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added n= option to supershape to give number of points

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Adrian Mariano 2022-08-06 10:28:36 -04:00
parent f7b67232b2
commit b9713845f7
1 changed files with 17 additions and 15 deletions
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shapes2d.scad
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@ -1399,18 +1399,22 @@ function _superformula(theta,m1,m2,n1,n2=1,n3=1,a=1,b=1) =
// Function&Module: supershape()
// Usage: As Module
// supershape(step, [m1=], [m2=], [n1=], [n2=], [n3=], [a=], [b=], [r=/d=]) [ATTACHMENTS];
// supershape([step],[n=], [m1=], [m2=], [n1=], [n2=], [n3=], [a=], [b=], [r=/d=]) [ATTACHMENTS];
// Usage: As Function
// path = supershape(step, [m1=], [m2=], [n1=], [n2=], [n3=], [a=], [b=], [r=/d=]);
// path = supershape([step], [n=], [m1=], [m2=], [n1=], [n2=], [n3=], [a=], [b=], [r=/d=]);
// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable
// See Also: circle(), ellipse()
// Description:
// When called as a function, returns a 2D path for the outline of the [Superformula](https://en.wikipedia.org/wiki/Superformula) shape.
// When called as a module, creates a 2D [Superformula](https://en.wikipedia.org/wiki/Superformula) shape.
// Note that the "hull" type anchoring (the default) is more intuitive for concave star-like shapes, but the anchor points do not
// necesarily lie on the line of the anchor vector, which can be confusing, especially for simpler, ellipse-like shapes.
// necesarily lie on the line of the anchor vector, which can be confusing, especially for simpler, ellipse-like shapes.
// Note that the default step angle of 0.5 is very fine and can be slow, but due to the complex curves of the supershape,
// many points are often required to give a good result.
// Arguments:
// step = The angle step size for sampling the superformula shape. Smaller steps are slower but more accurate.
// step = The angle step size for sampling the superformula shape. Smaller steps are slower but more accurate. Default: 0.5
// ---
// n = Produce n points as output. Alternative to step. Not to be confused with shape parameters n1 and n2.
// m1 = The m1 argument for the superformula. Default: 4.
// m2 = The m2 argument for the superformula. Default: m1.
// n1 = The n1 argument for the superformula. Default: 1.
@ -1419,7 +1423,6 @@ function _superformula(theta,m1,m2,n1,n2=1,n3=1,a=1,b=1) =
// a = The a argument for the superformula. Default: 1.
// b = The b argument for the superformula. Default: a.
// r = Radius of the shape. Scale shape to fit in a circle of radius r.
// ---
// d = Diameter of the shape. Scale shape to fit in a circle of diameter d.
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#subsection-spin). Default: `0`
@ -1449,26 +1452,25 @@ function _superformula(theta,m1,m2,n1,n2=1,n3=1,a=1,b=1) =
// Examples:
// linear_extrude(height=0.3, scale=0) supershape(step=1, m1=6, n1=0.4, n2=0, n3=6);
// linear_extrude(height=5, scale=0) supershape(step=1, b=3, m1=6, n1=3.8, n2=16, n3=10);
function supershape(step=0.5, m1=4, m2, n1=1, n2, n3, a=1, b, r, d,anchor=CENTER, spin=0, atype="hull") =
function supershape(step=0.5, n, m1=4, m2, n1=1, n2, n3, a=1, b, r, d,anchor=CENTER, spin=0, atype="hull") =
assert(in_list(atype, _ANCHOR_TYPES), "Anchor type must be \"hull\" or \"intersect\"")
let(
n = first_defined([n, ceil(360/step)]),
angs = lerpn(360,0,n,endpoint=false),
r = get_radius(r=r, d=d, dflt=undef),
m2 = is_def(m2) ? m2 : m1,
n2 = is_def(n2) ? n2 : n1,
n3 = is_def(n3) ? n3 : n2,
b = is_def(b) ? b : a,
steps = ceil(360/step),
step = 360/steps,
angs = [for (i = [0:steps]) step*i],
rads = [for (theta = angs) _superformula(theta=theta,m1=m1,m2=m2,n1=n1,n2=n2,n3=n3,a=a,b=b)],
scale = is_def(r) ? r/max(rads) : 1,
path = [for (i = [steps:-1:1]) let(a=angs[i]) scale*rads[i]*[cos(a), sin(a)]]
// superformula returns r(theta), the point in polar coordinates
rvals = [for (theta = angs) _superformula(theta=theta,m1=m1,m2=m2,n1=n1,n2=n2,n3=n3,a=a,b=b)],
scale = is_def(r) ? r/max(rvals) : 1,
path = [for (i=idx(angs)) scale*rvals[i]*[cos(angs[i]), sin(angs[i])]]
) reorient(anchor,spin, two_d=true, path=path, p=path, extent=atype=="hull");
module supershape(step=0.5,m1=4,m2=undef,n1,n2=undef,n3=undef,a=1,b=undef, r=undef, d=undef, anchor=CENTER, spin=0, atype="hull") {
module supershape(step=0.5,n,m1=4,m2=undef,n1,n2=undef,n3=undef,a=1,b=undef, r=undef, d=undef, anchor=CENTER, spin=0, atype="hull") {
check = assert(in_list(atype, _ANCHOR_TYPES), "Anchor type must be \"hull\" or \"intersect\"");
path = supershape(step=step,m1=m1,m2=m2,n1=n1,n2=n2,n3=n3,a=a,b=b,r=r,d=d);
path = supershape(step=step,n=n,m1=m1,m2=m2,n1=n1,n2=n2,n3=n3,a=a,b=b,r=r,d=d);
attachable(anchor,spin,extent=atype=="hull", two_d=true, path=path) {
polygon(path);
children();