A computational approach to the cartographic dot distribution problem

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Hickey, Mutahar
McGrew, J. Michael
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Thesis (M.S.)
Department of Computer Science
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In the field of cartography, there is occasionally a need to create a distribution of dots on a map. These dots should give an impression of the density of some countable object set. This type of map is called a "Dot Distribution Map".Up to the current time, if the dots are to represent reality at all, they have to be placed by hand by a cartographer using a digitizing tablet or other input device. This is due to the fact that a census of a region gives only a total, yet it is known that the densities vary within that region. A cartographer can look at all the data available about a region and then can make judgements about how the densities will change within the region. He then can place dots which represent his interpretation of reality.This thesis states that there exists an algorithm which would assign dots to a map based upon the common belief that the density will gradate smoothly from one region with one census value to another region with a different census value.The approach taken was to relate the Map regions to polygons and to then subdivide the polygons into triangles. These triangles would then be subdivided into six children recursively and the data stored in a hex-tree. This is the current level of development. the next steps will be:Generate a surface above the 2-D map based upon the known input data of counts for the various regions.From the centroid for each existing leaf on the Hex-Tree, find the corresponding Zi value from the surface information. From each of these leaves, recursively subdivide the triangle further until the number of dots indicated by the Zt. value can be placed on the map.