Efficient Shape Description Using NURBS
In this paper we present an efficient method for smooth surface generation from unorganised points using NURBS. This is a preferred alternative to using triangular meshes, which are expensive to store, transmit, render and are difficult to manipulate. The proposed method does not require triangulation prior to surface fitting because it generates NURBS directly. Two fundamental problems must be addressed to accomplish this task: parameterisation of measured data and overcoming ill-conditioning of the least squares surface fitting. We propose to solve the parameterisation problem by employing a suitable base surface, automatically generated from the data points, or provided as a CAD model if available. Ill-conditioning was solved by introducing additional fitting criteria in the minimisation functional, which constrain the fitted surface in the regions with insuficient number of data points. Surface fitting is performed by treating the surface as a whole without the need to either identify or re-measure the regions with insuficient data. The accuracy of fitting is dictated by the number of control points. The improvements in data compression, shape analysis and rendering are presented. The realised computational speed and the quality of the results were found to be highly encouraging.
KeywordsControl Point Base Surface NURBS Surface Generalise Cylinder 12th Annual International Symposium
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