Fat Arcs for Implicitly Defined Curves

Abstract

Abstract. We present an algorithm generating a collection of fat arcs which bound the zero set of a given bivariate polynomial in BernsteinBézier representation. We demonstrate the performance of the algorithm (in particular the convergence rate) and we apply the results to the computation of intersection curves between implicitly defined algebraic surfaces and rational parametric surfaces.

A Symbolic-Numeric Algorithm for Genus Computation

“…In the future, we intend to use algebraic methods to compute the complex solutions for Sing(C) as proposed in [7]. We also mention the work in progress in the same direction of research done in parallel by [4], and by [25]. Further work in this direction is still required so that we can use these methods for our systems.…”