Scattered data approximation by LR B-spline surfaces. A study on refinement strategies for efficient approximation

Abstract: Locally refined spline surfaces (LRB) is a representation well suited for scattered data approximation. When a data set has local details in some areas and is largely smooth in other, LR B-splines allow the spatial distribution of degrees of freedom to follow the variations of the data set. An LRB surface approximating a data set is refined in areas where the accuracy does not meet a required tolerance. In this paper we address, in a systematic study, different LRB refinement strategies and polynomial degrees for surface approximation. We study their influence on data volume and accuracy when applied to geospatial data sets with different structural behaviour. The performance of the refinement strategies is to some degree coherent and the article concludes with some recommendations. An overall evaluation indicates that bi-quadratic LRB are preferable for the uses cases tested, and that the strategies we denote as 'full span' have the overall best performance.