www.elsevier.com/locate/cagd An algorithm is proposed to give a global approximation of an implicit real plane algebraic curve with rational quadratic B-spline curves. The algorithm consists of four steps: topology determination, curve segmentation, segment approximation and curve tracing. Due to the detailed geometric analysis, high accuracy of approximation may be achieved with a small number of quadratic segments. The final approximation keeps many important geometric features of the original curve such as the topology, convexity and sharp points. Our method is implemented and experiments show that it may achieve better approximation bound with less segments than previously known methods. We also extend the method to approximate spatial algebraic curves.

Let E ae R s be compact and d E n denote the dimension of the space of polynomials of degree at most n in s variables restricted to E. We introduce the notion of an asymptotic interpolation measure (AIM). Such a measure, if it exists, describes the asymptotic behavior of any scheme n = fx k;n g d E n k=1 , n = 1; 2; : : :, of nodes for multivariate polynomial interpolation for which the norms of the corresponding interpolation operators do not grow geometrically large with n. We demonstrate the existence of AIM's for the finite union of compact subsets of certain algebraic curves in R 2 . It turns out that the theory of logarithmic potentials with external fields plays a useful role in the investigation. Furthermore, for the sets mentioned above we give a computationally simple construction for "good" interpolation schemes. 1 Introduction With \Pi n (R s ) denoting the set of all real polynomials of degree at most n in s variables, i.e., \Pi n (R s ) := 8 ! : p(x) : p...