elliptical-torus.scad

use <MCAD/general/sweep.scad>
use <MCAD/general/facets.scad>
use <scad-utils/shapes.scad>
use <scad-utils/transformations.scad>

$fs = 0.4;
$fa = 1;


function cot (angle) = 1 / tan (angle);

module elliptical_torus (r_x, r_y, cross_section_r)
{
    cross_section = circle (r = cross_section_r,
        $fn = get_fragments_from_r (cross_section_r));

    // from http://math.stackexchange.com/questions/432902/
    function radius_at_angle (angle) = (
        (r_x * r_y) /
        sqrt (pow (r_x * sin (angle), 2) + pow (r_y * cos (angle), 2))
    );

    // g, flattening factor as per wiki
    flattening_factor = 1 - r_y / r_x;
    function tangential_angle (polar_angle) = (
        ((polar_angle % 360 > 180) ? 180 : 0) +
        atan (-1 / (tan (polar_angle) / pow (1 - flattening_factor, 2)))
    );

    sweep (
        cross_section,
        [
            for (t = gen_facet_series (min (r_x, r_y)))
            let (angle = t * 360)
            translation ([r_x * cos (angle), r_y * sin (angle), 0]) *
            rotation ([0, 0, 90 + tangential_angle (angle)]) *
            rotation ([90, 0, 0])
        ],
        true
    );
}

elliptical_torus (r_x = 40, r_y = 20, cross_section_r = 2);