Surface parameterization of nonsimply connected planar Bézier regions

A technique is described for constructing three-dimensional vector graphics representations of planar regions bounded by cubic Bézier curves, such as smooth glyphs. It relies on a novel algorithm for compactly partitioning planar Bézier regions into nondegenerate Coons patches. New optimizations are also described for Bézier inside–outside tests and the computation of global bounds of directionally monotonic functions over a Bézier surface (such as its axis-aligned 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.