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The Computer Journal 1987 30(4):355-361; doi:10.1093/comjnl/30.4.355
© 1987 by British Computer Society
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A General PASCAL Program for Map Overlay of Quadtrees and Related Problems*

F. W. Burton1 § ++, V. J. Kollias2 ¶ {dagger} and J. G. Kollias3 {ddagger}

1 Department of Computer Science, 3180 MEB, University of Utah, Salt Lake City, Utah 84112, USA, 2 Laboratory of Soils and Agricultural Chemistry, Athens Faculty of Agriculture, Iera Odos 75, Votanicos, Athens, Greece, 3 Department of Electrical Engineering, Division of Computer Science, National Technical University of Athens, Zografou, 15773 Athens, Greece

A simple but general map overlay function is defined for quadtrees. It is shown that many common quadtree operations, including union, intersection, relative complement, masking, copy, complement and generalisation of quadtrees, can all be viewed as special cases of map overlay, depending on how pixel values of the result of an overlay are determined from the corresponding pixels of the maps being overlaid.

It is shown that some operations, such as union, can be more efficiently performed by specialised algorithms. A more general overlay function is given, which is optimal (to within a constant factor) with respect to both time and space for all of the above operations. This overlay function requires two functions as parameters. One function determines when the quadtrees being overlaid are simple enough to be processed without further subdivision. The other performsthe overlay for simple cases.

Received January 1986. revised April 1986.

* This material is based upon work supported by the National Science Foundation under grant no. E08-8312748. Travel support was provided by NATO under collaborative research grant no.401/84.

§ Department of Electrical Engineering and Computer Sciences, Box 104, University of Colorado at Dencer, 1100 Fourteenth Street, Denver, Colorado 80202, U.S.A.

Laboratory of Soils and Agricultural Chemistry, Athens Faculty of Agriculture, Iera Odos 75, Votanicos, Athens, Greece

{ddagger} Department of Electrical Engineering, Division of Computer Science, National Technical University of Athens, Zografou, 15773 Athens, Greece

++ Now at: Department of Computer Science, 3180 MEB, University of Utah, Salt Lake City, Utah 84112, U.S.A.

{dagger} To whom correspondence should be addressed.


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