Quasi-conformal mapping with genetic algorithms applied to coordinate transformations

  • Authors:

  • F. J. González-Matesanz;J. A. Malpica

  • Affiliations:

  • Mathematics Department, Alcalá University, Madrid, Spain;Mathematics Department, Alcalá University, Madrid, Spain

  • Venue:
  • Computers & Geosciences
  • Year:
  • 2006

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Abstract

In this paper, piecewise conformal mapping for the transformation of geodetic coordinates is studied. An algorithm, which is an improved version of a previous algorithm published by Lippus [2004a. On some properties of piecewise conformal mappings. Eesti NSV Teaduste Akademmia Toimetised Fuusika-Matemaakika 53, 92-98; 2004b. Transformation of coordinates using piecewise conformal mapping. Journal of Geodesy 78 (1-2), 40] is presented; the improvement comes from using a genetic algorithm to partition the complex plane into convex polygons, whereas the original one did so manually. As a case study, the method is applied to the transformation of the Spanish datum ED50 and ETRS89, and both its advantages and disadvantages are discussed herein.