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A geodesic grid allows local to global assimilation of ecologically significant information at its own level of granularity. [ 13 ] When modeling the weather , ocean circulation, or the climate , partial differential equations are used to describe the evolution of these systems over time.
In geometry, a geodesic (/ ˌ dʒ iː. ə ˈ d ɛ s ɪ k,-oʊ-,-ˈ d iː s ɪ k,-z ɪ k /) [1] [2] is a curve representing in some sense the locally [a] shortest [b] path between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection.
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Mathematically it is a space partitioning: it consists of a set of non-empty regions that form a partition of the Earth's surface. [1] In a usual grid-modeling strategy, to simplify position calculations, each region is represented by a point, abstracting the grid as a set of region-points. Each region or region-point in the grid is called a cell.
The MODLAND Integerized Sinusoidal Grid, based on the sinusoidal projection, is a geodesic grid developed by the NASA's Moderate-Resolution Imaging Spectroradiometer science team. [ 4 ] See also
Geodesic polyhedra are available as geometric primitives in the Blender 3D modeling software package, which calls them icospheres: they are an alternative to the UV sphere, having a more regular distribution. [4] [5] The Goldberg–Coxeter construction is an expansion of the concepts underlying geodesic polyhedra.
English: Part a shows a rectilinear grid in the horizontal plane. Part b shows a curvilinear grid in the horizontal plane. Part c shows a z-level grid structure in the vertical plane. Part d shows a s-level grid structure in the vertical plane. This figure is taken from Delandmeter and van Sebille 2019 (Delandmeter, P. and van Sebille, E.:
This is analogous to the Earth's surface, where the geodesic between two points along a great circle is the shortest route only up to the antipodal point; beyond that, there are shorter paths. Beyond a conjugate point, a geodesic in Lorentzian geometry may not be maximizing proper time (for timelike geodesics), and the geodesic may enter a ...