Surface Parametrization of Nonsimply Connected Planar B\'ezier Regions

TL;DR

This paper introduces a new method for surface parametrization of complex planar Bzier regions, enabling advanced 3D vector graphics and typography features in the Asymptote language.

Contribution

It presents a novel algorithm for partitioning Bzier regions into Coons patches and optimizations for inside-outside tests and bounds computation.

Findings

Efficient partitioning of Bzier regions into Coons patches.

Optimized algorithms for inside-outside testing.

Enhanced global bounds computation for Bzier surfaces.

Abstract

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.