-

module trapezoidal_thread (
    pitch,
    length,
    upper_angle,
    lower_angle,
    outer_flat_length,
    major_radius,
    minor_radius,
    internal = false,
    n_starts = 1
)
{
    // trapezoid calculation:
    /*
                upper flat
            ___________________
           /|                 |\
          / |                 | \
    left /__|_________________|__\ right
   angle|   |   lower flat    |   |angle
        |   |                 |   |
        |left                 |right
         flat                 |flat
    */
    // looking at the tooth profile along the upper part of a screw held
    // horizontally, which is a trapezoid longer at the bottom flat
    tooth_height = major_radius - minor_radius;
    left_angle = 90 - upper_angle;
    right_angle = 90 - lower_angle;
    upper_flat = outer_flat_length;
    left_flat = tooth_height / tan (left_angle);
    right_flat = tooth_height / tan (right_angle);
    lower_flat = upper_flat + left_flat + right_flat;
    clearance = 0.3/8 * tooth_height;

    function tooth_profile () = [
        [0, 0],
        [tooth_height, right_flat],
        [tooth_height, right_flat + upper_flat],
        [0, lower_flat]
    ];

    // facet calculation
    facets = $fn > 0 ? $fn :
    max (30, min (2 * PI * minor_radius / $fs, 360 / $fa));
    fa = 360 / facets;

    slices = length2twist (length) / fa;

    // convert length along the tooth profile to angle of twist of the screw
    function length2twist (length) = length / pitch * (360 / n_starts);
    function twist2length (angle) = angle / (360 / n_starts) * pitch;

    path_transforms = [
        for (i=[0:slices + length2twist (pitch) / fa])
        let (a=i * fa)
        (
            rotation (axis=[0, 0, a]) *
            translation ([0, 0, twist2length (a) - pitch]) *
            translation ([minor_radius, 0, 0]) *
            rotation ([90, 0, 0])
        )
    ];

    cylinder (r=minor_radius, h=length);

    difference () {
        for (i=[0:n_starts])
        rotate ([0, 0, i / n_starts * 360])
        sweep (tooth_profile (), path_transforms);

        translate ([0, 0, length + pitch / 2])
        cube ([major_radius * 2 + .1, major_radius * 2+ .1, pitch],
            center=true);

        translate ([0, 0, -pitch / 2])
        cube ([major_radius * 2 + .1, major_radius * 2+ .1, pitch],
            center=true);
    }
}