Understanding hierarchical B-splines with a case study: approximation of point clouds from TLS observations

摘要

Static or kinematic Terrestrial Laser Scanners (TLS) are a way to acquire all kinds of scenes or objects, offering the possibility to collect millions of 3D points in a short time. The corresponding point clouds (PC) can be analysed in standard software or mathematically approximated. Regression B-spline surfaces allows great flexibility to model PC, since no predetermined geometric primitives such as circles, planes or cylinders restrict the fitting. These surfaces are defined by a tensor product of B-spline basis functions, which limit the local refinement. This drawback can be circumventing by using hierarchical B-splines. In this contribution, we propose to explain in a didactical way the mathematical concepts and apply hierarchical B-splines approximation to TLS observations from a bridge under load. This example highlights the high potential of hierarchical refinement to gain a finer local control over the surface to approximate. It paves the way to model PC from TLS observations and performs rigorous test for deformation based on a fine mathematical approximation of the surface.