Proposal of Effective Orthogonal and Hexagonal Hierarchical Structures for Disc Queries - Uher, Vojtech; Gajdos, Petr; Snasel, Vaclav (2018 3rd International Conference on Control, Robotics and Cybernetics (CRC), 2018)
The Fixed-Radius Nearest Neighbors (FRNN) query is a common task in scientific areas dealing with multidimensional point clouds (PCs) such as computer graphics, image processing, geographic information systems, machine learning and pattern recognition. We especially focus on 2D points in this paper. The FRNN means search all the points within defined radius for tasks when local properties of data are crucial. As this procedure is time consuming, an effective accelerating structure indexing the points is required. The standard methods are based on the orthogonal grids subdividing the space into uniform cells or hierarchies of orthogonal grids. However, several papers highlight the regular hexagonal grids for their superior theoretical metrics, e.g. better coverage of query discs, uniform distance to all six neighbors or lower number of passed cells. This paper provides a comparison of effectiveness of orthogonal and hexagonal hierarchies and traditional algorithms for FRNN disc queries. To do this, we propose a novel hierarchical method based on the hexagonal space-filling curve called the Node-Gosper curve which defines the hierarchical location of points in the hexagonal grids and their linear order. This method is tested with similar structure based on the orthogonal Z-order curve to show the real features of both approaches in practice.