From spline to Class-A curves through multi-scale analysis filtering

This paper reports the work on a novel wavelet-based multi-scale filtering application used to generate very smooth subset of profiles known as Class-A curves. The multi-scale representation, based on B-spline wavelets, allows to split a spline curves in terms of a coarser least-square approximation and details coefficients. It raises that non-Class-A curves are determined by geometric imperfections strongly connected to the details coefficients. The extraction and manipulation of details with multi-scale filtering allows to select and evaluate geometric imperfections. Finally, an efficient algorithm devoted to improve a given non-Class-A profile to a Class-A curve has been implemented and tested with several examples in order to check and visualize the results. r 2006 Elsevier Ltd. All rights reserved.