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Curve mesh fairing and \(GC^ 2\) surface interpolation. (English) Zbl 0762.65007

The article presents a method for constructing a fair surface through a given \(m\times n\) matrix of data \((x_ j,y_ i,z_{ji})\) where the \(z\)-component is considered as affected by a normally distributed noise. The method works in two stages: First, a curve mesh is constructed which is faired in the sense that it minimizes a so-called fairness functional, which is the \(L^ 2\)-norm of the second derivative, subject to constraints of accuracy and compatibility. The effect of this process is demonstrated by two examples. In the second step through the resulting curve mesh a Boolean sum surface with continuous curvature is constructed.

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)
65D10 Numerical smoothing, curve fitting
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