Global error bounds and amelioration of sweep surfaces

Abstract

With the prescription of a (piecewise) polynomial or rational cross section and axis curves, contemporary sweep or generalized cylinder constructors are incapable of creating an exact or even an approximation with a bounded error of the actual sweep surface that is represented in the same functional space, in general. An approach is presented to bound the maximal error of the sweep approximation. This bound is automatically exploited to adaptively refine and improve the sweep approximation to match a prescribed tolerance. Finally, methods are considered to eliminate the self-intersecting regions in the sweep surface resulting from an axis curve with large curvature.