// recrangularSignetRingGenerator.scad
// Adam Zeloof
// 2.15.2022
include <ringSizes.scad>

module ringtop(w, h, t, r) {
    // based on an answer found at https://math.stackexchange.com/questions/543496
    P = [w/2,h];
    d = sqrt(P[0]^2+P[1]^2);
    rho = r/d;
    ad = rho^2;
    bd = rho*sqrt(1-ad);
    T = [ad*P[0] + bd*P[1], ad*P[1] - bd*P[0]];
    linear_extrude(t) polygon([[0,0], T, P, [-P[0],P[1]], [-T[0],T[1]]]);
}

module rectangularSignetRing(size, wall, t, w, h, res) {
    id = us_size(size);
    difference() {
        difference() {
            union() {
                cylinder(h=t, r=id/2+wall, $fn=res);
                ringtop(w, h, t, id/2+wall);
            }
            translate([-w/2, h, 0]) cube([w, w, t]);
        }
        cylinder(h=t, r=id/2, $fn=res);
    }
}