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79 lines
1.6 KiB
OpenSCAD
79 lines
1.6 KiB
OpenSCAD
// The math of the shells: https://www.youtube.com/watch?v=pKHWzmxw_NI
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use <surface/sf_thickenT.scad>
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alpha = 85;
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beta = 5;
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phi = 0;
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omega = 0;
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mu = 1;
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a = 2;
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b = 3;
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theta_s = -2400;
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theta_step = 20;
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theta_e = 720;
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s_s = -150;
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s_step = 20;
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s_e = 90;
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thickness = 1.5;
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seashell();
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module seashell() {
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e = 2.7182818284590452;
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real_e = e * 0.3615; // avoid inf
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pow_a = a ^ 2 / 100;
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pow_b = b ^ 2 / 100;
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function cot(degree) = 1 / tan(degree);
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function radius(theta) =
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real_e ^ (theta * cot(alpha));
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function x(theta, s) =
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let(r = radius(theta))
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r * (
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(cos(theta + omega) * cos(s + phi) - sin(mu) * sin(theta + omega) * sin(s + phi)) /
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sqrt((cos(s) ^ 2) / pow_a + (sin(s) ^ 2) / pow_b)
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+ sin(beta) * cos(theta)
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);
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function y(theta, s) =
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let(r = radius(theta))
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r * (
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(sin(mu) * cos(theta + omega) * sin(s + phi) + sin(theta + omega) * cos(s + phi)) /
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sqrt((cos(s) ^ 2) / pow_a + (sin(s) ^ 2) / pow_b)
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+ sin(beta) * sin(theta)
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);
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function z(theta, s) =
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let(r = radius(theta))
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r * (
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(cos(mu) * sin(s + phi)) /
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sqrt((cos(s) ^ 2) / pow_a + (sin(s) ^ 2) / pow_b)
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- cos(beta)
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);
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points = [
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for(s = [s_s:s_step:s_e], theta = [theta_s:theta_step:theta_e])
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[x(theta, s), y(theta, s), z(theta, s)]
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];
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slen = floor((s_e - s_s) / s_step);
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thetalen = floor((theta_e - theta_s) / theta_step);
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c = thetalen + 1;
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triangles = [
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for(s = [0:slen - 1], theta = [0:thetalen - 1])
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each [
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[theta + s * c, theta + 1 + s * c, theta + (s + 1) * c],
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[theta + 1 + s * c, theta + 1 + (s + 1) * c, theta + (s + 1) * c]
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]
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];
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sf_thickenT(points, thickness, triangles);
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}
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