Abstract:
We discuss algorithms that realize or exploit continuity in dynamic geometry. In particular, we examine certified homotopy continuation of systems of plane algebraic curves and of geometric constructions, generation and identification of real algebraic loci, and GPU-based visualization of plane algebraic curves as domain-coloured Riemann surfaces. Moreover, we provide a sampler of plane algebraic curves, which we construct as loci and visualize as domain-coloured Riemann surfaces.