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Thiessen, Dirichlet, Voronoi (and, of course, Decartes)
While we are on the subject of points and their surrounding areas, let’s look at the creation of a set of polygons, each created from a single point Each polygon has the following property: Every interior point of the polygon is closer to its generating point than to the generating point of any other polygon. This idea has “been invented” by at least three different people (and was used informally by Descartes), giving rise to Thiessen polygons, Dirichlet domains, and Voronoi cells. The polygons tessellate a portion of the Cartesian plane. Unlike the procedures used above, the value at the point has no bearing on the size, shape, or extent of the area around it. Only the position of the point is important.
Making Thiessen polygons is a little more involved than making the other rasters we have used, because they expand the extent of the raster area. There are ways to correct this, but we will use a “workaround” to accomplish the same thing. This will (a) make the polygons, and (b) acquaint you with the idea of workarounds which is a handy frame of mind to be in when dealing with today’s very complex and not particularly robust software.
We will first use “Only Points” to make a shapefile. Then we will convert that shapefile into a raster.
____ 20. In ArcMap start a new blank map. Add as data Only_Points.shp. Label the points layer with the FID field. Open the attribute table. (You will find a field there named Population. ...

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