Exact and approximate representations of trimmed surfaces with NURBS and Bézier surfaces

Abstract

A trimmed surface is usually represented as a parametric surface with a set of trimming curves. However, many CAD processes and algorithms cannot be applied to trimmed surfaces directly because of the complexity in manipulating trimmed surfaces. Moreover, trimmed surfaces will create gaps between different trimmed surfaces. Thus it is desirable to represent a trimmed surface by a group of regular surfaces, such as NURBS or Bezier surfaces. The present paper provides an algorithm to split a trimmed NURBS surface into several NURBS or Bezier surfaces. The surface patches which domains are far away from the trimming curves coincide with the given trimmed NURBS surface and the patches which domains are close to the trimming curves are represented with high degree Bezier surface patches (exact) or bi-cubic B-spline surfaces (approximate). The algorithm is simple, efficient and easy to implement. Compared with previous approaches ([1] and [3]), the new algorithm doesn't change the parameterization of most regions and is easy to maintain the continuity. Since our algorithm can keep most of the patches unchanged, most of the surface patches will be C2 continuous. Furthermore, the surface patches can be locally merged to be G1 in the neighbor of trimming curves which is very difficult for those in [1] and [3].