Calibration of a Terrestrial Laser Scanner - Institute of Geodesy and ...

m\m)rdr4.3 Modeling and Visualization 83Table 4.1: Software for processing laser scanning data. The results are based on a questionnaire carried out by theISPRS working group V/3.Software Manufacturer Use [%]Cyclone HDS Leica Geosystems 28Geomagic Raindrop 17RiScanPRO Riegl 11CloudWorx HDS Leica Geosystems 9Polyworks InnovMetric 8rest various 274.3.1 Geometrical PrimitivesThe modeling of geometrical primitives is extensively automated. The parameters for geometrical objectsare computed by a least square adjustment using Gauss-Markov or Gauss-Helmert. The following objectsare considered as geometrical primitives and can be mostly computed semi-automatically or fully automat¬ically:• patch or plane: pin—= 0• sphere: \pt——= 0• cylinder : a(pl——= 0The vector n describes the unit normal, p defines each point of the point cloud, m is the center point of thesphere or the cylinder, and a characterizes the orientation of the principal axis of the cylinder.The para¬meters r and d define the radius and the diameter, respectively. A more detailed description for calculatinggeometrical primitives can be found in [Hovenbitzer, 2003].4.3.2 TriangulationTriangulation or mesh generation can be described as the process of finding geometrical objects in a givendata set, i.e.triangles in 2D and tetrahedra in 3D. Typically, this process is based on Delauny triangulation ormarching cubes [Hoppe et al., 1992] and [Carr et al., 2001]. Some possible constraints for building trianglesor tetrahedra are defined by [Hoscheck and Lasser, 1992]• criterion of the shortest diagonal,• criterions of the minimum/maximum angle and maximum/minimum angle, respectively, and• criterion of the circumscribed circle.The last criterion leads to the Delauny triangulation, which postulatesthat the circumscribed circle of eachtriangle must not contain a fourth point of the data set [deBerg et al., 2002]. The Delauny triangulationcomputes uniform triangles and avoids both long and short triangles as well as overlapping triangles.More information can be found in a number of publications, e.g. [deBerg et al., 2002], [Carr et al., 2001][Hoppe et al., 1992], [Hoscheck and Lasser, 1992], [Rietdorf, 2005].