Rational Approximation on Closed Curves

Rational quadratic approximation to real algebraic curves

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 f...

Polygonal approximation of closed discrete curves

Optimal polygonal approximation of closed curves differs from the case of open curve in the sense that the location of the starting point must also be determined. Straightforward exhaustive search would take N times more time than the corresponding optimal algorithm for an open curve, because there are N possible points to be considered as the starting point. Faster sub-optimal solution can be ...

High order approximation of rational curves by polynomial curves

We show that many rational parametric curves can be interpolated, in a Hermite sense, by polynomial curves whose degree, relative to the number of data being interpolated, is lower than usual. The construction unifies and generalizes the families of circle and conic approximations of Lyche and Mørken and the author in which the approximation order is twice the degree of the polynomial.

Rational Curves on Varieties

Rational points on curves