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Replaced override anchoring with builtin perimeter anchoring, minor fixes, documentation cleanup

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Alex Matulich 2024-12-09 20:40:42 -08:00
parent 835cbc0f00
commit cba3391131
1 changed files with 26 additions and 46 deletions
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shapes2d.scad
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@ -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