diff --git a/shapes2d.scad b/shapes2d.scad index 45fda07..865a14d 100644 --- a/shapes2d.scad +++ b/shapes2d.scad @@ -1988,6 +1988,84 @@ function reuleaux_polygon(n=3, r, d, anchor=CENTER, spin=0) = +// Function&Module: squircle() +// Synopsis: Creates a shape between a circle and a square, centered on the origin. +// SynTags: Geom, Path +// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable +// See Also: circle(), square(), supershape() +// Usage: As Module +// squircle(squareness, size) [ATTACHMENTS]; +// Usage: As Function +// path = squircle(squareness, size); +// Description: +// A squircle is a shape intermediate between a square/rectangle and a circle/ellipse. A squircle is a special case of supershape (shown in `supershape()` example 3), but this implementation uses a different method that requires just two parameters, and the vertex distribution is optimized for smoothness. +// 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 squircles. +// When called as a module, creates a 2D squircle with the desired squareness. Uses "intersect" type anchoring. +// 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. Default: 0.7 +// size = Bounding box of the squircle, same as the `size` parameter in `square()`, can be a single number or an `[xsize,ysize]` vector. Default: [10,10] +// $fn = Number of points. Special variables `$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 sharper curves. Default if not set: 40 +// Examples(2D): +// squircle(squareness=0.4, size=50); +// squircle(0.8, [80,60], $fn=64); +// Examples(2D): Ten increments of squareness parameter +// for(sq=[0:0.1:1]) +// stroke(squircle(sq, 100, $fn=128), closed=true, width=0.5); +// Examples(2D): Standard vector anchors are based on extents +// squircle(0.8, 50) show_anchors(custom=false); +// Examples(2D): Named anchors exist for the sides and corners +// squircle(0.8, 50) show_anchors(std=false); +module squircle(squareness=0.7, size=[10,10], anchor=CENTER, spin=0) { + check = assert(squareness >= 0 && squareness <= 1); + bbox = is_num(size) ? [size,size] : point2d(size); + assert(all_positive(bbox), "All components of size must be positive."); + path = squircle(squareness, size); + anchors = let(sq = _linearize_squareness(squareness)) [ + for (i = [0:1:3]) let( + ca = 360 - i*90, + cp = polar_to_xy(squircle_radius(sq, bbox[0]/2, ca), ca) + ) named_anchor(str("side",i), cp, unit(cp,BACK), 0), + for (i = [0:1:3]) let( + ca = 360-45 - i*90, + cp = polar_to_xy(squircle_radius(sq, bbox[0]/2, ca), ca) + ) named_anchor(str("corner",i), cp, unit(cp,BACK), 0) + ]; + attachable(anchor,spin, two_d=true, path=path, extent=false, anchors=anchors) { + polygon(path); + children(); + } +} + + +function squircle(squareness=0.7, size=[10,10]) = + assert(squareness >= 0 && squareness <= 1) [ + let( + sq = _linearize_squareness(squareness), + bbox = is_num(size) ? [size,size] : point2d(size), + aspect = bbox[1] / bbox[0], + r = 0.5 * bbox[0], + astep = $fn>=12 ? 90/round($fn/4) : 9 + ) for(a=[360:-astep:0.01]) let( + theta = a + sq * sin(4*a) * 30/PI, // tighter angle steps at corners + p = squircle_radius(sq, r, theta) + ) [p*cos(theta), aspect*p*sin(theta)] +]; + + +function squircle_radius(squareness, r, angle) = let( + s2a = abs(squareness*sin(2*angle)) + ) s2a>0 ? r*sqrt(2)/s2a * sqrt(1 - sqrt(1 - s2a*s2a)) : r; + + +function _linearize_squareness(s) = + // from Chamberlain Fong (2016). "Squircular Calculations". arXiv. + // https://arxiv.org/pdf/1604.02174v5 + let(c = 2 - 2*sqrt(2), d = 1 - 0.5*c*s) + 2 * sqrt((1+c)*s*s - c*s) / (d*d); + + + // Section: Text // Module: text()