The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences
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Articles | Volume XLVI-4/W2-2021
Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XLVI-4/W2-2021, 1–8, 2021
https://doi.org/10.5194/isprs-archives-XLVI-4-W2-2021-1-2021
Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XLVI-4/W2-2021, 1–8, 2021
https://doi.org/10.5194/isprs-archives-XLVI-4-W2-2021-1-2021

  19 Aug 2021

19 Aug 2021

FAST ROBUST ARITHMETICS FOR GEOMETRIC ALGORITHMS AND APPLICATIONS TO GIS

T. Bartels1 and V. Fisikopoulos2 T. Bartels and V. Fisikopoulos
  • 1Technical University of Berlin, Germany
  • 2Oracle, Greece

Keywords: Spatial Predicates, Delaunay Triangulation, Floating-Point, Robustness, Triangulated Irregular Network

Abstract. Geometric predicates are used in many GIS algorithms, such as the construction of Delaunay Triangulations for Triangulated Irregular Networks (TIN) or geospatial predicates. With floating-point arithmetic, these computations can incur roundoff errors that may lead to incorrect results and inconsistencies, causing computations to fail. This issue has been addressed using a combination of exact arithmetics for robustness and floating-point filters to mitigate the computational cost of exact computations. The implementation of exact computations and floating-point filters can be a difficult task, and code generation tools have been proposed to address this. We present a new C++ meta-programming framework for the generation of fast, robust predicates for arbitrary geometric predicates based on polynomial expressions. We show examples of how this approach produces correct results for GIS data sets that could lead to incorrect predicate results for naive implementations. We also show benchmark results that demonstrate that our implementation can compete with state-of-the-art solutions.