Fast exact parallel map overlay using a two-level uniform grid

Abstract

We present EPUG-Overlay (Exact Parallel Uniform Grid Overlay), an algorithm to overlay two maps that is fast and parallel, has no roundoff errors, and is freely available. EPUG-Overlay combines several novel aspects. It represents coordinates with rational numbers, thereby ensuring exact computations with no roundoff errors and the ensuing sliver problems and topological impossibilities. For efficiency, EPUG-Overlay performs the map overlay in parallel, thereby utilizing the ubiquitous multicore architecture. Our application goes beyond merely using existing packages, which are inefficient when used in parallel on large problems. Indeed, overlaying two maps with 53,000,000 edges and 730,000 faces took only 322 elapsed seconds (plus 116 seconds for I/O) on a dual 8-core 3

PinMesh—Fast and exact 3D point location queries using a uniform grid

“…al. [17] found them to be much slower. They are less parallelizable, slower to traverse and to construct.…”

“…To handle very uneven data, 2-level grids have been used successfully in applications like ray-tracing [13], exact parallel 2D polygonal map intersection [17], etc. Although 3-level grids and general trees seem to be attractive extensions, Magalhães et.…”