GEOMETRIC MODELING USING RATIONAL GAUSSIAN CURVES AND SURFACES

A geometric modelling system based on rational Gaussian (RaG) curves a nd surfaces is introduced. The generation of simple geometric primitiv es such as lines, circles, and ellipses with RaG curves, and the gener ation of planes, spheres, ellipsoids, cylinders, cones, and tori with RaG surfaces are discussed. The design of freeform closed, half-closed , and open shapes using RaG surfaces is also considered. The control p oints of a RaG surface are not required to form a topologically rectan gular grid, but, rather, they can form an arbitrary grid.