From cba3391131358c114d80001fdf0bbeef96222298 Mon Sep 17 00:00:00 2001 From: Alex Matulich Date: Mon, 9 Dec 2024 20:40:42 -0800 Subject: [PATCH] Replaced override anchoring with builtin perimeter anchoring, minor fixes, documentation cleanup --- shapes2d.scad | 72 +++++++++++++++++++-------------------------------- 1 file changed, 26 insertions(+), 46 deletions(-) diff --git a/shapes2d.scad b/shapes2d.scad index 8688c2c..11fb6e6 100644 --- a/shapes2d.scad +++ b/shapes2d.scad @@ -1994,97 +1994,77 @@ function reuleaux_polygon(n=3, r, d, anchor=CENTER, spin=0) = // Topics: Shapes (2D), Paths (2D), Path Generators, Attachable // See Also: circle(), square(), supershape() // Usage: As Module -// squircle(squareness, size, [style]) [ATTACHMENTS]; +// squircle(size, [squareness], [style]) [ATTACHMENTS]; // Usage: As Function -// path = squircle(squareness, size, [style]); +// path = squircle(size, [squareness], [style]); // Description: // A [squircle](https://en.wikipedia.org/wiki/Squircle) is a shape intermediate between a square/rectangle and a circle/ellipse.Squircles are sometimes used to make dinner plates (more area for the same radius as a circle), keyboard buttons, and smartphone icons. Old CRT television screens also resembled elongated squircles. // . -// There are multiple approaches to constructing a squircle. One approach is a special case of superellipse (shown in {{supershape}} example 3), and uses exponents to adjust the shape. Another, called Fernández-Guasti squircle or FG squircle, arises from work in optics and uses a "squareness" parameter between 0 and 1 to adjust the shape. +// There are multiple approaches to constructing a squircle. One approach is a special case of superellipse (shown in {{supershape}} example 3), and uses exponents between 2 and infinity to adjust the shape. Another, the Fernández-Guasti squircle or FG squircle, arises from work in optics and uses a "squareness" parameter between 0 and 1 to adjust the shape. We use the same squareness parameter for both types, adjusting the internal FG parameter or superellipse exponent as needed to achieve the same squircle corner extents. // . // The FG style and superellipse style squircles are visually almost indistinguishable, with the superellipse having slightly rounder "corners" than FG for a given value of squareness. Either style requires just the two parameters `squareness` and `size`. The vertex distribution is adjusted to be more dense at the corners for smoothness at low values of `$fn`. // . // When called as a module, creates a 2D squircle with the desired squareness. // When called as a function, returns a 2D path for a squircle. // Arguments: -// squareness = Value between 0 and 1. Controls the shape of the squircle. When `squareness=0` the shape is a circle, and when `squareness=1` the shape is a square. Otherwise, this parameter sets the location of a squircle "corner" at the specified interpolated position between a circle and a square. For the "superellipse" style, the special case where the superellipse exponent is 4 (also known as *Lamé's quartic curve*) results in a squircle at the geometric mean between radial points on the circle and square, corresponding to squareness=0.456786. Default: 0.5 -// size = Same as the `size` parameter in `square()`, can be a single number or an `[xsize,ysize]` vector. Default: [1,1] +// size = Same as the `size` parameter in `square()`, can be a single number or a vector `[xsize,ysize]`. +// squareness = Value between 0 and 1. Controls the shape, setting the location of a squircle "corner" at the specified interpolated position between a circle and a square. When `squareness=0` the shape is a circle, and when `squareness=1` the shape is a square. For the "superellipse" style, the special case where the superellipse exponent is 4 (also known as *Lamé's quartic curve*) results in a squircle at the geometric mean between radial points on the circle and square, corresponding to squareness=0.456786. Default: 0.5 // style = method for generating a squircle, "fg" for Fernández-Guasti and "superellipse" for superellipse. Default: "fg" // atype = anchor type, "box" for bounding box corners and sides, "perim" for the squircle corners -// $fn = Number of points. The special variables `$fs` and `$fa` are ignored. If set, `$fn` must be 12 or greater, and is rounded to the nearest multiple of 4. Points are generated non-uniformly around the squircle so they are more dense at sharper curves. Default if not set: 40 +// $fn = Number of points. The special variables `$fs` and `$fa` are ignored. If set, `$fn` must be 12 or greater, and is rounded to the nearest multiple of 4. Points are generated so they are more dense around sharper curves. Default if not set: 48 // Examples(2D): -// squircle(squareness=0.4, size=50); -// squircle(0.8, [80,60], $fn=64); +// squircle(size=50, squareness=0.4); +// squircle([80,60], 0.7, $fn=64); // Examples(2D): Ten increments of squareness parameter for a superellipse squircle // for(sq=[0:0.1:1]) -// stroke(squircle(sq, 100, style="superellipse", $fn=128), closed=true, width=0.5); +// stroke(squircle(100, sq, style="superellipse", $fn=128), closed=true, width=0.5); // Examples(2D): Standard vector anchors are based on the bounding box -// squircle(0.6, 50) show_anchors(); +// squircle(50, 0.6) show_anchors(); // Examples(2D): Perimeter anchors, anchoring at bottom left and spinning 20° -// squircle(0.5, [60,40], anchor=(BOTTOM+LEFT), atype="perim", spin=20) +// squircle([60,40], 0.5, anchor=(BOTTOM+LEFT), atype="perim", spin=20) // show_anchors(); -module squircle(squareness=0.5, size=[1,1], style="fg", atype="box", anchor=CENTER, spin=0) { +module squircle(size, squareness=0.5, style="fg", atype="box", anchor=CENTER, spin=0) { check = assert(squareness >= 0 && squareness <= 1); anchorchk = assert(in_list(atype, ["box", "perim"])); size = is_num(size) ? [size,size] : point2d(size); assert(all_positive(size), "All components of size must be positive."); + path = squircle(size, squareness, style, atype, _module_call=true); if (atype == "box") { - path = squircle(squareness, size, style); - attachable(anchor, spin, two_d=true, size=size) { + attachable(anchor, spin, two_d=true, size=size, extent=false) { polygon(path); children(); } } else { // atype=="perim" - override_path = squircle(squareness, size, style, atype, _return_override=true); - attachable(anchor, spin, two_d=true, size=size, extent=false, override=override_path[1]) { - polygon(override_path[0]); + attachable(anchor, spin, two_d=true, extent=true, path=path) { + polygon(path); children(); } } } -function squircle(squareness=0.5, size=[1,1], style="fg", atype="box", anchor=CENTER, spin=0, _return_override=false) = +function squircle(size, squareness=0.5, style="fg", atype="box", anchor=CENTER, spin=0, _module_call=false) = assert(squareness >= 0 && squareness <= 1) - assert(is_num(size) || is_vector(size,2)) + assert(is_num(size) || is_vector(size,2)) assert(in_list(atype, ["box", "perim"])) let( - path = - style == "fg" ? _squircle_fg(squareness, size) - : style == "superellipse" ? _squircle_se(squareness, size) - : assert(false, "Style must be \"fg\" or \"superellipse\""), size = is_num(size) ? [size,size] : point2d(size), - a = 0.5 * size[0], - b = 0.5 * size[1], - override = atype == "box" ? undef - : let( - sn = style=="fg" ? _linearize_squareness(squareness) - : _squircle_se_exponent(squareness), - derivq1 = style=="fg" ? // 1+derivative of squircle in first quadrant - function (x) let(s2=sn*sn, a2=a*a, b2=b*b, x2=x*x, denom=a2-s2*x2) a2*b*(s2-1)*x/(denom*denom*sqrt((a2-x2)/denom)) + 1 - : function (x) let(n=sn) 1 - (b/a)*((a/x)^n - 1)^(1/n-1), - xc = root_find(derivq1, 0.01, a-0.01), // find where slope=-1 - yc = style=="fg" ? - let(s2=sn*sn, a2=a*a, b2=b*b, x2=xc*xc) sqrt(b2*(a2-x2)/(a2-s2*x2)) - : b*(1-(xc/a)^sn)^(1/sn), - corners = [[xc,yc], [-xc,yc], [-xc,-yc], [xc,-yc]], - anchorpos = [[1,1],[-1,1],[-1,-1],[1,-1]] - ) [ for(i=[0:3]) [anchorpos[i], [corners[i]]] ] - ) _return_override - ? [reorient(anchor, spin, two_d=true, size=size, p=path, extent=false, override=override), override] - : reorient(anchor, spin, two_d=true, size=size, p=path, extent=false, override=override); + path = style == "fg" ? _squircle_fg(size, squareness) + : style == "superellipse" ? _squircle_se(size, squareness) + : assert(false, "Style must be \"fg\" or \"superellipse\""), + ) reorient(anchor, spin, two_d=true, size=atype=="box"?size:undef, path=_module_call?undef:path, p=path, extent=true); /* FG squircle functions */ -function _squircle_fg(squareness, size) = [ +function _squircle_fg(size, squareness) = [ let( sq = _linearize_squareness(squareness), size = is_num(size) ? [size,size] : point2d(size), aspect = size[1] / size[0], r = 0.5 * size[0], - astep = $fn>=12 ? 90/round($fn/4) : 9 + astep = $fn>=12 ? 90/round($fn/4) : 360/48 ) for(a=[360:-astep:0.01]) let( theta = a + sq * sin(4*a) * 30/PI, // tighter angle steps at corners p = squircle_radius_fg(sq, r, theta) @@ -2104,13 +2084,13 @@ function _linearize_squareness(s) = /* Superellipse squircle functions */ -function _squircle_se(squareness, size) = [ +function _squircle_se(size, squareness) = [ let( n = _squircle_se_exponent(squareness), size = is_num(size) ? [size,size] : point2d(size), ra = 0.5*size[0], rb = 0.5*size[1], - astep = $fn>=12 ? 90/round($fn/4) : 9, + astep = $fn>=12 ? 90/round($fn/4) : 360/48, fgsq = _linearize_squareness(min(0.998,squareness)) // works well for distributing theta ) for(a=[360:-astep:0.01]) let( theta = a + fgsq*sin(4*a)*30/PI, // tighter angle steps at corners