  // last point when closed=false
-    cuts = path_cut_points(path, distlist, closed=closed)
+       length = path_length(path,closed),
+       // In the open path case decrease N by 1 so that we don't try to get
+       // path_cut to return the endpoint (which might fail due to rounding)
+       // Add last point later
+       N = is_def(N) ? N-(closed?0:1) : round(length/spacing),
+       distlist = rangex(N,e=length), 
+       cuts = path_cut_points(path, distlist, closed=closed)
    )
-   concat(subindex(cuts,0),closed?[]:[last(path)]);  // Then add last point here
+   [ each subindex(cuts,0),
+     if (!closed) last(path)     // Then add last point here
+   ];
 
 
 

rounding.scad

@@ -346,7 +346,7 @@ function _bezcorner(points, parm) =
                         ] : _smooth_bez_fill(points,parm),
                 N = max(3,$fn>0 ?$fn : ceil(bezier_segment_length(P)/$fs))
         )
-        bezier_curve(P,N,endpoint=true);
+        bezier_curve(P,N+1,endpoint=true);
 
 function _chamfcorner(points, parm) =
         let(

shapes2d.scad

@@ -533,7 +533,7 @@ module dashed_stroke(path, dashpat=[3,3], width=1, closed=false) {
 function arc(N, r, angle, d, cp, points, width, thickness, start, wedge=false, long=false, cw=false, ccw=false, endpoint=true) =
     assert(is_bool(endpoint))
     !endpoint ? assert(!wedge, "endpoint cannot be false if wedge is true")
-               list_head(arc(N,r,angle,d,cp,points,width,thickness,start,wedge,long,cw,ccw,true)) :
+               list_head(arc(N+1,r,angle,d,cp,points,width,thickness,start,wedge,long,cw,ccw,true)) :
     assert(is_undef(N) || is_integer(N), "Number of points must be an integer")
     // First try for 2D arc specified by width and thickness
     is_def(width) && is_def(thickness)? (
@@ -1875,7 +1875,7 @@ function reuleaux_polygon(N=3, r, d, anchor=CENTER, spin=0) =
                 sa = ca + 180 + (90/N),
                 ea = ca + 180 - (90/N),
                 cp = polar_to_xy(r, ca)
-            ) each arc(N=ssegs, r=slen, cp=cp, angle=[sa,ea], endpoint=false)
+            ) each arc(N=ssegs-1, r=slen, cp=cp, angle=[sa,ea], endpoint=false)
         ],
         anchors = [
             for (i = [0:1:N-1]) let(

tests/test_shapes2d.scad

@@ -40,7 +40,7 @@ test_turtle();
 
 module test_arc() {
     assert_approx(arc(N=8, d=100, angle=135, cp=[10,10]), [[60,10],[57.1941665154,26.5139530978],[49.0915741234,41.1744900929],[36.6016038258,52.3362099614],[21.1260466978,58.7463956091],[4.40177619483,59.6856104947],[-11.6941869559,55.0484433951],[-25.3553390593,45.3553390593]]);
-    assert_approx(arc(N=8, d=100, angle=135, cp=[10,10],endpoint=false), [[60,10],[57.1941665154,26.5139530978],[49.0915741234,41.1744900929],[36.6016038258,52.3362099614],[21.1260466978,58.7463956091],[4.40177619483,59.6856104947],[-11.6941869559,55.0484433951]]);    
+    assert_approx(arc(N=8, d=100, angle=135, cp=[10,10],endpoint=false), [[60,10],[57.8470167866,24.5142338627],[51.5734806151,37.778511651],[41.7196642082,48.6505226681],[29.1341716183,56.1939766256],[14.9008570165,59.7592363336],[0.245483899194,59.0392640202],[-13.5698368413,54.0960632174]]);
     assert_approx(arc(N=8, d=100, angle=[45,225], cp=[10,10]), [[45.3553390593,45.3553390593],[26.5139530978,57.1941665154],[4.40177619483,59.6856104947],[-16.6016038258,52.3362099614],[-32.3362099614,36.6016038258],[-39.6856104947,15.5982238052],[-37.1941665154,-6.51395309776],[-25.3553390593,-25.3553390593]]);
     assert_approx(arc(N=8, d=100, start=45, angle=135, cp=[10,10]), [[45.3553390593,45.3553390593],[31.6941869559,55.0484433951],[15.5982238052,59.6856104947],[-1.12604669782,58.7463956091],[-16.6016038258,52.3362099614],[-29.0915741234,41.1744900929],[-37.1941665154,26.5139530978],[-40,10]]);
     assert_approx(arc(N=8, d=100, start=45, angle=-90, cp=[10,10]), [[45.3553390593,45.3553390593],[52.3362099614,36.6016038258],[57.1941665154,26.5139530978],[59.6856104947,15.5982238052],[59.6856104947,4.40177619483],[57.1941665154,-6.51395309776],[52.3362099614,-16.6016038258],[45.3553390593,-25.3553390593]]);