Knot and link diagrams are projections of one or more 3-dimensional simpleclosed curves into $R^2$, such that no more than two points project to the samepoint in $R^2$. These diagrams are drawings of 4-regular plane multigraphs.Knots are typically smooth curves in $R^3$, so their projections should besmooth curves in $R^2$ with good continuity and large crossing angles: exactlythe properties of Lombardi graph drawings (defined by circular-arc edges andperfect angular resolution). We show that several knots do not allow plane Lombardi drawings. On the otherhand, we identify a large class of 4-regular plane multigraphs that do haveLombardi drawings. We then study two relaxations of Lombardi drawings and showthat every knot admits a plane 2-Lombardi drawing (where edges are composed oftwo circular arcs). Further, every knot is near-Lombardi, that is, it can bedrawn as Lombardi drawing when relaxing the angular resolution requirement byan arbitrary small angular offset $\varepsilon$, while maintaining a$180^\circ$ angle between opposite edges.
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机译：结图和链接图是一个或多个3维单闭合曲线到$ R ^ 2 $的投影，因此在$ R ^ 2 $的同一点上投影的点不超过两个。这些图是4个规则平面多图的图，结通常是$ R ^ 3 $中的平滑曲线，因此它们的投影应该是$ R ^ 2 $中的平滑曲线，具有良好的连续性和较大的交叉角：正是Lombardi图的性质（由圆弧边缘和完美的角度分辨率定义）。我们证明了几个结不允许平面隆巴迪图纸。另一方面，我们确定了具有Lombardi绘图的一大类4正则平面多重图。然后，我们研究了Lombardi图的两个松弛，并表明每个结点都承认一个平面2-Lombardi图（边缘由两个圆弧组成）。此外，每个结都接近伦巴第，也就是说，当通过任意小的角偏移量\ varepsilon $放宽对角分辨率的要求时，可以将其绘制成伦巴第图，同时保持相对边缘之间的夹角为180°。
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