Paper detail

Surface Parametrization 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 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.