3.5.2 Surface Coarsening, Data Reduction

Surface triangulations can consist of a too large number of very small triangles which do not convey important geometrical information. For example surface triangles which have been extracted from cellular data are of the same size as the sampling cells. In this case data reduction is mandatory. An algorithm based on the standard method as proposed in [153] allows such a decimation of a general triangulation including edges with more than two adjacent facets [85]. By taking various parameters like the aspect ratio and the distance of a point to a plane into account, redundant points are discarded together with incident triangles. The resulting hole (ring) is triangulated. A smoothing effect can be observed under certain conditions but it cannot be guaranteed. The local operation and an example is depicted in Fig. 3.20.

Figure 3.20: Detail of a trench consisting of 2912 triangles before and 288 triangles after data reduction by locally discarding points.

At the top of the trench the original structural edge has been converted into a less smooth surface. Depending on the locally applied parameters either the reduction effect is limited or ripple effects might occur. More global techniques, e.g. extracting all contour and structural information beforehand (see Section 6.3) or generally elaborated schemes utilizing for instance energy functions [68] can be employed.