Scattered Data Approximation by LR B-Spline Surfaces: A Study on Refinement Strategies for Efficient Approximation

Abstract

Locally refined B-spline (LRB) surfaces provide a representation that is well suited to scattered data approximation. When a data set has local details in some areas and is largely smooth elsewhere, 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 the resulting data volume and accuracy when applied to geospatial data sets with different structural behaviour. The relative performance of the refinement strategies is reasonably coherent for the different data sets and this paper concludes with some recommendations. An overall evaluation indicates that bi-quadratic LRB are preferable for the use cases tested, and that the strategies we denote as “full span" have the overall best performance.