  Canonical orderings of planar graphs have frequently been used in graph
drawing and other graph algorithms. In this paper we introduce the notion of an
$(r,s)$-canonical order, which unifies many of the existing variants of
canonical orderings. We then show that $(3,1)$-canonical ordering for
4-connected triangulations always exist; to our knowledge this variant of
canonical ordering was not previously known. We use it to give much simpler
proofs of two previously known graph drawing results for 4-connected planar
triangulations, namely, rectangular duals and rectangle-of-influence drawings.
