Development of a multi-resolution framework for NUBS

Abstract

The piecewise polynomial B-spline representation is a flexible tool in Computer Aided Geometric Design (CAGD) for representing and designing the geometric objects. In the field of Computer Graphics (CG), Computer Aided Design (CAD), or Computer Aided Engineering (CAE), a very useful property for a given spline model is to have locally supported basis functions. This allows localized modification of the shape. Unfortunately this property can also become a serious disadvantage when the user wishes to edit the global shape of a complex object. A multi-resolution representation is proposed as a solution to alleviate this problem. In this work, we propose a multi-resolution representation for Non-uniform B-splines (NUBS). The proposed multi-resolution model has three features that it uses control point decimation strategy for decomposing NUBS curves and it is efficient in both time and space utilization. A comparative study of the proposed work is also made with an alternate approach in the literature, which is based upon knot decimation.