Smoothing in 3D with reference points and polynomials

Abstract

We introduce a new parametric approach to noisy three-dimensional data smoothing founded on a special representation of bivariate polynomials that uses reference points. The model in construction has to fulfill the quasi-smooth condition which can be easily ensured by proper allocation and assessment of reference points as well as some additional coefficient constraints. The estimate of approximants is considered for a two-part model. The proposed model offers a reasonable compromise between accuracy and smoothness. We plan to confirm this statement by putting our approach to the test along with a B-spline based one.