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

TL;DR

This paper systematically studies various refinement strategies for locally refined B-spline surfaces in scattered data approximation, focusing on accuracy, data volume, and efficiency, with recommendations for practical use.

Contribution

It provides a comprehensive comparison of refinement strategies and polynomial degrees for LRB surfaces, highlighting the effectiveness of bi-quadratic LRB and 'full span' strategies.

Findings

Bi-quadratic LRB surfaces are preferable for tested cases.

'Full span' refinement strategies perform best overall.

Refinement strategies significantly influence data volume and accuracy.

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.