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Merge pull request #1524 from amatulic/anachronist_dev
Formatting improvements to squircle() as suggested in discussion
This commit is contained in:
Revar Desmera
GitHub
commit
f152d9ec63
1 changed files with 130 additions and 127 deletions
257
shapes2d.scad
257
shapes2d.scad
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@ -1751,6 +1751,136 @@ module glued_circles(r, spread=10, tangent=30, d, anchor=CENTER, spin=0) {
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}
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// Function&Module: squircle()
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// Synopsis: Creates a shape between a circle and a square, centered on the origin.
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// SynTags: Geom, Path
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// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable
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// See Also: circle(), square(), supershape()
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// Usage: As Module
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// squircle(size, [squareness], [style]) [ATTACHMENTS];
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// Usage: As Function
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// path = squircle(size, [squareness], [style]);
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// Description:
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// 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.
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// .
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// Multiple definitions exist for the squircle. We support two versions: the superellipse {{supershape()}} Example 3, also known as the Lamé upper squircle), and the Fernandez-Guasti squircle. They are visually almost indistinguishable, with the superellipse having slightly rounder "corners" than FG at the same corner radius. These two squircles have different, unintuitive methods for controlling how square or circular the shape is. A `squareness` parameter determines the shape, specifying the corner position linearly, with 0 being on the circle and 1 being the square. Vertices are positioned to be more dense near the corners to preserve smoothness at low values of `$fn`'.
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// .
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// For the "superellipse" style, the special case where the superellipse exponent is 4 results in a squircle at the geometric mean between radial points on the circle and square, corresponding to squareness=0.456786.
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// .
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// When called as a module, creates a 2D squircle with the desired squareness.
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// When called as a function, returns a 2D path for a squircle.
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// Arguments:
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// size = Same as the `size` parameter in `square()`, can be a single number or a vector `[xsize,ysize]`.
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// 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. Default: 0.5
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// ---
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// style = method for generating a squircle, "fg" for Fernández-Guasti and "superellipse" for superellipse. Default: "fg"
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// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
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// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#subsection-spin). Default: `0`
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// atype = anchor type, "box" for bounding box corners and sides, "perim" for the squircle corners. Default: "box"
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// $fn = Number of points. The special variables `$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
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// Examples(2D):
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// squircle(size=50, squareness=0.4);
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// squircle([80,60], 0.7, $fn=64);
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// Example(2D,VPD=265,NoAxes): Ten increments of squareness parameter for a superellipse squircle
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// color("green") for(sq=[0:0.1:1])
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// stroke(squircle(100, sq, style="superellipse", $fn=96), closed=true, width=0.5);
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// Example(2D): Standard vector anchors are based on the bounding box
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// squircle(50, 0.6) show_anchors();
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// Example(2D): Perimeter anchors, anchoring at bottom left and spinning 20°
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// squircle([60,40], 0.5, anchor=(BOTTOM+LEFT), atype="perim", spin=20)
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// show_anchors();
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module squircle(size, squareness=0.5, style="fg", anchor=CENTER, spin=0, atype="box" ) {
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check = assert(squareness >= 0 && squareness <= 1);
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anchorchk = assert(in_list(atype, ["box", "perim"]));
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size = is_num(size) ? [size,size] : point2d(size);
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assert(all_positive(size), "All components of size must be positive.");
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path = squircle(size, squareness, style, atype="box");
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if (atype == "box") {
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attachable(anchor, spin, two_d=true, size=size, extent=false) {
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polygon(path);
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children();
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}
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} else { // atype=="perim"
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attachable(anchor, spin, two_d=true, extent=true, path=path) {
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polygon(path);
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children();
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}
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}
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}
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function squircle(size, squareness=0.5, style="fg", anchor=CENTER, spin=0, atype="box") =
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assert(squareness >= 0 && squareness <= 1)
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assert(is_num(size) || is_vector(size,2))
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assert(in_list(atype, ["box", "perim"]))
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let(
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size = is_num(size) ? [size,size] : point2d(size),
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path = style == "fg" ? _squircle_fg(size, squareness)
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: style == "superellipse" ? _squircle_se(size, squareness)
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: assert(false, "Style must be \"fg\" or \"superellipse\"")
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) reorient(anchor, spin, two_d=true, size=atype=="box"?size:undef, path=atype=="box"?undef:path, p=path, extent=true);
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/* FG squircle functions */
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function _squircle_fg(size, squareness) = [
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let(
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sq = _linearize_squareness(squareness),
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size = is_num(size) ? [size,size] : point2d(size),
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aspect = size[1] / size[0],
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r = 0.5 * size[0],
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astep = $fn>=12 ? 90/round($fn/4) : 360/48
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) for(a=[360:-astep:0.01]) let(
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theta = a + sq * sin(4*a) * 30/PI, // tighter angle steps at corners
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p = squircle_radius_fg(sq, r, theta)
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) p*[cos(theta), aspect*sin(theta)]
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];
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function squircle_radius_fg(squareness, r, angle) = let(
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s2a = abs(squareness*sin(2*angle))
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) s2a>0 ? r*sqrt(2)/s2a * sqrt(1 - sqrt(1 - s2a*s2a)) : r;
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function _linearize_squareness(s) =
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// from Chamberlain Fong (2016). "Squircular Calculations". arXiv.
