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scale-specific automated map line simplification by vertex clustering on a hexagonal tessellation

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Scale-specific automated map line simplification by vertex clustering on a hexagonal tessellation Research Purpose To make maps at smaller scales from higher-scale data, cartographers need to generalize. Increasingly, topographic mapping agencies seek automated processes to achieve generalization. Since few automated processes in use today are scale-specific, this research has focused on developing a scale-specific algorithm for line simplification. This poster describes the algorithm, and demonstrates its simplification of a portion of the coast of Maine. ! ! ! ! ! ! ! ! ! ! ! ! ! !! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !! ! ! ! ! ! ! !! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !!! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! Algorithm Description A tessellation of regular hexagons is imposed on the input line, with hexagons scaled in direct relation to the target scale and drawing resolution on the target map. Inside each hexagon, input line vertices are clustered and collapsed to a single vertex. These vertices are then linked together to form the output line. Hexagon Scaling The width of hexagons, r, in meters, is determined according to r = 5(l)(s) where l is the line weight the line shall be drawn with on the target map (i.e., the resolution of the map), and s is the target scale denominator. The coefficient of 5 follows from Tobler’s (1987) rule of thumb sampling resolution. Portion of the coast of Maine 1:24,000 1:50,000 1:100,000 1:200,000 1:250,000 1:1,000,000 1:500,000 Future Work Depending on how vertices are clustered within hexagons, the algorithm can produce occasional line self-crossings. A post-processing routine taking advantage of vertex sequencing along the polyline is under development to address this issue. Iterating through instances of self-crossing, the sequence between each two crossing line segments is reversed to “untangle” self-crossings. 1:150,000 P. Raposo Citation: Tobler, W. R. (1987). Measuring spatial resolution. Paper presented at the International Workshop On Geographic Information Systems, Beijing, China. Data used in this poster taken from Esri and the USGS. 4 6 3 5 9 8 7 2 1 17 18 20 19 16 15 14 12 11 10 13 5 4 3 6 7 8 2 1 18 20 19 17 11 12 13 14 15 9 16 10 4 5 3 9 8 7 6 2 1 18 20 19 17 15 14 13 10 16 12 11 4 5 3 6 7 8 2 1 18 20 19 17 11 12 13 14 15 9 16 10 b b b

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poster by second-year master's candidate Paulo Raposo

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Page 1: Scale-specific automated map line simplification by vertex clustering on a hexagonal tessellation

Scale-specific automated map line simplification by vertex clustering on a hexagonal tessellationResearch PurposeTo make maps at smaller scales from higher-scale data, cartographers need to generalize. Increasingly, topographic mapping agencies seek automated processes to achieve generalization. Since few automated processes in use today are scale-specific, this research has focused on developing a scale-specific algorithm for line simplification.

This poster describes the algorithm, and demonstrates its simplification of a portion of the coast of Maine.

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Algorithm DescriptionA tessellation of regular hexagons is imposed on the input line, with hexagons scaled in direct relation to the target scale and drawing resolution on the target map. Inside each hexagon, input line vertices are clustered and collapsed to a single vertex. These vertices are then linked together to form the output line.

Hexagon ScalingThe width of hexagons, r, in meters, is determined according to

r = 5(l)(s)where l is the line weight the line shall be drawn with on the target map (i.e., the resolution of the map), and s is the target scale denominator. The coefficient of 5 follows from Tobler’s (1987) rule of thumb sampling resolution.

Portion of the coast of Maine1:24,000

1:50,000

1:100,000

1:200,000 1:250,000 1:1,000,0001:500,000

Future WorkDepending on how vertices are clustered within hexagons, the algorithm can produce occasional line self-crossings. A post-processing routine taking advantage of vertex sequencing along the polyline is under development to address this issue. Iterating through instances of self-crossing, the sequence between each two crossing line segments is reversed to “untangle” self-crossings.

1:150,000

P. Raposo

Citation: Tobler, W. R. (1987). Measuring spatial resolution. Paper presented at the International Workshop On Geographic Information Systems, Beijing, China. Data used in this poster taken from Esri and the USGS.

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