BelfrySCAD · adrianVmariano · Aug 25, 2025 · Aug 23, 2025 · Aug 23, 2025 · Aug 23, 2025
diff --git a/drawing.scad b/drawing.scad
@@ -696,13 +696,20 @@ module dashed_stroke(path, dashpat=[3,3], width=1, closed=false, fit=true, round
 // Usage: as module
 //   arc(...) [ATTACHMENTS];
 // Description:
-//   If called as a function, returns a 2D or 3D path forming an arc.  If `wedge` is true, the centerpoint of the arc appears as the first point in the result.
-//   If called as a module, creates a 2D arc polygon or pie slice shape.  Numerous methods are available to specify the arc.
+//   If called as a function, returns a 2D or 3D path forming an arc.  Numerous methods are available to specify the arc as listed in the Arguments section.
+//   If `wedge` is true, the centerpoint of the arc appears as the first point in the result.
+//   If called as a module, the arc must be 2D and the module creates the 2D arc polygon or pie slice shape.  
 //   .
-//   The `rounding` parameter is permitted only when `wedge=true` and applies specified radius roundings at each of the corners, with `rounding[0]` giving
-//   the rounding at the center point, and then the other two the two outer corners in the direction that the arc travels.  If you don't need to control
-//   the exact point count, you should use `$fs` and `$fa` to control the number of points on the roundings and arc.  If you give `n` then each arc
-//   section in your curve uses `n` points, so the total number of points is `n` times one plus the number of non-zero roundings you specified.
+//   If `endpoint=false`, which is only accepted by the functional form, then the arc stops one step before the final point.  
+//   The `rounding` parameter, which is permitted only when `wedge=true`, applies specified radius roundings at each of the corners, with `rounding[0]` giving
+//   the rounding at the center point, and then the other two the two outer corners in the direction that the arc travels.  
+//   .
+//   If you give `n` for an arc without roundings then the curve of the arc will use `n` points.  If `endpoint=false` the arc still has `n` points, but
+//   they are closer together.  When wedge is true the output has an extra point.  If you use rounding on a wedge then each rounding will have the specified
+//   number of points, but note that the points of adjacent rounded areas overlap.  It may be easier to think that each curve in the output has n-1 facets.  With rounding,
+//   the total number of points on a wedge will be $n + 1 + (n-1) k$ where $k$ is the number of roundings that are nonzero.  
+//   To get enough points on corner roundings you may need an `n` that is very large and produces more points than needed on the main curved portion of the arc.
+//   Using `$fs` and `$fa` makes it possible to have differing numbers of points on the various roundings in your arc based on their radius and angle.
 // Arguments:
 //   n = Number of vertices to use in the arc.  If `wedge=true` you will get `n+1` points.  
 //   r = Radius of the arc.
@@ -791,7 +798,7 @@ function arc(n, r, angle, d, cp, points, corner, width, thickness, start, wedge=
         is_def(rounding) ? assert(wedge,"rounding is only supportd with wedge=true") move(cp,zrot(start,_rounded_arc(r, rounding, angle, n)))
      :
         let(
-            n = is_def(n) ? n : max(3, ceil(segs(r)*abs(angle)/360)),
+            n = is_def(n) ? n : max(wedge?2:3,1+segs(r,angle)), //max(3, ceil(segs(r)*abs(angle)/360)),
             arcpoints = [for(i=[0:n-1]) let(theta = start + i*angle/(n-1)) r*[cos(theta),sin(theta)]+cp]
         )
         [
@@ -892,14 +899,15 @@ function arc(n, r, angle, d, cp, points, corner, width, thickness, start, wedge=
 module arc(n, r, angle, d, cp, points, corner, width, thickness, start, wedge=false, rounding, anchor=CENTER, spin=0)
 {
     path = arc(n=n, r=r, angle=angle, d=d, cp=cp, points=points, corner=corner, width=width, thickness=thickness, start=start, wedge=wedge, rounding=rounding);
-    attachable(anchor,spin, two_d=true, path=path, extent=false) {
-        polygon(path);
+    assert(len(path[0])==2 || sum(v_abs(column(path,2)))==0, "Module form of arc() only works with 2D inputs.");
+    path2d = path2d(path);
+    attachable(anchor,spin, two_d=true, path=path2d, extent=false) {
+        polygon(path2d);
         children();
     }
 }
 
