However the extreme deviations in the sampled points

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Unformatted text preview: (1) Evaluation of Geometric Deviations in Sculptured Surfaces 137 where r is the residual error between the ith measured point and the substitute geometry fitted to the n data points, and p is an exponent. Least square (p=2) and minimum deviation zone functions (p=∞) are typically utilized in the fitting process. The criterion in the least square function requires that the sum of square errors be minimized. For the minimum deviation zone function, equation (1) becomes [Nassef & ElMaraghy, 1999]: L∞ = max ( ri ) i (2) The minimum deviation zone function has received much attention in recent years [Yau, 1997] [Choi & Kurfess, 1998], because the studies show that it yields a smaller zone value than that evaluated by using a least squares fit [Choi et al., 1998] [Lin et al., 1995]; and it best conforms to the standard definition of the tolerance zone in ASME Y14.5. In addition, it numerically simulates the physical fitting process in traditional metrology. However, such an extreme fit has l...
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