2010/05/17 by Orest Shardt, Shardt, Orest, John C. Bowman +1
Computer Science · Engineering · Mathematics · #65D17 #68U05 #68U15 #Advanced Numerical Analysis Techniques #Algorithm #Artificial intelligence #Asymptote #Bounded function #Bounding overwatch #Bézier curve #Computation #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #Computer Graphics and Visualization Techniques #Computer graphics #Computer graphics (images) #Computer science #FOS: Computer and information sciences #Geometry #Graphics #I.3.5 #J.2 #J.6 #Mathematical analysis #Mathematics #Monotonic function #Optics #Parametrization (atmospheric modeling) #Physics #Planar #Surface (topology) #Vector graphics #acm:65D17 #acm:68U05 #acm:68U15 #cs.CG #msc:65D17 #msc:68U05 #msc:68U15
paper · pdf · doi:10.48550/arxiv.1005.2822
published in arXiv (Cornell University) (Cornell University) · 29 pages, 12 figures; interactive 3D figures require Adobe Reader 9.0
openalex publication_date 2010/05/17 · arxiv created 2010/08/07 · arxiv updated 2015/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.