Measurement-based modification of NURBS surfaces

Abstract

A frequent requirement in computer aided design and manufacture is to update or refine an existing CAD model using measured data. Least squares surface fitting is known to suffer from stability problems, caused by an insufficient measurement density in some regions. This is particularly evident in situations involving local surface updating and when knot insertion is applied for local surface refinement. This paper presents a new method to update the CAD model consisting of NURBS surfaces, trimmed or untrimmed, based on a set of unorganised measured points in three-dimensional space. The proposed method overcomes the fundamental problem of singular or ill-conditioned matrices resulting from incomplete data sets. This was achieved by introducing additional fitting criteria in the minimisation functional, which constrain the fitted surface in the regions with insufficient number of data points. Two main benefits were realised by this approach. First, local surface updating can be performed by treating the surface as a whole, without the need to specially identify the regions with insufficient data, nor to re-measure those regions. Second, the quality of the unmeasured regions may be controlled to suit specific needs. The results were found to be highly encouraging and the method was found to be especially useful in situations involving knot insertion and large surface deformations.