Approximate Conversion of Spline Curves

Abstract

In German car body industries (VDA) different manufacturers and their subcontractors have different geometric modeling systems for curve and surface representations. For exchanging data between the different geometric modeling systems conversions of curve and surface representation are required in order to compensate differences in the types of polynomial bases, maximum polynomial degrees and mesh sizes. Conversion means reducing the degree of a spline curve (and splitting more than one segment) or elevating the degree of more than one spline segment (and merging to one segment). For this purpose a set of methods was developed by DANNENBERG and NOWACKI [ 2]. They have extended a conversion method introduced by HÖLZLE [ 8] for plane curves to surfaces by interpreting a surface as a net of curves. The extension of the algorithm to surfaces is implemented in the VDA-Software, but often a great number of new patches is obtained. So the question arises how to develop a method which yields to a more economical patch number. In the present paper a new conversion method for spline curves is introduced, which works yery effectively for plane spline curves. The method can be extended to approximate conversion of spline surfaces and to approximation of offset curves and offset surfaces by spline curves and spline surfaces (s. [6,7]).