| OCR Text |
Show CHAPTER 2 RESULTS ON INDIVIDUAL COMPONENTS Before studying the interaction of the components making up an automatic curve fitting routine, it is important to understand the individual function of each part. Each part should work as well as possible alone before being combined with others. In this chapter, we will discuss some existing methods in greater detail, limitations of these methods, and new methods reported herein that are proposed to overcome these limitations, and are well-suited to parametric B-spline approximation. 2.1 Initial Parametrization, Weighting, and Corner Placement Parametrization plays an important part in automatic parametric B-spline approximation to data. Regardless of what combined methods are used, an initial parametrization must be estimated. Individual methods which are affected by the initial parametrization include adaptive knots, variable knots, reparametrization, and any parametric approximation, smoothing or otherwise. As will be seen, the compactness and smoothness of the final approximation produced by a combination of these methods still depends on the initial parametrization. No degree of optimization can compensate for a sufficiently poor initial parametrization. In this section, an initial parametrization will be discussed, which overcomes some of the limitations of simpler parametrizations. It is based on some observations on the limitations of chord length parametrization, and the effects of the parametrization on an approximating curve. |