 
-
 
 function _rounded_arc(radius, rounding=0, angle, n) =
     assert(is_finite(angle) && abs(angle)<360, "angle must be strictly between -360 and 360")
@@ -928,7 +936,6 @@ function _rounded_arc(radius, rounding=0, angle, n) =
 
         edge_gap1=radius-arc1_cut-radius_of_ctrpt_edge,
         edge_gap2=radius-arc2_cut-radius_of_ctrpt_edge,
-
         angle_span1 = rounding[1]>0 ? [-dir*90, dir*arc1_angle] : -[dir*90, dir*180 - arc1_angle],
         angle_span2 = [angle-dir*arc2_angle + (rounding[2]<0 ? dir*180 : 0), angle+dir*90]
     )
@@ -942,10 +949,12 @@ function _rounded_arc(radius, rounding=0, angle, n) =
                                    polar_to_xy(r=radius_of_ctrpt_edge, theta=0)],
                                    endpoint=edge_gap1!=0,n=n)
            else repeat([0,0],rounding[0]>0 && abs(angle)==180 && is_def(n) ? n : 1),                        
-      each if (rounding[1]!=0) arc(r=abs(rounding[1]),cp=pt1,angle=angle_span1,endpoint=dir*arc1_angle==angle,n=n), // first corner
+      each if (rounding[1]!=0) arc(r=abs(rounding[1]),cp=pt1,angle=angle_span1,
+                                   endpoint=dir*arc1_angle==angle,n=u_add(n,dir*arc1_angle==angle?0:-1)),            // first corner
       each if (arc1_angle+arc2_angle<abs(angle))
-                      arc(r=radius, angle=[dir*arc1_angle,angle - dir*arc2_angle], endpoint=rounding[2]==0, n=n),   // main arc section
-      each if (rounding[2]!=0) arc(r=abs(rounding[2]),cp=pt3,  angle=angle_span2, endpoint=edge_gap2!=0, n=n)       // second corner
+                      arc(r=radius, angle=[dir*arc1_angle,angle - dir*arc2_angle], endpoint=rounding[2]==0,    // main arc section
+                          n=u_add(n,rounding[2]==0?0:-1)),   
+      each if (rounding[2]!=0) arc(r=abs(rounding[2]),cp=pt3,  angle=angle_span2, endpoint=edge_gap2!=0, n=n)  // second corner
     ];
 
 

