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Shortest-path Graph
In mathematics and geographic information science, a shortest-path graph is an undirected graph defined from a set of points in the Euclidean plane. The shortest-path graph is proposed with the idea of inferring edges between a point set such that the shortest path taken over the inferred edges will roughly align with the shortest path taken over the imprecise region represented by the point set. The edge set of the shortest-path graph varies based on a single parameter ''t'' ≥ 1. When the weight of an edge is defined as its Euclidean length raised to the power of the parameter ''t'' ≥ 1, the edge is present in the shortest-path graph if and only if it is the least weight path between its endpoints. Properties of shortest-path graph When the configuration parameter ''t'' goes to infinity, shortest-path graph become the minimum spanning tree of the point set. The graph is a subgraph of the point set's Gabriel graph and therefore also a subgraph of its D ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lake Michigan Shortest Path Graph T=2
A lake is often a naturally occurring, relatively large and fixed body of water on or near the Earth's surface. It is localized in a basin or interconnected basins surrounded by dry land. Lakes lie completely on land and are separate from the ocean, although they may be connected with the ocean by rivers. Lakes, as with other bodies of water, are part of the water cycle, the processes by which water moves around the Earth. Most lakes are fresh water and account for almost all the world's surface freshwater, but some are salt lakes with salinities even higher than that of seawater. Lakes vary significantly in surface area and volume of water. Lakes are typically larger and deeper than ponds, which are also water-filled basins on land, although there are no official definitions or scientific criteria distinguishing the two. Lakes are also distinct from lagoons, which are generally shallow tidal pools dammed by sandbars or other material at coastal regions of oceans or large la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
