Induced cyclic ordering in link diagrams

Question

Let $L$ be a link in $\mathbb{R}^{3}$, and $p : \mathbb{R}^{3} \rightarrow \mathbb{R}^{2}$ a regular projection (i.e. injective everywhere, except at a finite number of crossing points) and so $p(L)$ is a link diagram. Can someone give me an explicit description of how the regular projection induces a unique cyclic ordering around the crossings of the link diagram?