Surface Parametrization of Nonsimply Connected Planar Bézier Regions

Computer Science – Computational Geometry

Scientific paper

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29 pages, 12 figures; interactive 3D figures require Adobe Reader 9.0

Scientific paper

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.

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