Exploiting the Implicit Support Function for a Topologically Accurate Approximation of Algebraic Curves

Describing the topology of real algebraic curves is a classical problem in computational algebraic geometry. It is usually based on algebraic techniques applied directly to the curve equation. We use the implicit support function representation for this purpose which can in certain cases considerably simplify this task. We describe possible strategies and demonstrate them on a simple example. We also exploit the implicit support function for a features-preserving approximation of the graph topologically equivalent to the curve. This contribution is meant as a first step towards an algorithm combining classical approaches with the dual description via the support function.