  Knot and link diagrams are projections of one or more 3-dimensional simple
closed curves into $R^2$, such that no more than two points project to the same
point in $R^2$. These diagrams are drawings of 4-regular plane multigraphs.
Knots are typically smooth curves in $R^3$, so their projections should be
smooth curves in $R^2$ with good continuity and large crossing angles: exactly
the properties of Lombardi graph drawings (defined by circular-arc edges and
perfect angular resolution).
  We show that several knots do not allow plane Lombardi drawings. On the other
hand, we identify a large class of 4-regular plane multigraphs that do have
Lombardi drawings. We then study two relaxations of Lombardi drawings and show
that every knot admits a plane 2-Lombardi drawing (where edges are composed of
two circular arcs). Further, every knot is near-Lombardi, that is, it can be
drawn as Lombardi drawing when relaxing the angular resolution requirement by
an arbitrary small angular offset $\varepsilon$, while maintaining a
$180^\circ$ angle between opposite edges.
