Locally refined spline surfaces for representation of terrain data

In this paper we describe the use of a novel representation, LR B-spline surfaces, and apply this representation in the treatment of geographical data. These data sets are typically very large and LR B-spline surfaces offer a compact representation of overall smooth data with local details. We briefly describe the properties of the LR B-spline representation, and discuss the details of two approximation methods adapted for LR B-splines: least squares approximation and multilevel B-spline approximation (MBA). The described techniques are demonstrated on several examples of terrain data in the form of point clouds. Graphical abstractAn LR B-spline surface approximating a point cloud representing Gaustatoppen in Norway. The point cloud covers 7kmí¿7km and orth is pointing upwards to the right. The photograph has a slightly different view.Display Omitted HighlightsLR B-splines is a new surface representation for local refinement of spline spaces.Least squares approximation is adapted for LR B-splines.Multilevel B-spline approximation is adapted for LR B-splines.The methods are applied to approximate terrain data.