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// https://arxiv.org/pdf/1604.02174v5
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let(c = 2 - 2*sqrt(2), d = 1 - 0.5*c*s)
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2 * sqrt((1+c)*s*s - c*s) / (d*d);
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/* Superellipse squircle functions */
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function _squircle_se(size, squareness) = [
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let(
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n = _squircle_se_exponent(squareness),
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size = is_num(size) ? [size,size] : point2d(size),
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ra = 0.5*size[0],
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rb = 0.5*size[1],
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astep = $fn>=12 ? 90/round($fn/4) : 360/48,
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fgsq = _linearize_squareness(min(0.998,squareness)) // works well for distributing theta
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) for(a=[360:-astep:0.01]) let(
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theta = a + fgsq*sin(4*a)*30/PI, // tighter angle steps at corners
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x = cos(theta),
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y = sin(theta),
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r = (abs(x)^n + abs(y)^n)^(1/n) // superellipse
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//r = _superformula(theta=theta, m1=4,m2=4,n1=n,n2=n,n3=n,a=1,b=1)
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) [ra*x, rb*y] / r
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];
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function squircle_radius_se(n, r, angle) = let(
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x = cos(angle),
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y = sin(angle)
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) (abs(x)^n + abs(y)^n)^(1/n) / r;
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function _squircle_se_exponent(squareness) = let(
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// limit squareness; error if >0.99889, limit is smaller for r>1
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s=min(0.998,squareness),
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rho = 1 + s*(sqrt(2)-1),
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x = rho / sqrt(2)
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) log(0.5) / log(x);
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// Function&Module: keyhole()
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// Synopsis: Creates a 2D keyhole shape.
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// SynTags: Geom, Path
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@ -1988,133 +2118,6 @@ function reuleaux_polygon(n=3, r, d, anchor=CENTER, spin=0) =
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// Function&Module: squircle()
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// Synopsis: Creates a shape between a circle and a square, centered on the origin.
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// SynTags: Geom, Path
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// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable
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// See Also: circle(), square(), supershape()
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// Usage: As Module
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// squircle(size, [squareness], [style]) [ATTACHMENTS];
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// Usage: As Function
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// path = squircle(size, [squareness], [style]);
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// Description:
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// 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.
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// .
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// 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.
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// .
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// 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`.
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// .
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// When called as a module, creates a 2D squircle with the desired squareness.
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// When called as a function, returns a 2D path for a squircle.
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// Arguments:
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// size = Same as the `size` parameter in `square()`, can be a single number or a vector `[xsize,ysize]`.
