Introduction

Abstract

AbstractWith the development of high rate sensors based on LIDAR (light detection and ranging) and sonar technology, geospatial data representing terrain or seabed often contains millions of points. Performing a surface approximation of the point clouds is an elegant way to reduce noisy and unorganized data to a mathematical surface with just a few coefficients to estimate. Traditional spline surfaces are able to compactly represent smooth shapes, but lack the ability to adapt the representation locally to the point clouds. Locally Refined (LR) B-spline surfaces address that challenge as they have the nice property of being locally refinable. Their format can be made compatible with most Geographic Information System (GIS) software, and they facilitate various applications such as the drawing of contour lines or spatio-temporal deformation analysis. This introduction aims to explain the need for surface approximation, and present the state of the art in that domain. We compare the LR B-spline approach with different methods for surface approximation including raster, and triangular irregular networks.