diff --git a/gears.scad b/gears.scad
@@ -934,6 +934,8 @@ function spur_gear(
     let(
         profile_shift = auto_profile_shift(teeth,PA,helical,profile_shift=profile_shift),
         pr = pitch_radius(circ_pitch, teeth, helical),
+                feee=echo(pr_spur = pr, circ_pitch, teeth, helical), 
+
         or = outer_radius(circ_pitch, teeth, helical=helical, profile_shift=profile_shift, internal=internal,shorten=shorten),
         rr = _root_radius_basic(circ_pitch, teeth, clearance, profile_shift=profile_shift, internal=internal),
         anchor_rad = atype=="pitch" ? pr
@@ -2772,10 +2774,21 @@ function worm(
                 profile_shift=0
             ), 1, -2)
         ),
+
         rack_profile = [
             for (t = xcopies(trans_pitch, n=2*ceil(l/trans_pitch)+1))
                 each apply(t, tooth)
         ],
+        nrp = select(rack2d(
+                pitch=circ_pitch,
+                teeth=2*ceil(l/trans_pitch)+1,
+                pressure_angle=PA,
+                clearance=clearance,
+                backlash=backlash,
+                helical=helical,
+                profile_shift=0
+            ), 1, -2),
+        ff=echo(tooth=tooth, rack_profile=rack_profile,nrp=nrp), 
         steps = max(36, segs(d/2)),
         step = 360 / steps,
         zsteps = ceil(l / trans_pitch / starts * steps),
@@ -3139,43 +3152,49 @@ function worm_gear(
     let(
         gear_arc = 2 * PA,
         helical = asin(worm_starts * circ_pitch / PI / worm_diam),
+        //fee=echo(helical=helical), 
         full_tooth = apply(
             zrot(90) * scale(0.99),
             _gear_tooth_profile(
                 circ_pitch, teeth=teeth,
                 pressure_angle=PA,
                 profile_shift=-profile_shift,
                 clearance=clearance,
-                helical=helical,
+                helical=helical, internal=false,
                 center=true
             )
         ),
         ftl = len(full_tooth),
         tooth_half1 = (select(full_tooth, 0, ftl/2-1)),
         tooth_half2 = (select(full_tooth, ftl/2, -1)),
         tang = 360 / teeth,
-        rteeth = quantdn(teeth * gear_arc / 360, 2) / 2 + 0.5,
+        rteeth = (quantdn(teeth * gear_arc / 360, 2) / 2 + 0.5),
         pr = pitch_radius(circ_pitch, teeth, helical=helical),
+        //feee=echo(pr_worm = pr, circ_pitch, teeth, helical), 
+        circum = 2*PI*pr,
+        tan_helical = tan(helical),
         oslices = slices * 4,
         rows = [
             for (data = [[tooth_half1,1], [tooth_half2,-1]])
             let (
-                tooth_half = data[0],
+                tooth_half = (data[0]),
                 dir = data[1]
             )
             for (pt = tooth_half) [
                 for (i = [0:1:oslices])
                 let (
                     u = i / oslices,
                     w_ang = worm_arc * (u - 0.5),
-                    g_ang_delta = w_ang/360 * tang * worm_starts * (left_handed?1:-1),
-                    m = zrot(dir*rteeth*tang+g_ang_delta, cp=[worm_diam/2+pr,0,0]) *
+                    g_ang_delta = w_ang/360 * tang * worm_starts * (left_handed?1:-1) *0 ,
+                    m = //zrot(dir*rteeth*tang+g_ang_delta, cp=[worm_diam/2+pr,0,0]) *
                         left(crowning) *
                         yrot(w_ang) *
                         right(worm_diam/2+crowning) *
-                        zrot(-dir*rteeth*tang+g_ang_delta, cp=[pr,0,0]) *
-                        xrot(180)
-                ) apply(m, point3d(pt))
+                        //zrot(-dir*rteeth*tang+g_ang_delta, cp=[pr,0,0]) *
+                        xrot(180),
+                   pt = apply(m, point3d(pt)),
+                   angled_pt = zrot((left_handed?-1:1)*360*pt.z*tan_helical/circum,pt,cp=[worm_diam/2+pr,0,0])
+                ) angled_pt
             ]
         ],
         midrow = len(rows)/2,

diff --git a/masks3d.scad b/masks3d.scad
@@ -297,7 +297,7 @@ module rounding_edge_mask(l, r, ang, r1, r2, excess=0.01, d1, d2,d,r,length, h,
             assert(all_positive([length]), "length/l/h/height must be a positive value")
             assert(is_finite(ang) && ang>0 && ang<180, "ang must be a number between 0 and 180")
             assert(all_nonnegative([chamfer1,chamfer2,rounding1,rounding2]), "chamfers and roundings must be nonnegative");
-    steps = ceil(segs(max(r1,r2))*(180-ang)/360);
+    steps = max(2,segs(max(r1,r2), 180-ang)); 
     function make_path(r) =
          r==0 ? repeat([0,0],steps+1)
               : arc(n=steps+1, r=r, corner=[polar_to_xy(r,ang),[0,0],[r,0]]);

