Abstract

This paper is concerned with the problem of filtering the noise encountered in the measurements taken from a smooth (GC2-continuous) surface in the three-dimensional space. For this purpose, the data points are firstly considered to belong to a three-dimensional entity which is drastically simpler than a surface, namely the noisy curvature-continuous quadrilateral curve-mesh connecting the data points. The curve-mesh concept, apparently introduced by Hosaka (1969), is then combined with the concept of fairing in a statistical framework introduced by Reinsen (1967; 1971), yielding a constrained minimization problem for the fairing curve-mesh. After establishing that this problem has a unique solution in an appropriate Hilbert space, a convergent Newton-Raphson-type algorithm for constructing it in a cubic-spline subspace is presented in detail. Finally, the numerical performance of this algorithm in the context of a Monte-Carlo experimentation with the so-called Franke’s principal test function (1979,1980,1982) is discussed.

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