diff --git a/drawing.scad b/drawing.scad index 365d6a81..38ab16aa 100644 --- a/drawing.scad +++ b/drawing.scad @@ -710,6 +710,8 @@ module dashed_stroke(path, dashpat=[3,3], width=1, closed=false, fit=true, round // 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. +// . +// The module form with `wedge=false` must have 3 points on the arc to produce non-empty geometry. If you specify `n=2` in this case it is an error. If you use `$fn`, `$fa` and/or `$fs` to control the faceting the point count will be rounded up so that the output always has at least 3 points (2 facets). The functional form does **not** round the point count up to 3, so this means that for small point counts, the module and function will produce different results. // Arguments: // n = Number of vertices to use in the arc. If `wedge=true` you will get `n+1` points. // r = Radius of the arc. @@ -763,11 +765,11 @@ module dashed_stroke(path, dashpat=[3,3], width=1, closed=false, fit=true, round // arc(r=25, angle=[-30,45], rounding=[0,-12, -27], wedge=true); // stroke(arc(r=25, angle=[-30,45], wedge=true), color="red",closed=true, width=.5); -function arc(n, r, angle, d, cp, points, corner, width, thickness, start, wedge=false, long=false, cw=false, ccw=false, endpoint=true, rounding) = +function arc(n, r, angle, d, cp, points, corner, width, thickness, start, wedge=false, long=false, cw=false, ccw=false, endpoint=true, rounding, _minpts=2) = assert(is_bool(endpoint)) !endpoint ? assert(!wedge, "endpoint cannot be false if wedge is true") - list_head(arc(u_add(n,1),r,angle,d,cp,points,corner,width,thickness,start,wedge,long,cw,ccw,true,rounding)) + list_head(arc(u_add(n,1),r,angle,d,cp,points,corner,width,thickness,start,wedge,long,cw,ccw,true,rounding,_minpts)) : assert(is_undef(start) || is_def(angle), "start requires angle") assert(is_undef(angle) || !any_defined([thickness,width,points,corner]), "Cannot give angle with points, corner, width or thickness") @@ -779,7 +781,7 @@ function arc(n, r, angle, d, cp, points, corner, width, thickness, start, wedge= assert(!any_defined([r,cp,points,angle,start]),"Conflicting or invalid parameters to arc") assert(width>0, "Width must be postive") assert(thickness>0, "Thickness must be positive") - arc(n,points=[[width/2,0], [0,thickness], [-width/2,0]],wedge=wedge,rounding=rounding) + arc(n,points=[[width/2,0], [0,thickness], [-width/2,0]],wedge=wedge,rounding=rounding,_minpts=_minpts) : is_def(angle)? let( parmok = !any_defined([points,width,thickness]) && @@ -798,7 +800,8 @@ 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(wedge?2:3,1+segs(r,angle)), //max(3, ceil(segs(r)*abs(angle)/360)), + n = is_def(n) ? assert(n>=_minpts,str("\nThe n parameter must be at least ",_minpts)) n + : max(wedge?2:_minpts,1+segs(r,angle)), arcpoints = [for(i=[0:n-1]) let(theta = start + i*angle/(n-1)) r*[cos(theta),sin(theta)]+cp] ) [ @@ -814,7 +817,7 @@ function arc(n, r, angle, d, cp, points, corner, width, thickness, start, wedge= plane = [corner[2], corner[0], corner[1]], points2d = project_plane(plane, corner) ) - lift_plane(plane,arc(n,corner=points2d,wedge=wedge,r=r, d=d,rounding=rounding)) + lift_plane(plane,arc(n,corner=points2d,wedge=wedge,r=r, d=d,rounding=rounding,_minpts=_minpts)) ) : assert(is_path(corner) && len(corner) == 3) let(col = is_collinear(corner[0],corner[1],corner[2])) @@ -832,7 +835,7 @@ function arc(n, r, angle, d, cp, points, corner, width, thickness, start, wedge= ang_range = dir ? [theta_start, theta_start+angle] : [theta_start+angle, theta_start] ) - arc(n,cp=cp,r=r,angle=ang_range,wedge=wedge,rounding=rounding) + arc(n,cp=cp,r=r,angle=ang_range,wedge=wedge,rounding=rounding,_minpts=_minpts) : assert(is_def(points), "Arc not specified: must give points, angle, or width and thickness") assert(is_path(points,[2,3]),"Point list is invalid") // If arc is 3D, transform points to 2D and make a recursive call, then remap back to 3D @@ -844,7 +847,7 @@ function arc(n, r, angle, d, cp, points, corner, width, thickness, start, wedge= center2d = is_def(cp) ? project_plane(plane,cp) : undef, points2d = project_plane(plane, points) ) - lift_plane(plane,arc(n,cp=center2d,points=points2d,wedge=wedge,long=long,rounding=rounding)) + lift_plane(plane,arc(n,cp=center2d,points=points2d,wedge=wedge,long=long,rounding=rounding,_minpts=_minpts)) : len(points)==2? // Arc defined by center plus two points, will have radius defined by center and points[0] // and extent defined by direction of point[1] from the center @@ -867,7 +870,7 @@ function arc(n, r, angle, d, cp, points, corner, width, thickness, start, wedge= dir*angle, sa = atan2(v1.y,v1.x) ) - arc(n,cp=cp,r=r,start=sa,angle=final_angle,wedge=wedge,rounding=rounding) + arc(n,cp=cp,r=r,start=sa,angle=final_angle,wedge=wedge,rounding=rounding,_minpts=_minpts) : // Final case is arc passing through three points, starting at point[0] and ending at point[3] let(col = is_collinear(points[0],points[1],points[2])) assert(!col, "Collinear inputs do not define an arc") @@ -885,11 +888,11 @@ function arc(n, r, angle, d, cp, points, corner, width, thickness, start, wedge= // generate the proper number of points. ang_range = dir ? [theta_start, theta_start+angle] : [theta_start+angle, theta_start], - arcpts = is_def(rounding)? arc(n,cp=cp,r=r,angle=ang_range,wedge=wedge,rounding=rounding) + arcpts = is_def(rounding)? arc(n,cp=cp,r=r,angle=ang_range,wedge=wedge,rounding=rounding,_minpts=_minpts) : [ if (wedge) cp, points[dir ? 0 : 1], - each select(arc(n,cp=cp,r=r,angle=ang_range),1,-2), + each select(arc(n,cp=cp,r=r,angle=ang_range,_minpts=_minpts),1,-2), points[dir ? 1 : 0] ] ) @@ -898,7 +901,7 @@ 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); + 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, _minpts=3); 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) {