Hybrid symbolic and numeric operators as tools for analysis of freeform surfaces

Freeform surfaces are commonly used in Computer Aided Geometric Design?? so accurate analysis of surface properties is becoming increasingly important In this paper we de ne surface slope and surface speed?? develop visualization tools?? and demonstrate that they can be useful in the design process Generally?? surface properties such as curvature and twist are evaluated at a nite set of predetermined samples on the surface This paper takes a di erent approach A small set of tools is used to symbolically compute surfaces representing curvature?? twist and other properties These surfaces are then analyzed using numeric techniques The combination of symbolic computation to provide an exact property rep resentation up to machine accuracy and numerical methods to extract data is demonstrated to be powerful and robust This approach supports a uniform treat ment once the surfaces are computed and also provides global information?? so questions such as is a surface developable or what are the hyperbolic regions of a surface can be answered robustly