Solution (source code)

= Solution

Label the unbounded region $r_0$ and the three lobe regions $a,b,c$ in cyclic order, and label the central region $d$. The <Dehn presentation of a knot group> Heegaard diagram is obtained by thickening the projection graph: take one alpha compressing curve for each of $a,b,c,d$, one beta curve for each crossing, and place the basepoint in $r_0$. Orient and order the crossing curves so that their cyclic region words are
$$
ad^{-1}br_0^{-1},
\qquad bd^{-1}cr_0^{-1},
\qquad cd^{-1}ar_0^{-1}.
$$
This intersection data, together with $r_0=1$, specifies the requested pointed Heegaard diagram up to the usual isotopies and handle slides.