USING RATIONAL NUMBERS AND PARALLEL COMPUTING TO EFFICIENTLY AVOID ROUND-OFF ERRORS ON MAP SIMPLIFICATION

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Maurício G. Gruppi
Salles V. G. de Magalhães
Marcus V. A. Andrade
W. Randolph Franklin
Wenli Li

Resumo

This paper presents EPLSimp, an algorithm for map generalization that avoids the creation of topological inconsistencies. EPLSimp is based on Visvalingam-Whyatt's (VW) algorithm on which least "important" points are removed first. Unlike VW's algorithm, when a point is deleted a verification is performed in order to check if this deletion would create topological inconsistencies. This was done by using arbitrary precision rational numbers to completely avoid errors caused by floating-point arithmetic. EPLSimp was carefully implemented to be efficient, although using rational numbers adds an overhead to the computation. This efficiency was achieved by using a uniform grid for indexing the geometric data and parallel computing to speed up the process. As result, simplified models completely free of topologically inconsistent results and round-off errors due to the use of multiple precision rational numbers. In addition, there was a considerable speedup arising from the use of parallel computing.

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GRUPPI, M. G.; MAGALHÃES, S. V. G. de; ANDRADE, M. V. A.; FRANKLIN, W. R.; LI, W. USING RATIONAL NUMBERS AND PARALLEL COMPUTING TO EFFICIENTLY AVOID ROUND-OFF ERRORS ON MAP SIMPLIFICATION. Revista Brasileira de Cartografia, [S. l.], v. 68, n. 6, 2018. DOI: 10.14393/rbcv68n6-44497. Disponível em: https://seer.ufu.br/index.php/revistabrasileiracartografia/article/view/44497. Acesso em: 24 jun. 2024.
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