Proceedings of the twelfth annual symposium on Computational geometry
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
A core library for robust numeric and geometric computation
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Entropy-preserving cuttings and space-efficient planar point location
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A simple entropy-based algorithm for planar point location
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Expected time analysis for Delaunay point location
Computational Geometry: Theory and Applications
Planning Algorithms
Advanced programming techniques applied to Cgal's arrangement package
Computational Geometry: Theory and Applications
Computational Geometry: Theory and Applications
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Improved implementation of point location in general two-dimensional subdivisions
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Practical distribution-sensitive point location in triangulations
Computer Aided Geometric Design
| Hi-index | 0.00 |
We study the performance in practice of various point-location algorithms implemented in CGAL (the Computational Geometry Algorithms Library), including a newly devised landmarks algorithm. Among the other algorithms studied are: a naïve approach, a “walk along a line” strategy, and a trapezoidal decomposition-based search structure. The current implementation addresses general arrangements of planar curves, including arrangements of nonlinear segments (e.g., conic arcs) and allows for degenerate input (for example, more than two curves intersecting in a single point or overlapping curves). The algorithms use exact geometric computation and thus result in the correct point location. In our landmarks algorithm (a.k.a. jump & walk), special points, “landmarks,” are chosen in a preprocessing stage, their place in the arrangement is found, and they are inserted into a data structure that enables efficient nearest-neighbor search. Given a query point, the nearest landmark is located and a “walk” strategy is applied from the landmark to the query point. We report on various experiments with arrangements composed of line segments or conic arcs. The results indicate that compared to the other algorithms tested, the landmarks approach is the most efficient, when the overall (amortized) cost of a query is taken into account, combining both preprocessing and query time. The simplicity of the algorithm enables an almost straightforward implementation and rather easy maintenance. The generic programming implementation allows versatility both in the selected type of landmarks and in the choice of the nearest-neighbor search structure. The end result is an efficient point-location algorithm that bypasses the alternative CGAL implementations in most practical aspects.