Surface Modeling of Complicated Geometries with Incomplete Erroneous Data Points-An Extension to B-Spline Approach

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Abstract
Based on the analogy between the B-spline curve modeling and the force-deflection behavior of a beam subjected to lateral point loads, an extension to the B-spline surface modeling method was introduced. The proposed method has strong extrapolating capability and can develop accurate surface models over an incomplete net of data points without affecting the original data. Extrapolation of the incomplete part of the data net is conducted simultaneously with interpolation of the existing part, with no need to recalculation. Approximation or data smoothing is a natural extension of the method, however, the smoothing intensity can be controlled continuously without reducing the number of spline intervals. The performance of the method was evaluated on some known analytical surfaces and produced more accurate results in comparison with the regular B-spline approach. The results indicate that the proposed method can also filter erroneous data points and reconstruct the original surface successfully