bare/gpt-5-nano / tier-2-offset-handle-mug

```openscad
$fn = 100;

// Main cup (outer cylinder with inner hollow bottom 6 mm)
module mug_body() {
    outer = cylinder(h = 90, r = 40, $fn = $fn);
    inner = translate([0, 0, 6]) cylinder(h = 84, r = 35, $fn = $fn);
    difference() {
        outer;
        inner;
    }
}

// D-shaped handle cross-section (2D, to be extruded then rotated into place)
module handle_cross_section() {
    Th = 12;       // thickness into +X direction (before rotation)
    Hh = 60;       // height of cross-section (maps to mug height after rotation)
    hole_w = 25;   // inner space width
    hole_h = 30;   // inner space height
    hole_x = 0;    // inner hole touches left boundary
    hole_y = (Hh - hole_h)/2; // center vertically within cross-section

    r = Hh/2; // radius for the semicircular outer part

    pts = [];
    // left-bottom to left-top and then to right-bottom
    pts = concat(pts, [[0, 0]]);
    pts = concat(pts, [[Th, 0]]);
    // semicircular arc on the right side (center at (Th, Hh/2), from -90° to +90°)
    for (a = [-90:5:90]) {
        ang = a * PI / 180;
        pts = concat(pts, [ [ Th + r * cos(ang), Hh/2 + r * sin(ang) ] ]);
    }
    // top-left corner to close the shape
    pts = concat(pts, [[0, Hh]]);

    difference() {
        polygon(points = pts);
        translate([hole_x, hole_y]) square([hole_w, hole_h], center = false);
    }
}

// 3D handle: extrude the 2D cross-section and rotate to align height with mug
module handle3d() {
    // After rotating -90° around X, the cross-section's height (Y) maps to Z (height)
    rotate([-90, 0, 0]) {
        linear_extrude(height = 18) {
            handle_cross_section();
        }
    }
}

// Assemble mug with handle on the +X side.
// The handle is positioned to slightly overlap the mug wall to ensure union (no gaps).
union() {
    mug_body();

    // Position the handle:
    // - Place so its left face is near the mug's outer surface at x ≈ 40 (we use 39 for slight overlap)
    // - Center the handle vertically around z = 45 mm (mug height is 90 mm)
    //   After rotation, vertical alignment maps accordingly; we translate in Z to center at 45.
    translate([39, 0, 15]) handle3d();
}
```