Rational quadratic approximation to real plane algebraic curves

An algorithm is proposed to give a global approximation to an implicit real plane algebraic curve with rational quadratic B-splines. The algorithm consists of three steps: curve segmentation, segment approximation and curve tracing. The curve is first divided into so-called triangle convex segments. Then each segment is approximated with several rational quadratic Bezier curves. At last, the curve segments are connected into several maximal branches and each branch is represented by a B-spline curve resulting in a C¹ global parameterization for the curve branch. Due to the detailed geometric analysis, high accuracy of approximation may be achieved with a small number of quadratic segments. The final approximation based on quadratic spline curves keeps many important geometric features and gives a refined topological structure of the original curve.