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Final fix for exact squareness linearity in squircle()

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Alex Matulich 2024-12-06 08:28:03 -08:00
parent 504c92bba9
commit 6c92e0313a
1 changed files with 12 additions and 6 deletions
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18
shapes2d.scad
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@ -1929,7 +1929,7 @@ function _superformula(theta,m1,m2,n1,n2=1,n3=1,a=1,b=1) =
// Usage: As Function
// path = reuleaux_polygon(n, r|d=, ...);
// Description:
// When called as a module, creates a 2D Reuleaux Polygon; a constant width shape that is not circular. Uses "intersect" type anchoring.
// When called as a module, reates a 2D Reuleaux Polygon; a constant width shape that is not circular. Uses "intersect" type anchoring.
// When called as a function, returns a 2D path for a Reulaux Polygon.
// Arguments:
// n = Number of "sides" to the Reuleaux Polygon. Must be an odd positive number. Default: 3
@ -2021,14 +2021,14 @@ module squircle(squareness=0.7, size=[10,10], anchor=CENTER, spin=0) {
bbox = is_num(size) ? [size,size] : point2d(size);
assert(all_positive(bbox), "All components of size must be positive.");
path = squircle(squareness, size);
anchors = [
anchors = let(sq = _linearize_squareness(squareness)) [
for (i = [0:1:3]) let(
ca = 360 - i*90,
cp = polar_to_xy(squircle_radius(squareness, bbox[0]/2, ca), ca)
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(squareness, bbox[0]/2, ca), ca)
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) {
@ -2041,8 +2041,7 @@ module squircle(squareness=0.7, size=[10,10], anchor=CENTER, spin=0) {
function squircle(squareness=0.7, size=[10,10]) =
assert(squareness >= 0 && squareness <= 1) [
let(
sqlim = max(0, min(1, squareness)),
sq = sqrt(sqlim*(2-sqlim)), // somewhat linearize squareness response
sq = _linearize_squareness(squareness),
bbox = is_num(size) ? [size,size] : point2d(size),
aspect = bbox[1] / bbox[0],
r = 0.5 * bbox[0],
@ -2058,6 +2057,13 @@ 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/vc/arxiv/papers/1604/1604.02174v1.pdf
let(c = 2 - 2*sqrt(2), d = 1 - 0.5*c*s)
2 * sqrt((1+c)*s*s - c*s) / (d*d);
// Section: Text