Fitting missing data by means of adaptive meshes of Bézier curves

Abstract

In this paper we present a method to fit missing data – i.e., to fit a dataset containing a region in which no data are provided– by means of a C1-quadratic patch. Such a patch is constructed to faithfully extend the shape and the geometric features of the dataset. To this end, a mesh of curves gathering the information about the shape of the dataset will be considered and extended to the interior of the hole. Next, a (unique) patch fitting such a mesh of curves will be computed. Several numerical and graphical examples showing the effectiveness of the proposed method are provided.