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shapes2d.scad
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@ -477,41 +477,60 @@ module star(n, r, d, ir, id, step, realign=false, anchor=CENTER, spin=0)
function _superformula(theta,m1,m2,n1,n2=1,n3=1,a=1,b=1) =
pow(pow(abs(cos(m1*theta/4)/a),n2)+pow(abs(sin(m2*theta/4)/b),n3),-1/n1);
// Function&Module: superformula_shape()
// Function&Module: supershape()
// Usage:
// superformula_shape(step,m1,m2,n1,n2,n3,[a],[b]);
// supershape(step,[m1],[m2],[n1],[n2],[n3],[a],[b],[r|d]);
// 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.
// Arguments:
// step = The angle step size for sampling the superformula shape. Smaller steps are slower but more accurate.
// scale = The scaling multiplier for the size of the shape.
// m1 = The m1 argument for the superformula.
// m2 = The m2 argument for the superformula.
// n1 = The n1 argument for the superformula.
// n2 = The n2 argument for the superformula.
// n3 = The n3 argument for the superformula.
// a = The a argument for the superformula.
// b = The b argument for the superformula.
// 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.
// n2 = The n2 argument for the superformula. Default: n1.
// n3 = The n3 argument for the superformula. Default: n2.
// 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#anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
// Example(2D):
// superformula_shape(step=0.5,scale=100,m1=16,m2=16,n1=0.5,n2=0.5,n3=16);
// supershape(step=0.5,m1=16,m2=16,n1=0.5,n2=0.5,n3=16,r=50);
// Example(2D): Called as Function
// stroke(close=true, superformula_shape(step=0.5,scale=100,m1=16,m2=16,n1=0.5,n2=0.5,n3=16));
function superformula_shape(step=0.5,scale=1,m1,m2,n1,n2=1,n3=1,a=1,b=1, anchor=CENTER, spin=0) =
// stroke(close=true, supershape(step=0.5,m1=16,m2=16,n1=0.5,n2=0.5,n3=16,d=100));
// Examples2(2D):
// for(n=[2:5]) right(2.5*(n-2)) supershape(m1=4,m2=4,n1=n,a=1,b=2); // Superellipses
// m=[2,3,5,7]; for(i=[0:3]) right(2.5*i) supershape(.5,m1=m[i],n1=1);
// m=[6,8,10,12]; for(i=[0:3]) right(2.7*i) supershape(.5,m1=m[i],n1=1,b=1.5); // m should be even
// m=[1,2,3,5]; for(i=[0:3]) fwd(1.5*i) supershape(m1=m[i],n1=0.4);
// supershape(m1=5, n1=4, n2=1); right(2.5) supershape(m1=5, n1=40, n2=10);
// m=[2,3,5,7]; for(i=[0:3]) right(2.5*i) supershape(m1=m[i], n1=60, n2=55, n3=30);
// n=[0.5,0.2,0.1,0.02]; for(i=[0:3]) right(2.5*i) supershape(m1=5,n1=n[i], n2=1.7);
// supershape(m1=2, n1=1, n2=4, n3=8);
// supershape(m1=7, n1=2, n2=8, n3=4);
// supershape(m1=7, n1=3, n2=4, n3=17);
// supershape(m1=4, n1=1/2, n2=1/2, n3=4);
// supershape(m1=4, n1=4.0,n2=16, n3=1.5, a=0.9, b=9);
// for(i=[1:4]) right(3*i) supershape(m1=i, m2=3*i, n1=2);
// m=[4,6,10]; for(i=[0:2]) right(i*5) supershape(m1=m[i], n1=12, n2=8, n3=5, a=2.7);
function supershape(step=0.5,m1=4,m2=undef,n1=1,n2=undef,n3=undef,a=1,b=undef,r=undef,d=undef,anchor=CENTER, spin=0) =
let(
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-1]) step*i],
rads = [for (a = angs) scale*_superformula(theta=a,m1=m1,m2=m2,n1=n1,n2=n2,n3=n3)],
path = [for (i = [0:steps-1]) let(a=angs[i]) rads[i]*[cos(a), sin(a)]]
) rot(spin, p=move(-max(rads)*normalize(anchor), p=path));
module superformula_shape(step=0.5,scale=1,m1,m2,n1,n2=1,n3=1,a=1,b=1, anchor=CENTER, spin=0)
polygon(superformula_shape(step=step,scale=scale,m1=m1,m2=m2,n1=n1,n2=n2,n3=n3,a=a,b=b, anchor=anchor, spin=spin));
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 = [0:steps-1]) let(a=angs[i]) scale*rads[i]*[cos(a), sin(a)]]
) rot(spin, p=move(-scale*max(rads)*normalize(anchor), p=path));
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)
polygon(supershape(step=step,m1=m1,m2=m2,n1=n1,n2=n2,n3=n3,a=a,b=b, r=r,d=d, anchor=anchor, spin=spin));
// vim: noexpandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap