Team 1034 Page 3 of 21 3 Illustration of creating divisions by first subdividing the map. Left: Pop- ulation density distribution of hypothetical map with five desired districts Middle: A subdivision of the map into two regions generated from two un- shown generator points. Right: Final division of each subregion from the middle figure into desired final division 4 New York State population density map. Data obtained from a 792-by-660 pixel raster image; color and height indicate the relative population density at each point. 5 Depiction of the implamentation of Voronoi diagrams with the manhat tan metric in the three step process of: assigning degeneracies to generator points, using the degenerate points to generate regions using the Voronoi agram method, and creating subregions of the regions generated by de- generate points. Only the last two steps are depicted. The process for Voronoiesque diagrams is the same.(Dots in each region represent genera- tor point locations. 6 Voronoi diagrams generated with three distance metrics before subdivision f densely populated regions (Dots in each region represent generator point 7 Districts created by the Voronoiesque diagram for New York state AverageS locations.) population per region =(3.34+ 0.74)%.(Dots in each region represent generator Do int locations. 8 Illustration of Voronoi diagram generation which takes geographic obstacles into accounTeam 1034 Page 3 of 21 3 Illustration of creating divisions by first subdividing the map. Left: Pop￾ulation density distribution of hypothetical map with five desired districts. Middle: A subdivision of the map into two regions generated from two un￾shown generator points. Right: Final division of each subregion from the middle figure into desired final divisions. . . . . . . . . . . . . . . . . . . . . 10 4 New York State population density map. Data obtained from a 792-by-660 pixel raster image; color and height indicate the relative population density at each point. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 5 Depiction of the implamentation of Voronoi diagrams with the Manhat￾tan metric in the three step process of: assigning degeneracies to generator points, using the degenerate points to generate regions using the Voronoi diagram method, and creating subregions of the regions generated by de￾generate points. Only the last two steps are depicted. The process for Voronoiesque diagrams is the same. (Dots in each region represent genera￾tor point locations.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 6 Voronoi diagrams generated with three distance metrics before subdivision of densely populated regions. (Dots in each region represent generator point locations.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 7 Districts created by the Voronoiesque diagram for New York state. Average population per region = (3.34 ± 0.74)%. (Dots in each region represent generator point locations.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 8 Illustration of Voronoi diagram generation which takes geographic obstacles into account. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19