Spatial reasoning: improving computational efficiency

When spatial data is analysed the result is often very computer intensive: even by the standards of contemporary technologies, the machine power needed is great and the processing times significant. This is particularly so in 3-D and 4-D scenarios. What we describe here is a technique, which tackles this and associated problems. The technique is founded in the idea of quad-tesseral addressing, a technique, which was originally applied to the analysis of atomic structures. It is based on ideas concerning Hierarchical clustering developed in the 1960s and 1970s to improve data access time [G.M. Morton, A computer oriented geodetic database and a new technique on file sequencing, IBM Canada, 1996.], and on atomic isohedral (same shape) tiling strategies developed in the 1970s and 1980s concerned with group theory [B. Grunbaum, G.C. Shephard, Tilings and Patterns, Freeman, New York, 1987.]. The technique was first suggested as a suitable representation for GIS in the early 1980s when the two strands were brought together and a tesseral arithmetic applied [F.C. Holdroyd, The Geometry of Tiling Hierarchies, Ars Combanitoria 16B (1983) 211-244., S.B.M. Bell, B.M. Diaz, F.C. Holroyd, M.J.J. Jackson, Spatially referenced methods of processing raster and vector data, Image and Vision Computing 1 (4) (1983) 211-220., Diaz, S.B.M. Bell, Spatial Data Processing Using Tesseral Methods, Natural Environment Research Council, Swindon, 1986.]. Here, we describe how that technique can equally be applied to the analysis of environmental interaction with built forms. The way in which the technique deals with the problems described is first to linearise the three-dimensional (3-D) space being investigated. Then, the reasoning applied to that space is applied within the same environment as the definition of the problem data. We show, with an illustrative example, how the technique can be applied. The problem then remains of how to visualise the results of the analysis so undertaken. We show how this has been accomplished so that the 3-D space and the results are represented in a way which facilitates rapid interpretation of the analysis, which has been carried out.