diff --git a/regions.scad b/regions.scad
@@ -1016,7 +1016,7 @@ function offset(
     path, r=undef, delta=undef, chamfer=false,
     closed=true, check_valid=true,
     quality=1, error=true, return_faces=false, firstface_index=0,
-    flip_faces=false, same_length=false
+    flip_faces=false, same_length=false, _reduce_output_count=false
 ) =
     assert(!(same_length && return_faces), "\nCannot combine return_faces with same_length.")
     is_region(path)?
@@ -1097,7 +1097,7 @@ function offset(
                                             goodsegs[i][0]-goodpath[i]))
                     assert(!outsidecorner[i] || vang!=0,    // If outsidecorner[i] is true then vang>0 needed to give valid step count
                            "\nOffset computation failed, probably because validity check mistakenly removed a valid segment.  Increasing quality might fix this.")
-                    1+floor(segs(r)*vang/360)
+                    segs(r,vang)+(_reduce_output_count ? 0 : 1)
                 ],
         // newcorners is a list where each entry is a list of the points that correspond to a single point in the sharpcorners 
         // list: newcorners[i] is the point list that replaces goodpath[i].  Without rounding or chamfering (or reversals),
@@ -1134,7 +1134,7 @@ function offset(
                   )
                   arc(cp=goodpath[i], cw=cw, ccw=ccw,
                       points=basepts,
-                      n=steps[i]+3)
+                      n=steps[i])
               ],
         pointcount = [for(entry=newcorners) len(entry)],
         edges = flatten(newcorners),

diff --git a/rounding.scad b/rounding.scad
@@ -1679,7 +1679,7 @@ function _make_offset_polyhedron(path,offsets, offset_type, flip_faces, quality,
                     check_valid=check_valid, quality=quality,
                     return_faces=true,
                     firstface_index=vertexcount,
-                    flip_faces=flip_faces
+                    flip_faces=flip_faces, _reduce_output_count=true
             )
         )
         _make_offset_polyhedron(
@@ -4180,6 +4180,7 @@ function _prism_fillet_prism(name, basepoly, bot, top, d, k, N, overlap, uniform
 //   ---
 //   shift1 = shift connection point on object1, a scalar for cylinders, extrusions, or edges, a 2-vector for faces, not permitted for spheres
 //   shift2 = shift connection point on object2, a scalar for cylinders, extrusions, or edges, a 2-vector for faces, not permitted for spheres
+//   shift = shift connection point on both objects; the shift must be valid for both object types
 //   spin_align = align the spin of the connecting prism to specified object (1 or 2) or if you give 12 or 21, the average of the two spins.  Default: 1
 //   scale = scale the profile by this factor at anchor2.  Default: 1
 //   n = number of facets to use for the fillets.  Default: 15
@@ -4658,7 +4659,7 @@ function _find_center_anchor(desc1, desc2, anchor2, flip) =
 
 
 
-module prism_connector(profile, desc1, anchor1, desc2, anchor2, shift1=0, shift2=0, spin_align=1,
+module prism_connector(profile, desc1, anchor1, desc2, anchor2, shift1, shift2, shift, spin_align=1,
                        scale=1,
                        fillet, fillet1, fillet2,
                        overlap, overlap1, overlap2,
@@ -4667,6 +4668,8 @@ module prism_connector(profile, desc1, anchor1, desc2, anchor2, shift1=0, shift2
                        smooth_normals, smooth_normals1, smooth_normals2, 
                        debug=false, debug_pos=false)
 {
+    shift1_input = first_defined([shift1,shift,0]);
+    shift2_input = first_defined([shift2,shift,0]);
     base_fillet = first_defined([fillet1,fillet,0]);
     aux_fillet = first_defined([fillet2,fillet,0]);
 
@@ -4716,7 +4719,7 @@ module prism_connector(profile, desc1, anchor1, desc2, anchor2, shift1=0, shift2
     base_anch_pos = base_anch[1];
     base_anch_dir = base_anch[2];
 
