beziers.scad

@@ -634,7 +634,7 @@ function path_to_bezpath(path, closed, tangents, uniform=false, size, relsize) =
                   second + L*tangent2 
                  ],
         select(path,lastpt)
-    ];
+];
 
 
 
@@ -689,8 +689,7 @@ function path_to_bezcornerpath(path, closed, size, relsize) =
             sizevect[i], relative),
         [path[pathlen-1]]
     ]
-    )
+) flatten(roundpath);
-    flatten(roundpath);
 
 
 /// Internal function: _bez_path_corner()
@@ -744,7 +743,9 @@ let(
     // bz6 is p3
     bz3 = p2 + middir * bzdist, // center control point
     bz2 = bz3 + midto12unit*(d1<d3 ? cornerlegmin : cornerlegmax),
-    bz1 = p1 - (d1<=d3 ? leglenmin : leglenmax)*p21unit,
+    bz1 = p1 - (d1<=d3 ? leglenmin :
+        leglenmax)*p21unit,
+        //norm(0.333*(bz2-p1)))*p21unit,
     bz4 = bz3 - midto12unit*(d3<d1 ? cornerlegmin : cornerlegmax),
     bz5 = p3 - (d3<=d1 ? leglenmin : leglenmax)*p23unit
 ) [p1, bz1, bz2, bz3, bz4, bz5]; // do not include last control point

rounding.scad

@@ -735,20 +735,18 @@ function _rounding_offsets(edgespec,z_dir=1) =
 //   pts = [[-3.3, 1.7], [-3.7, -2.2], [3.8, -4.8], [-0.9, -2.4]];
 //   stroke(smooth_path(pts, uniform=false, relsize=0.1),width=.1);
 //   color("red")move_copies(pts)circle(r=.15,$fn=12);
-module smooth_path(path, tangents, size, relsize, method="edges", splinesteps=10, uniform, closed=false) {no_module();}
+module smooth_path(path, tangents, size, relsize, method="edges", splinesteps=10, uniform=false, closed=false) {no_module();}
-function smooth_path(path, tangents, size, relsize, method="edges", splinesteps=10, uniform, closed) =
+function smooth_path(path, tangents, size, relsize, method="edges", splinesteps=10, uniform=false, closed) =
-is_1region(path)
+  is_1region(path) ? smooth_path(path[0], tangents, size, relsize, method, splinesteps, uniform, default(closed,true)) :
-    ? smooth_path(path[0], tangents, size, relsize, method, splinesteps, uniform, default(closed,true))
+  assert(method=="edges" || method=="corners", "method must be \"edges\" or \"corners\".")
-    : assert(method=="edges" || method=="corners", "method must be \"edges\" or \"corners\".")
+  assert(method=="edges" || is_undef(tangent), "The tangents parameter is incompatible with method=\"corners\".")
-assert(method=="edges" || (is_undef(tangents) && is_undef(uniform)), "The tangents and uniform parameters are incompatible with method=\"corners\".")
+  let (
-let (
+     bez = method=="edges" ?
-    uniform = default(uniform,false),
+        path_to_bezpath(path, tangents=tangents, size=size, relsize=relsize, uniform=uniform, closed=default(closed,false))
-    bez = method=="edges"
-        ? path_to_bezpath(path, tangents=tangents, size=size, relsize=relsize, uniform=uniform, closed=default(closed,false))
         : path_to_bezcornerpath(path, size=size, relsize=relsize, closed=default(closed,false)),
      smoothed = bezpath_curve(bez,splinesteps=splinesteps)
-)
+  )
-closed ? list_unwrap(smoothed) : smoothed;
+  closed ? list_unwrap(smoothed) : smoothed;
 
 
 

shapes2d.scad

@@ -1793,7 +1793,7 @@ module glued_circles(r, spread=10, tangent=30, d, anchor=CENTER, spin=0) {
 // Examples(2D):
 //   squircle(size=50, squareness=0.4);
 //   squircle([80,60], 0.7, $fn=64);
-// Example(3D,VPD=48,VPR=[40,0,40],NoAxes): Corner differences between the three squircle styles for squareness=0.5. Style "superellipse" is pink, "fg" is gold, "bezier" is blue.
+// Example(2D,VPD=48,VPR=[40,0,40],NoAxes): Corner differences between the three squircle styles for squareness=0.5. Style "superellipse" is pink, "fg" is gold, "bezier" is blue.
 //   color("pink") squircle(size=50, style="superellipse", squareness=0.5, $fn=256);
 //   color("yellow") up(1) squircle(size=50, style="fg", squareness=0.5, $fn=256);
 //   color("lightblue") up(2) squircle(size=50, style="bezier", squareness=0.5, $fn=256);
@@ -1854,11 +1854,9 @@ function _squircle_fg(size, squareness) = [
     ) p*[cos(theta), aspect*sin(theta)]
 ];
 
-function squircle_radius_fg(squareness, r, angle) =
+function squircle_radius_fg(squareness, r, angle) = let(
-    let(
     s2a = abs(squareness*sin(2*angle))
-    )
+    ) s2a>0 ? r*sqrt(2)/s2a * sqrt(1 - sqrt(1 - s2a*s2a)) : r;
-    s2a>0 ? r*sqrt(2)/s2a * sqrt(1 - sqrt(1 - s2a*s2a)) : r;
 
 function _linearize_squareness(s) =
     // from Chamberlain Fong (2016). "Squircular Calculations". arXiv.
@@ -1886,33 +1884,27 @@ function _squircle_se(size, squareness) = [
     ) [ra*x, rb*y] / r
 ];
 
-function squircle_radius_se(n, r, angle) =
+function squircle_radius_se(n, r, angle) = let(
-    let(
     x = cos(angle),
     y = sin(angle)
-    )
+) (abs(x)^n + abs(y)^n)^(1/n) / r;
-    (abs(x)^n + abs(y)^n)^(1/n) / r;
 
-function _squircle_se_exponent(squareness) =
+function _squircle_se_exponent(squareness) = let(
-    let(
     // limit squareness; error if >0.99889, limit is smaller for r>1
     s=min(0.998,squareness),
     rho = 1 + s*(sqrt(2)-1),
     x = rho / sqrt(2)
-    )
+) log(0.5) / log(x);
-    log(0.5) / log(x);
 
 
 /* Bezier squircle function */
 
-function _squircle_bz(size, squareness) =
+function _squircle_bz(size, squareness) = let(
-    let(
     splinesteps = $fn>=12 ? round($fn/4) : 10,
     size = is_num(size) ? [size,size] : point2d(size),
     sq = square(size, center=true),
     bez = path_to_bezcornerpath(sq, relsize=1-squareness, closed=true)
-    )
+) bezpath_curve(bez, splinesteps=splinesteps);
-    bezpath_curve(bez, splinesteps=splinesteps);