Scanline Forced Delaunay Tens for Surface Representation

The general idea that a Delaunay TIN (DT) is more appropriate than non-Delaunay TINs, due to ‘better’ shaped triangles, might be true for many applications, but not for height dependent analytical queries. This is because the distribution of the triangle tessellation is defined in the two-dimensional XY-plane, by ignoring the Z-value in the Delaunay empty circum circle criterion. Alternatively, Data Dependent Triangulations (DDT) aim to identify which triangulation of a given function z=f(x,y) over a given set of points will optimize some quality, i.e. the minimal spatial area of the surface or the volume below the resulting surface. This might be a good approach, but still there is no certainty the TIN represents the actual surface. Besides that, a 2D-TIN (Delaunay or not) is only capable to solve 2D (or 2.5D) data distributions. The reconstruction of the surface given by a set of surface points alone is therefore not unambiguous. This paper describes a surface reconstruction method based on the scanlines, the lines-of-sight or measurements between the observer (or the measurement platform) and the target (the measured point). As the scanlines do not belong to the surface, we have to use a ‘real’ 3D triangulation construction method, resulting in a Tetrahedronized Irregular Network. This TEN is capable to store all kinds of surfacefeatures (as the target-points) and the scanlines as well. The scanlines are forced to split by adding Steiner points until they are part of the Delaunay TEN. This procedure gives us the additional information needed to use the TEN to reconstruct the surface. The method is demonstrated by the non-trivial case of a set of measured points in a regular square distribution showing the improved surface reconstruction technique.