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When each cell of a grid is subject to a recursive partition, resulting in a "series of discrete global grids with progressively finer resolution", [2] forming a hierarchical grid, it is called a hierarchical DGG (sometimes "global hierarchical tessellation" [3] or "DGG system"). Discrete global grids are used as the geometric basis for the ...
Triangulated irregular network TIN overlaid with contour lines. In computer graphics, a triangulated irregular network (TIN) [1] is a representation of a continuous surface consisting entirely of triangular facets (a triangle mesh), used mainly as Discrete Global Grid in primary elevation modeling.
This is an example of a "space-driven" or data independent method, as opposed to "data-driven" or data dependent method, as discussed further in Rigaux et al. (2002)). [3] A grid-based spatial index has the advantage that the structure of the index can be created first, and data added on an ongoing basis without requiring any change to the ...
There are several discrete fixed-point theorems, stating conditions under which a discrete function has a fixed point. For example, the Iimura-Murota-Tamura theorem states that (in particular) if f {\displaystyle f} is a function from a rectangle subset of Z d {\displaystyle \mathbb {Z} ^{d}} to itself, and f {\displaystyle f} is hypercubic ...
A "global DEM" refers to a discrete global grid. DEMs are used often in geographic information systems (GIS), and are the most common basis for digitally produced relief maps . A digital terrain model ( DTM ) represents specifically the ground surface while DEM and DSM may represent tree top canopy or building roofs.
This is a discrete analogue of the Kakutani fixed-point theorem, and the function f is an analogue of a continuous selection function. [3.12] Suppose X is a finite integrally-convex subset of Z n {\displaystyle \mathbb {Z} ^{n}} , and it is also symmetric in the sense that x is in X iff - x is in X .
Such a grid does not have a straightforward relationship to latitude and longitude, but conforms to many of the main criteria for a statistically valid discrete global grid. [9] Primarily, the cells' area and shape are generally similar, especially near the poles where many other spatial grids have singularities or heavy distortion.
Example of a regular grid. A regular grid is a tessellation of n-dimensional Euclidean space by congruent parallelotopes (e.g. bricks). [1] Its opposite is irregular grid.. Grids of this type appear on graph paper and may be used in finite element analysis, finite volume methods, finite difference methods, and in general for discretization of parameter spaces.