GNAL/scad/spiral/spiral_7.scad

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OpenSCAD
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D=300; // start diameter
N=1; // number of spirals
FN=100;
$fn=FN;
include <../libraries/path_extrude.scad>;
bottom = 1.2;
top = .3;
top_offset = (bottom - top);
h = 2.2;
facetProfile = [[0, 0], [top_offset, -h], [bottom, -h], [bottom, 0]];
function X (start_r, spacing, fn, r, i) = (start_r + (r * spacing) + (i * calcIncrement(spacing, fn))) * cos(i * calcAngle(fn));
function Y (start_r, spacing, fn, r, i) = (start_r + (r * spacing) + (i * calcIncrement(spacing, fn))) * sin(i * calcAngle(fn));
function circ (d) = PI * d;
function calcFacetSize (end_d, fn) = circ( end_d ) / fn;
//function calcSteps(rotations, fn) = fn * rotations;
function calcAngle (fn) = 360 / fn;
function calcFn(start_d, start_fn, end_d, spacing, r) = start_fn +
( ((circ(calcR(start_d, spacing, r) * 2) - circ(start_d) )
/ (circ(end_d) - circ(start_d))) * ($fn - start_fn));
function calcR(start_d, spacing, r) = (start_d / 2) + (spacing * r);
function calcIncrement(spacing, fn) = spacing / fn;
/**
* spiral_7 - Combination of spiral_3 and spiral_4 that doesn't sacrifice
* performance. Hits an overflow when $fn is higher than 245 which creates
2020-05-27 13:52:15 +00:00
* 8418 vectors at 60 rotations. This is an edge case, only appearing in OpenSCAD
* 2019.05 (and maybe earlier), but should be explored.
**/
module spiral (rotations = 40, start_d = 48, spacing = 2.075, fn) {
end_d = start_d + (spacing * 2 * rotations);
end_r = end_d / 2;
start_r = start_d / 2;
facetSize = calcFacetSize(end_d, fn);
start_fn = round(circ(start_d) / facetSize);
echo(facetSize);
spiralPath = [ for (r = [0 : rotations - 1]) for (i = [0 : round(calcFn(start_d, start_fn, end_d, spacing, r )) - 1 ])
[
X(start_r, spacing, round(calcFn(start_d, start_fn, end_d, spacing, r )), r, i),
Y(start_r, spacing, round(calcFn(start_d, start_fn, end_d, spacing, r )), r, i),
0]
];
echo(len(spiralPath));
path_extrude(exShape=facetProfile, exPath=spiralPath);
}
spiral(N, D, 2.075, $fn);