To visualize the spatial structure and the connectivity of shared environmental conditions, we first localized potential lineage contact zones using lineage-specific minimum-convex polygons (Additional File 3 - Figure S3) and considered areas as potential contact zones where two polygons overlapped.
"Different colored weaving patterns composed of triangles, quadrilaterals and other polygons overlap, evolve and transform slowly in real time," notes the artist.
The CS has been extended to handle boundary conditions in 2D as well as to calculation of polygon overlap for polygons of more than three sides.
Inter-linguistic contact was calculated based on languages boundaries: for each language we counted the number of languages contained in, overlapping with, or contacting the area polygons of other languages.
To be inconsistent with the cellular clustering structure with highly overlapping partitions, the mobile nodes are grouped into Voronoi polygons with hexagon structure to reduce the cluster construction complexities.
The 10 by 10 meter size was selected because it is small enough to capture both the smallest drawn polygons while at the same time providing incremental variation at the aggregate level when multiple polygons are overlapped.
Among these methods the block-grid method (BGM), presented in [6 8], on polygons with interior angles (alpha_{j}pi), (j=1,2,ldots,N), where (alpha_{j}in { frac{1}{2},1,frac{3}{2},2 } ) (staircase polygons), requires the finite neighborhood of the singular vertices to be covered by sectors (blocks), and the remaining part of the domain by overlapping rectangles ('nonsingular' part).
Images on-screen were digitized through the Windows operating environment of ArcGIS under the following three main themes: line boundaries of the 25 LGAs and the three AGZs joining together (polygons), CBPP risk herd locations (points), overlapped by the number of cattle sero-positive of the disease (proportional circles).
