Transformation of coordinates using piecewise conformal mapping

A multiresolution-like algorithm for piecewise conformal mapping is presented. The algorithm is based on partitioning the complex plane into convex polygons, defining appropriate window functions for these polygons, and finding a conformal mapping for each polygon. The window functions are used to glue the pieces together into a single mapping. An application of this algorithm to determine a transformation from the Estonian coordinate system of L-EST92 into the respective system L-EST97, is presentedAcknowledgments.This work has been supported by Estonian Science Foundation grant nr. 5037. The author also thanks the Estonian Land Board, especially U. Mets and L. Tamme for their help in preparing the data, and the reviewers for valuable suggestions.