We present a certified algorithm that takes a smooth algebraic curve in \(\mathbb {R}^n\) and computes an isotopic approximation for a generic projection of the curve into \(\mathbb {R}^2\). Our algorithm is designed for curves given implicitly by the zeros of n − 1 polynomials, but it can be partially extended to parametrically defined curves. The main challenge in correctly computing the projection is to guarantee the topological correctness of crossings in the projection. Our approach combines certified path tracking and interval arithmetic in a two-step procedure: first, we construct an approximation to the curve in \(\mathbb {R}^n\), and, second, we refine the approximation until the topological correctness of the projection can be guaranteed. We provide a proof-of-concept implementation illustrating the algorithm.

We present a certified algorithm based on subdivision for computing an isotopic approximation to a pair of curves in the plane. Our algorithm is based on the certified curve approximation algorithm of Plantinga and Vegter. The main challenge in this computation is to correctly and efficiently compute the intersections of the curves. To address this issue, we introduce a new, but simple test that guarantees the global correctness of our output.

Article Share on ConceptDoppler: a weather tracker for internet censorshipCCS '07: Proceedings of the 14th ACM conference on Computer and communications securityOctober 2007 Pages 352–365https://doi.org/10.1145/1315245.1315290Online:28 October 2007Publication History 42citation1,097DownloadsMetricsTotal Citations42Total Downloads1,097Last 12 Months115Last 6 weeks7 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access