Scattered Data Interpolation With Hierarchical B-Splines

The problem of scattered data interpolation is the fitting of a smooth surface (or, more generally, a manifold) through a set of non-uniformly distributed data points that extends to all positions in a domain. It has many important practical values in many scientific and engineering fields, because data gained in practical problems are often sparse or irregular. The main intention of interpolation is to construct an underlying function (or surface) with which the value at any position in the domain can be calculated. The surface should try it best to transmit the information of scattered data to all positions in domain smoothly, which requires the interpolation function to satisfy stricter continuous condition.Common sources of scattered data include experiments, physical measurements, and computational values. Scattered data interpolation methods have applications in numerous scientific disciplines, including meteorology, geology, geophysics, geography, and engineering design.In this paper, we first introduce some methods of scattered data interpolation, and then based on hierarchical B-splines, we develop a technique to wok with data having an arbitrary number of dimensions for both its domain and range. An integrated algorithm to solve the problem of scattered data interpolation has been presented in this paper, and three applications of this algorithm are in the next section, including 3D deformation based on scattered data. Using the technique of multilevel B-splines, the final deformation function is C2 continuous and our approach is more efficient than existing methods when the surface of the object is complex. Specific examples are given to verify the feasibility and effectiveness of the algorithm.