Globally certified [formula omitted] approximation of planar algebraic curves

Abstract

Topology analysis and geometric feature determination for curves and surfaces are basic problems in geometric modeling and computer aided design. When the curves and surfaces are given in implicit expressions, the problems become more difficult. This paper presents a complete algorithm framework for the problem of certified G1 approximation of a planar algebraic curve under global error control. Compared to other work on topology and geometric analysis of algebraic curves, this method presents a new topology analysis as well as a geometric information computation. Moreover, this method uses generalized asymptotes as the approximation of the unbounded part, which makes it achieve global approximation with given precision.