A general PASCAL program for map overlay of quadtrees and related problems
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The domains of a structured spatial positioning systems are extended to a single 2D or 3D boundary rectangle (MBR - Minimal axes-parallel Boundary Rectangle) domain. We try to encapsulate the domains strictly for the inside and/or the boundary (surface) of the object during our attempts. In ease of such domains it is impossible to use traditional coordinates because of boundary irregularity. Therefore we applied 2D and 3D versions of subrange type data structure for spatial indexing, which are well known in dynamic program languages. The two important methods of combinatorics namely enumeration and ranking were also applied to the spatial index used by us, derived from rank which should not be confused with concept of 'rank' used in the APL and J programming languages. During development we had to partly modify and extend the traditional concepts of circumference and area, as well surface and volume. With the creation of nested superclasses and subclasses, it is possible for positioning systems belonging to different classes to inherit transformation parameters (translation, orientation, etc.). Polymorphism allows development of hidden virtual systems which may perform transformations between any kind of coordinates and linear indices. Thus our positioning systems can be rightly called object oriented including every advantage and disadvantage of it.