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Acceleration of algorithms is becoming a crucial problem, if larger data setsare to be processed. Evaluation of algorithms is mostly done by usingcomputational geometry approach and evaluation of computational complexity.However in todays engineering problems this approach does not respect thatnumber of processed items is always limited and a significant role plays alsospeed of read/write operations. One general method how to speed up an algorithmis application of space subdivision technique and usually the orthogonal spacesubdivision is used. In this paper non-orthogonal subdivisions are described.The proposed approach can significantly improve memory consumption and run-timecomplexity. The proposed modified space subdivision techniques are demonstratedon two simple problems Point-in-Convex Polygon and Point-in-Convex Polyhedrontests.

Polar, Spherical and Orthogonal Space Subdivisions for an Algorithm Acceleration: O(1) Point-in-Polygon/Polyhedron Test