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A geodesic grid is a global Earth spatial reference that uses polygon tiles based on the subdivision of a polyhedron (usually the icosahedron, and usually a Class I subdivision) to subdivide the surface of the Earth.
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.
Geodetic latitude and geocentric latitude have different definitions. Geodetic latitude is defined as the angle between the equatorial plane and the surface normal at a point on the ellipsoid, whereas geocentric latitude is defined as the angle between the equatorial plane and a radial line connecting the centre of the ellipsoid to a point on the surface (see figure).
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 index structure; indeed, if a common grid is used by disparate data collecting and indexing activities, such indices can easily be merged from a variety of sources.
For example on a sphere, any geodesic passing through the north-pole can be extended to reach the south-pole, and hence any geodesic segment connecting the poles is not (uniquely) globally length minimizing. This tells us that any pair of antipodal points on the standard 2-sphere are conjugate points.
The World Geodetic System (WGS) is a standard used in cartography, geodesy, and satellite navigation including GPS.The current version, WGS 84, defines an Earth-centered, Earth-fixed coordinate system and a geodetic datum, and also describes the associated Earth Gravitational Model (EGM) and World Magnetic Model (WMM).
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.
Example: grid with coordinates (φ,λ,z) where z is the elevation. A standard Geoid surface. The z coordinate is zero for all grid, thus can be omitted, (φ,λ). Ancient standards, before 1687 (the Newton's Principia publication), used a "reference sphere"; in nowadays the Geoid is mathematically abstracted as reference ellipsoid.