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// 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
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// style = method for generating a squircle, "fg" for Fernández-Guasti and "superellipse" for superellipse. Default: "fg"
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// atype = anchor type, "box" for bounding box corners and sides, "perim" for the squircle corners
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// $fn = Number of points. The special variables `$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
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// Examples(2D):
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// squircle(size=50, squareness=0.4);
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// squircle([80,60], 0.7, $fn=64);
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// Example(2D): Ten increments of squareness parameter for a superellipse squircle
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// for(sq=[0:0.1:1])
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// stroke(squircle(100, sq, style="superellipse", $fn=128), closed=true, width=0.5);
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// Example(2D): Standard vector anchors are based on the bounding box
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// squircle(50, 0.6) show_anchors();
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// Example(2D): Perimeter anchors, anchoring at bottom left and spinning 20°
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// squircle([60,40], 0.5, anchor=(BOTTOM+LEFT), atype="perim", spin=20)
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// show_anchors();
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module squircle(size, squareness=0.5, style="fg", atype="box", anchor=CENTER, spin=0) {
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check = assert(squareness >= 0 && squareness <= 1);
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anchorchk = assert(in_list(atype, ["box", "perim"]));
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size = is_num(size) ? [size,size] : point2d(size);
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assert(all_positive(size), "All components of size must be positive.");
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path = squircle(size, squareness, style, atype="box");
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if (atype == "box") {
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attachable(anchor, spin, two_d=true, size=size, extent=false) {
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polygon(path);
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children();
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}
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} else { // atype=="perim"
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attachable(anchor, spin, two_d=true, extent=true, path=path) {
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polygon(path);
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children();
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}
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}
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}
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function squircle(size, squareness=0.5, style="fg", atype="box", anchor=CENTER, spin=0) =
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assert(squareness >= 0 && squareness <= 1)
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assert(is_num(size) || is_vector(size,2))
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assert(in_list(atype, ["box", "perim"]))
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let(
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size = is_num(size) ? [size,size] : point2d(size),
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path = style == "fg" ? _squircle_fg(size, squareness)
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: style == "superellipse" ? _squircle_se(size, squareness)
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: assert(false, "Style must be \"fg\" or \"superellipse\"")
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) reorient(anchor, spin, two_d=true, size=atype=="box"?size:undef, path=atype=="box"?undef:path, p=path, extent=true);
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/* FG squircle functions */
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function _squircle_fg(size, squareness) = [
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let(
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sq = _linearize_squareness(squareness),
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size = is_num(size) ? [size,size] : point2d(size),
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aspect = size[1] / size[0],
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r = 0.5 * size[0],
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astep = $fn>=12 ? 90/round($fn/4) : 360/48
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) for(a=[360:-astep:0.01]) let(
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theta = a + sq * sin(4*a) * 30/PI, // tighter angle steps at corners
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p = squircle_radius_fg(sq, r, theta)
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) p*[cos(theta), aspect*sin(theta)]
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];
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function squircle_radius_fg(squareness, r, angle) = let(
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s2a = abs(squareness*sin(2*angle))
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) s2a>0 ? r*sqrt(2)/s2a * sqrt(1 - sqrt(1 - s2a*s2a)) : r;
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function _linearize_squareness(s) =
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// from Chamberlain Fong (2016). "Squircular Calculations". arXiv.
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// https://arxiv.org/pdf/1604.02174v5
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let(c = 2 - 2*sqrt(2), d = 1 - 0.5*c*s)
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2 * sqrt((1+c)*s*s - c*s) / (d*d);
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/* Superellipse squircle functions */
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function _squircle_se(size, squareness) = [
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let(
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n = _squircle_se_exponent(squareness),
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size = is_num(size) ? [size,size] : point2d(size),
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ra = 0.5*size[0],
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rb = 0.5*size[1],
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astep = $fn>=12 ? 90/round($fn/4) : 360/48,
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fgsq = _linearize_squareness(min(0.998,squareness)) // works well for distributing theta
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) for(a=[360:-astep:0.01]) let(
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theta = a + fgsq*sin(4*a)*30/PI, // tighter angle steps at corners
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x = cos(theta),
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y = sin(theta),
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r = (abs(x)^n + abs(y)^n)^(1/n) // superellipse
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//r = _superformula(theta=theta, m1=4,m2=4,n1=n,n2=n,n3=n,a=1,b=1)
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) [ra*x, rb*y] / r
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];
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function squircle_radius_se(n, r, angle) = let(
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x = cos(angle),
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y = sin(angle)
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) (abs(x)^n + abs(y)^n)^(1/n) / r;
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function _squircle_se_exponent(squareness) = let(
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// limit squareness; error if >0.99889, limit is smaller for r>1
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s=min(0.998,squareness),
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rho = 1 + s*(sqrt(2)-1),
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x = rho / sqrt(2)
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) log(0.5) / log(x);
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// Section: Text
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// Module: text()
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