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About this paper
Bruno Lévy
The authors present a mesh Boolean method that carries exact intersection coordinates and predicates through co-refinement and boundary selection. A multithread-friendly constrained Delaunay triangulation uses consistent tie-breaking to handle coplanar overlaps and reduce predicate calls. On the coplanar 20rods-20rods test, it runs in 0.9 seconds, versus 3.3 and 2.1 seconds; Cherchi et al.’s output has spurious facets. Floating-point conversion remains unresolved.
Key insights
- A clean separation between simple combinatorial algorithms and a meticulously engineered geometric kernel significantly improves robustness and maintainability of complex geometric software.
- Careful optimization of exact arithmetic kernels, particularly the multi-precision floating-point approach, can overcome limitations like exponent overflow in deeply nested computations and deliver competitive performance for real-world geometric problems.
- Designing the Constrained Delaunay Triangulation to minimize predicate calls and ensure uniqueness via symbolic perturbations is crucial for robustly handling complex degeneracies and co-planar regions.
Summary by alphaXiv.
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