Title
Exact and approximate representations of trimmed surfaces with NURBS and Beźier surfaces
Document Type
Conference Proceeding
Publication Date
11-17-2009
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 Beźier surfaces. The present paper provides an algorithm to split a trimmed NURBS surface into several NURBS or Beźier 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 Beźier 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]. © 2009 IEEE.
Publication Source (Journal or Book title)
Proceedings - 2009 11th IEEE International Conference on Computer-Aided Design and Computer Graphics, CAD/Graphics 2009
First Page
286
Last Page
291
Recommended Citation
Li, X., & Chen, F. (2009). Exact and approximate representations of trimmed surfaces with NURBS and Beźier surfaces. Proceedings - 2009 11th IEEE International Conference on Computer-Aided Design and Computer Graphics, CAD/Graphics 2009, 286-291. https://doi.org/10.1109/CADCG.2009.5246888