PATRA true-neighborhood-transformation in 2D Nets

During a transformation with identical points, the transformation parameters are defined in such a manner, that the misclosures at the identical points are minimised. Normally, the residual misclosures are not negligable. By taking the proximity into consideration, it is possible to eliminate the residual misclosures and then to adjust the remaining points accordingly. Two different methods of performing the close proximity adjustment have been realised in the Program System PATRA:

• Adjustment with Distance Weighting. For each net point, the influence by distance of all identical points on the individual coordinate elements is determined. A function for the distance weighting can be given, a possible function is, for example, s^-1.5.
• Adjustment by Area Fitting. The point cluster is divided into triangles by a Delaunay Triangulation. The adjustment of a net point is determined in such a manner, that the square sum of the scale changes of all triangles, weighted by the triangle's area, is minimised.