Surface Parametrization of Nonsimply Connected Planar B\'ezier Regions

A technique is described for constructing three-dimensional vector graphics representations of planar regions bounded by cubic B'ezier curves, such as smooth glyphs. It relies on a novel algorithm for compactly partitioning planar B'ezier regions into nondegenerate Coons patches. New optimizations are also described for B'ezier inside-outside tests and the computation of global bounds of directionally monotonic functions over a B'ezier surface (such as its bounding box or optimal field-of-view angle). These algorithms underlie the three-dimensional illustration and typography features of the TeX-aware vector graphics language Asymptote.