FOSS4G 2021 - Fast, Robust Arithmetics for Geometric Algorithms and Applications to GIS
Channel: FOSS4G
Date: 05/11/2021

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 round-off 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.

Among other applications, Delaunay triangulations are important for the construction of Triangulated Irregular Networks (TIN). TINs are used in GIS applications to represent terrains in Digital Elevation Models and to produce Digital Surface Models or Digital Terrain Models, as discussed in (Li, 2004). Predicate failures in the underlying Delaunay triangulation may lead to issues with the mesh quality and cause crashes due to invalid triangulations or failure to terminate as discussed in (Shewchuk, 1997). The issue of predicate robustness is therefore not limited to use cases with high precision requirements.

Authors and Affiliations –
Bartels, Tinko (1)
Fisikopoulos, Vissarion (2)

(1) Technical University of Berlin, Germany
(2) Oracle, Greece

Track –
Academic

Topic –
Academic

Level –
3 - Medium. Advanced knowledge is recommended.

Language of the Presentation –
English