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

TL;DR

This paper introduces non-orthogonal space subdivision methods to accelerate point-in-polygon and point-in-polyhedron tests, improving memory efficiency and runtime beyond traditional orthogonal subdivisions.

Contribution

It presents novel non-orthogonal subdivision techniques that enhance algorithm speed and memory use for geometric point-inclusion tests.

Findings

Significant reduction in memory consumption.

Improved runtime complexity for point-in-polyhedron tests.

Effective application to convex shape inclusion problems.

Abstract

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