The polar projection : an alternative approach for spatial analysis

The polar projection presented here results from the need to have a uniform yet fairly simple method for recording the various phenomena and relations pertaining to land development. The contact infrastructure anisotropy and variable population and development density lead to socioeconomic space discontinuities. In the "spherical" model all subareas are characterized by coordinates on some "basic" spherical surface. The basic "air" distance between them can thus be identified directly. However, from the points corresponding to the subareas we can draw the radii of the sphere to represent the concrete connection between two subareas available in this moment by means of a segment connecting the corresponding radii at different distances from the centre of the sphere. Thus connections longer or shorter than the basic distance are to be found on an other sphere than the basic sphere. Accordingly, the degree of connectedness is characterized by the corresponding length of radius to express several alternative connections to employ a spatial or time measure and to state whether the lengthening of the distance is due to a "roundabout" connection or to the low speed parameters etc. It is thus possible to dodge the difficulties which in such cases emerge because of the necessity to employ both types of models - the gravity and the "opportunity" models. In order to simplify things instead of concentric spheres we can use parallel planes, intersected by a bundle of lines. A projection of the developed area can consist of selecting the base surface where the element distribution density matches the "standard" density. Now any deviation from this standard density can be presented as moving the surface towards or further away from the pole. Using this approach to register the socioeconomic space, we can bring all information down to the length of the "projection ray". Many of the tasks pertaining to modeling events and processes require certain arithmetic operations or use of mathematical functions to measure results. This is performed "on the side" without visual "contact" with the area. A twin system, which can serve as the geometrical basis for registering and building certain relations may be involved.