Institutions of Higher Education and the Regional Economy: A Long-Term Spatial Analysis
Figure 1
Illustration of delaunay triangulation and voronoi polygons—an example with counties. (a) Identifying a delaunay triangle. The near-rectangular blocks represent selected counties in a certain state, and every county has one unique internal point, indicated by the solid dot in each block. is a Delaunary triangle since no other data point lies within its circumscribed circle. On the other hand, is not a Delaunay triangle because its circumscribed circle contains the internal point of county 4. This means that at least two of the three counties are not directly connected with one another; in this case, they are county 2 and county 5. (b) Delaunay Triangles. This graph shows the sets of Delaunay triangles covering a larger area of the state. Based on the triangles, seven natural neighbors (counties 2 through 8) are identified for county 1. (c) Voronoi Polygons. The Voronoi polygons associated with the Delaunay triangles are formed by the lines connecting the centers of the circumscribed circles. For example, point a is the center of the circle circumscribed about (as shown in part (a)), and point b is the center of the circle circumscribed about . Voronoi polygons approximate the geographic boundaries of the counties.
