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add circle_packing

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Justin Lin
2022-05-31 14:27:18 +08:00
parent e2ec67b67d
commit 8c3a7d7f7a
1 changed files with 63 additions and 0 deletions
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src/experimental/circle_packing.scad Normal file
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use <triangle/tri_delaunay.scad>;
use <triangle/tri_incenter.scad>;
function circle_packing(points, density = 1, min_r = 1) =
[
for(t = tri_delaunay(points, ret = "TRI_SHAPES"))
each circle_packing_triangle(t, density, min_r)
];
function circle_packing_triangle(t, density, min_r) =
let(
center = tri_incenter(t),
s1 = t[1] - t[0],
s2 = t[2] - t[1],
s3 = t[0] - t[2],
leng_s1 = norm(s1),
leng_s2 = norm(s2),
leng_s3 = norm(s3),
R = abs(cross(s1, s2)) / (leng_s1 + leng_s2 + leng_s3),
r = function(sin, leng_cv, pre_R) sin * (leng_cv - pre_R) / (1 + sin),
ca = center - t[0],
leng_ca = norm(ca),
unit_ca = ca / leng_ca,
sina = R / leng_ca,
cb = center - t[1],
leng_cb = norm(cb),
unit_cb = cb / leng_cb,
sinb = R / leng_cb,
cc = center - t[2],
leng_cc = norm(cc),
unit_cc = cc / leng_cc,
sinc = R / leng_cc,
_small_circles = function(density, pre_Ra = R, pre_Rb = R, pre_Rc = R)
density <= 0 ? [] :
let(
ra = r(sina, leng_ca, pre_Ra),
Ra = pre_Ra + ra,
rb = r(sinb, leng_cb, pre_Rb),
Rb = pre_Rb + rb,
rc = r(sinc, leng_cc, pre_Rc),
Rc = pre_Rc + rc
)
[
if(ra > min_r) [center - unit_ca * Ra, ra],
if(rb > min_r) [center - unit_cb * Rb, rb],
if(rc > min_r) [center - unit_cc * Rc, rc],
each _small_circles(density - 1, ra + Ra, rb + Rb, rc + Rc)]
)
[[center, R], each _small_circles(density - 1)];
/*
use <experimental/circle_packing.scad>;
$fn = 24;
density = 4;
min_r = 1;
points = [for(i = [0:100]) rands(-100, 100, 2)];
for(c = circle_packing(points, density, min_r)) {
translate(c[0])
sphere(c[1]);
}
*/