Abstract
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.
Highlights
Basic geometric predicates, such as computing the orientation of a triangle or testing if a point is inside a circle, are at the core of many computational geometry algorithms such as convex hull and Delaunay triangulation
On the other hand, computing with floating-point arithmetic, these computations can incur roundoff errors that may lead to incorrect results and inconsistencies, causing computations to fail (Kettner et al, 2004)
Delaunay triangulations are important for the construction of Triangulated Irregular Networks (TIN)
Summary
Basic geometric predicates, such as computing the orientation of a triangle or testing if a point is inside a circle, are at the core of many computational geometry algorithms such as convex hull and Delaunay triangulation. Those predicates appear in geospatial computations such as topological spatial relations that determine the relationship among geometries. 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 not limited to use cases with high precision requirements
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