On the Optimal Representation of Vector Location using Fixed-Width Multi-Precision Quantizers

Abstract

ABSTRACT:Current generation geospatial applications primarily rely on location representations that were developed for the manipulation and display of planar maps of portions of the earth's surface. The next generation of digital earth applications will require fundamentally new technological approaches to location representation. Improvements in the efficiency of the representation of vector location can result in substantial performance increases. We examine the advantages and limitations of the most common current approach: as tuples of fixed-width floating point representations of real numbers, and identify a list of desirable design features for an optimal replacement system. These include the use of explicitly discrete integer indexes, the use of an optimal quantification scheme, and the ability to represent point locations at multiple precisions, including the capability to exactly represent key point locations, and the ability to encode multi-precision quantizations. We describe a class of planar systems that meet these criteria, which we call Central Place Indexing (CPI) systems. We then extend these systems to the sphere to provide a class of optimal known fixed-width geospatial vector location representation systems we call CPI43 systems.

Possibilities of using raster data in client‐side web maps

“…Algorithmically there is one significant difference between rectangular and hexagonal processing: creating pyramids. The implementation does not use traditional hexagon aperture techniques (Sahr, ), but partitions each cell into six triangles, and weights them in order to calculate downsampled cell values (Figure ). As a consequence, cell orientations do not change, the number of cells is reduced quadratically at each level, and irregular hexagons with equal internal angles are also supported.…”

Hierarchical Hexagonal Clustering and Indexing

“…The fractal patterns usually have very complex shapes, and thus, they are not appropriate for point clustering. There are three reasonable variants of multi-resolution hexagonal grids often used in the Discrete Global Grid Systems [21][22][23]41,54]. Generally, the grids of aperture 3 and 4 are preferred (see Figure 6) to avoid the problems with fractal shapes.…”

“…Several papers discussed the problems of different grid systems and their mutual conversion to combine their best properties [21][22][23], but they all miss the correct hierarchical 1-to-7 refinement in the hexagonal grid ( Figure 2) for a correct hexagonal SFC. During the last years, the hexagons have gained increased interest in scientific areas including geographic information systems [19][20][21][22][23]40,41], data clustering and querying [36,38,39,42,43], data visualization [44,45], computer graphics [46] and computer or sensor networks [24,25]. Recently, the transportation network company Uber Technologies Inc. introduced a discrete global grid system [11] based on multi-resolution hexagonal grids.…”