Notes on the CAD-Compatible Conversion of Multi-Sided Surfaces

Abstract

Abstract. We investigate genuine multi-sided surface representations that can be converted into standard tensor product format, such as NURBS. Multi-sided patches offer versatility in shape design, and permit smooth, watertight connections between adjacent patches using prescribed cross-derivatives; however, they can seldom be utilized by the majority of CAD/CAM systems, which handle surfaces only in standard data formats. Tensor product surfaces, on the other hand, may be too rigid for shape design, and trimmed patches can only be smoothly connected up to user-defined tolerances. This motivates the search for schemes that benefit from both representations. We analyze four multi-sided surface representations that allow precise conversion into tensor product format, namely S-patches, Warren’s patch, Kato’s patch and a variant of the Charrot–Gregory patch. We compare these schemes from various aspects; in particular, we deal with surface equations, singularities, degrees of the converted surfaces, the control structure built and the computational efficiency of the conversion. Several examples help to gain deeper insights into the problem.