Curvature Computations on Surfaces in n-Space.

摘要

Many surface operations in CAGD (Computer aided geometric design) derive new surfaces from given ones subject to certain constraints. Examples include offset surfaces, where a distance constraint must be observed, and spherical blends, where a curvature and a continuity constraint must be satisfied. While there exist intuitive descriptions of the resulting surfaces that are easily grasped, a precise mathematical representation of the surfaces appears difficult to obtain in practice. Indeed, closed-form representations are available in principle with the help of elimination theory - e.g., (4,5) - or using Grobner bases techniques - e.g., (2,3,14). In practice, however, closed forms are usually unobtainable because the elimination problems that must be solved are well beyond the capabilities of machines and algorithms available to date; see, e.g., (16). In consequence, surface operations including offsets and blends have been treated individually in the literature, and specific approximation methods for the resulting surfaces have been given that are not general. (kr)