This open access book provides insights into the novel Locally Refined B-spline (LR B-spline)
surface format which is suited for representing terrain and seabed data in a compact way. It
provides an alternative to the well know raster and triangulated surface representations. An LR
B-spline surface has an overall smooth behavior and allows the modeling of local details with
only a limited growth in data volume. In regions where many data points belong to the same
smooth area LR B-splines allow a very lean representation of the shape by locally adapting the
resolution of the spline space to the size and local shape variations of the region. The
iterative method can be modified to improve the accuracy in particular domains of a point
cloud. The use of statistical information criterion can help determining the optimal threshold
the number of iterations to perform as well as some parameters of the underlying mathematical
functions (degree of the splines parameter representation). The resulting surfaces are well
suited for analysis and computing secondary information such as contour curves and minimum and
maximum points. Also deformation analysis are potential applications of fitting point clouds
with LR B-splines.
