As we translate real world phenomena into data structures that we can store in a computer, we must determine the most appropriate spatial representation and how it relates to the characteristics of such a phenomenon. All spatial representations are derivatives of graph theory and should therefore be described in such terms. This then helps to understand the principles of low-level GIS operations. A constraint-driven approach allows the reader to evaluate implementations of the geo-relational principle in terms of the hierarchical level of mathematical space adopted.
Gridding is the act of taking a field of measurements and discretizing it into a regular tessellation, often either a lattice of squares or hexagons. Gridding can either discretize continuous phenomena or aggregate discrete instances; in either case, gridding serves conceptually to assist analysis, for example in finding local minima or maxima (i.e., "hotspots"). The process of gridding often involves interpolation, which is the rational estimation of unknown data values within the bounds of known values. Contouring refers to the creation of isolines throughout a data surface, often one represented by a grid. This section describes gridding, interpolation, and contouring, highlighting a few example methods by which interpolation is frequently done in the geospatial analysis.