A Hybrid Symbolic-Numerical Approach in CAGD (HySaX)

Computer Aided Geometric Design (CAGD) plays an important role in the construction of such products as cars, airplanes, etc. A practical implementation has to balance three conflicting goals: efficiency, robustness, and accuracy. Typically, a numerical algorithm is efficient, but it is not fully robust and may fail in certain cases. On the other hand, algorithms based on exact arithmetic are fully robust and accurate, but are normally slow. Perhaps the goals of efficiency, robustness, and accuracy cannot be met simultaneously without some compromises. We propose to negotiate these compromises judiciously. That means, we will tackle the problems by a hybrid symbolic--numerical approach and develop algorithms which should fit these three main goals.