-    prelim_shift1 = _check_join_shift(1,base_type,shift1,true);
+    prelim_shift1 = _check_join_shift(1,base_type,shift1_input,true);
     shift1 = corrected_base_anchor ? corrected_base_anchor[1] + prelim_shift1 : prelim_shift1;
     aux_type = _get_obj_type(2,aux[1],aux_anchor,profile);
     aux_anch = _find_anchor(aux_anchor, aux[1]);
@@ -4727,7 +4730,7 @@ module prism_connector(profile, desc1, anchor1, desc2, anchor2, shift1=0, shift2
     aux_spin = aux_anch[3];
     aux_spin_dir = apply(rot(from=UP,to=aux_anch[2])*zrot(aux_spin),BACK);
     aux_axis = aux_type=="cyl" ? aux[1][5] : RIGHT;
-    prelim_shift2 = _check_join_shift(2,aux_type,shift2,false);
+    prelim_shift2 = _check_join_shift(2,aux_type,shift2_input,false);
     shift2 = corrected_aux_anchor ? corrected_aux_anchor[1] + prelim_shift2 : prelim_shift2;
 
 

diff --git a/tests/test_drawing.scad b/tests/test_drawing.scad
@@ -46,7 +46,7 @@ module test_arc() {
     assert_approx(arc(n=8, width=100, thickness=30), [[50,-3.5527136788e-15],[39.5300788555,13.9348601124],[25.3202618476,24.0284558904],[8.71492362453,29.3258437015],[-8.71492362453,29.3258437015],[-25.3202618476,24.0284558904],[-39.5300788555,13.9348601124],[-50,-1.42108547152e-14]]);
     assert_approx(arc(n=8, cp=[10,10], points=[[45,45],[-25,45]]), [[45,45],[36.3342442379,51.9107096148],[26.3479795075,56.7198412457],[15.5419588213,59.1862449514],[4.45804117867,59.1862449514],[-6.34797950747,56.7198412457],[-16.3342442379,51.9107096148],[-25,45]]);
     assert_approx(arc(n=24, cp=[10,10], points=[[45,45],[-25,45]], long=true), [[45,45],[51.3889035257,37.146982612],[56.0464336973,28.1583574081],[58.7777575294,18.4101349813],[59.4686187624,8.31010126292],[58.0901174104,-1.71924090789],[54.6999187001,-11.2583458482],[49.4398408296,-19.9081753929],[42.5299224539,-27.3068913894],[34.2592180667,-33.1449920477],[24.9737063235,-37.1782589647],[15.0618171232,-39.2379732261],[4.93818287676,-39.2379732261],[-4.97370632349,-37.1782589647],[-14.2592180667,-33.1449920477],[-22.5299224539,-27.3068913894],[-29.4398408296,-19.9081753929],[-34.6999187001,-11.2583458482],[-38.0901174104,-1.71924090789],[-39.4686187624,8.31010126292],[-38.7777575294,18.4101349813],[-36.0464336973,28.1583574081],[-31.3889035257,37.146982612],[-25,45]]);
-    assert_approx(arc($fn=24, cp=[10,10], points=[[45,45],[-25,45]], long=true), [[45,45],[53.2421021636,34.0856928585],[58.1827254512,21.3324740498],[59.4446596304,7.71403542491],[56.9315576496,-5.72987274525],[50.8352916125,-17.9728253654],[41.6213035891,-28.0800887515],[29.9930697126,-35.2799863457],[16.8383906815,-39.0228152281],[3.16160931847,-39.0228152281],[-9.9930697126,-35.2799863457],[-21.6213035891,-28.0800887515],[-30.8352916125,-17.9728253654],[-36.9315576496,-5.72987274525],[-39.4446596304,7.71403542491],[-38.1827254512,21.3324740498],[-33.2421021636,34.0856928585],[-25,45]]);
+    assert_approx(arc($fn=24, cp=[10,10], points=[[45,45],[-25,45]], long=true),[[45,45],[52.8660704987,34.7487373415],[57.8108891325,22.8108891325],[59.4974746831,10],[57.8108891325,-2.81088913246],[52.8660704987,-14.7487373415],[45,-25],[34.7487373415,-32.8660704987],[22.8108891325,-37.8108891325],[10,-39.4974746831],[-2.81088913246,-37.8108891325],[-14.7487373415,-32.8660704987],[-25,-25],[-32.8660704987,-14.7487373415],[-37.8108891325,-2.81088913246],[-39.4974746831,10],[-37.8108891325,22.8108891325],[-32.8660704987,34.7487373415],[-25,45]]);
 }
 test_arc();