bare-low/o3 / tier-2-offset-handle-mug

```openscad
// Parameters
$fn = 128;

//------------------
// Mug body
//------------------
module mug_body() {
    outer_radius = 40;        // 80 mm outer diameter
    inner_radius = 35;        // 70 mm inner diameter
    height       = 90;
    bottom_thk   = 6;
    
    difference() {
        // Outer shell
        cylinder(h = height, r = outer_radius);
        
        // Inner cavity (raised by bottom thickness)
        translate([0, 0, bottom_thk])
            cylinder(h = height - bottom_thk, r = inner_radius);
    }
}

//------------------
// Handle
//------------------
module handle() {
    inner_h   = 30;   // inner vertical clearance
    inner_w   = 25;   // inner horizontal clearance
    wall_thk  = 5;    // handle wall thickness
    depth     = 10;   // thickness (depth) of handle along Y
    
    // 2-D inner void of the handle (D-shape) in the X–Z plane
    module inner_shape() {
        union() {
            // Rectangle part
            translate([0, -inner_h/2])
                square([inner_w, inner_h], center = false);
            // Semicircular end
            translate([inner_w, 0])
                circle(r = inner_h/2);
        }
    }
    
    // 2-D outer profile (offset of inner shape)
    module outer_shape() {
        offset(delta = wall_thk) inner_shape();
    }
    
    // Build 3-D handle by extruding the 2-D profiles along Y
    translate([40, 0, 45])  // attach to +X side, centered vertically
    difference() {
        // Solid outer shell
        linear_extrude(height = depth, center = true)
            outer_shape();
        // Hollow out the finger space
        linear_extrude(height = depth, center = true)
            inner_shape();
    }
}

//------------------
// Assembly
//------------------
union() {
    mug_body();
    handle();
}
```