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The Extended General Spacefilling Curves Heuristic. Intl. Conf. on Pattern Recognition ICPR-98, Brisbane, Australia., 1998.In this paper an Extended General Spacefilling Curves Heuristic (EGSH) is introduced as an extension to the General Spacefilling Curves Heuristic (GSH) proposed by Bartholdi and Platzman . These are generic methods directly applicable to many problems in which data is represented in a multidimensional real vector space. A mapping is established between a region of the multidimensional space and an interval of the Real Line, and then the problem is solved in one dimension. This becomes quite useful if the problem has an easier, faster or more reliable solution in the real line. The proposed extension allows accurate solutions to many problems not reliably solvable by the original heuristic. A succesful application to function approximation is presented.