ABSTRACT
As with curves, the surface modeling problem may be considered first as an approximation problem, that is, to fit a surface to predefined data. Within this framework one finds the concepts of interpolation and approximation, the same as with curves. The other approach is to view a surface as an ab initio design problem, that is one wants to fit to an idea of a shape. This second approach requires that the specification method be as friendly and intuitive as possible while allowing a wide variety of shape possibilities. The methods might include construction operators for simple shapes, surfaces of revolution, and simple swept surfaces. The types of surfaces one might want to include are, of course, sculptured surfaces, as well as the more traditional boundaries of spheres, ellipsoids, cones, cylinders, pie wedges, etc. We shall approach the problem in an analogous fashion to the curve problem by first studying the problem from the first viewpoint and then adapting those methods to the second viewpoint.
