Symbolic Numerical Computation on Algebraic Curves and Surfaces - Period I (Subproject of SFB F 13 Numerical and Symbolic Scientific Computation)

In computer aided geometric design (cagd) algebraic curves and surfaces play an essential role in modeling physical and virtual objects. The main goal of the project is the improvement and/or perfection of existing methods and the derivation of new methods for designing, manipulating, and visualizing algebraic curves and surfaces. Algebraic curves and surfaces can be represented in different ways, e.g. implicitly by a defining polynomial equation, parametrically by rational functions, or locally by Puiseux series or places. Every one of these representations has its own particular advantages, and so we need to have efficient algorithms for changing representations.