Researches On The Scope Of Application Of Progressive Iterative Approximation And Its Utilization

In the field of Computer Aided Geometric Design (abbr. CAGD), a new data fittingtechnique, progressive iterative approximation (abbr. PIA), has been proposed andattracts plenty of attention. By adjusting the control points iteratively, PIA methodprovides a straight forward way to generate a sequence of curves/surfaces with betterand better precision for data fitting. The curves and surfaces has the PIA property aslong as the bases are normalized totally positive (abbr. NTP) and the correspondingcollocation matrix is nonsingular. Because of the widely applications of PIA property,main works are as follows:1. We extend the scope of application of the PIA property. If the collocation matrix isdiagonally dominant or generalized diagonally dominant, the corresponding baseson triangular domain possess generalized PIA property;2. Because of the widely applications of Said-Ball bases, we take Said-Ball bases asexamples and find that Said-Ball curves or Said-Ball surfaces on triangular domainhave generalized PIA property;3. A novel approach for offset approximation is proposed in this thesis and the methodis based on PIA property. The approach first samples points from offset curve. Basedon the PIA method, we approximate the offset points. Finally, the iterative process isreiterated until a satisfactory approximation error is reached, we obtain an offsetapproximation curve. Numerical examples are given to demonstrate theeffectiveness of our method.