×

Raster space with relativity. (English) Zbl 1062.68607

Summary: Practical needs in geographical information systems (GIS) have led to the investigation of formal, sound and computational methods for spatial analysis. Since models based on topology of \(\mathbb R^2\) have a serious problem of incapability of being applied directly for practical computations, we have noticed that models developed on the raster space can overcome this problem. Because some models based on vector spaces have been effectively used in practical applications, we then introduce the idea of using the raster space as our platform to study spatial entities of vector spaces. In this paper, we use raster spaces to study not only morphological changes of spatial entities of vector spaces, but also equal relations and connectedness of spatial entities of vector spaces. Based on the discovery that all these concepts contain relativity, we then introduce several new concepts, such as observable equivalence, strong connectedness, and weak connectedness. Additionally, we present a possible method of employing raster spaces to study spatial relations of spatial entities of vector spaces. Since the traditional raster spaces could not be used directly, we first construct a new model, called pansystems model, for the concept of raster spaces, then develop a procedure to convert a representation of a spatial entity in vector spaces to that of the spatial entity in a raster space. Such conversions are called approximation mappings.

MSC:

68U35 Computing methodologies for information systems (hypertext navigation, interfaces, decision support, etc.)
86A99 Geophysics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Li, Y., Liu, L., Shang, L. and Li, C. (1998), ”The invariance and the nonlinearity in modal logics”, Journal of Gansu Sciences, Vol. 10 No. 3, pp. 7–11.
[2] DOI: 10.1179/000870494787073682 · doi:10.1179/000870494787073682
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.