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Geodesic Grid
A geodesic grid is a spatial grid based on a geodesic polyhedron or Goldberg polyhedron. Construction A geodesic grid is a global Earth reference that uses triangular tiles based on the subdivision of a polyhedron (usually the icosahedron, and usually a Class I subdivision) to subdivide the surface of the Earth. 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. Primarily, the cells' area and shape are generally similar, especially near the poles where many other spatial grids have singularities or heavy distortion. The popular Quaternary Triangular Mesh (QTM) falls into this category. Geodesic grids may use the dual polyhedron of the geodesic polyhedron, which is the Goldberg polyhedron. Goldberg polyhedra are made up of hexagons and (if based on the icosahedron) 12 pentagons. One implementation that uses an icosahedron as the base polyhedron, hexagonal ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geodesic Grid (ISEA3H) Illustrated
In geometry, a geodesic () is a curve representing in some sense the shortest path ( arc) 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. It is a generalization of the notion of a "straight line". The noun '' geodesic'' and the adjective ''geodetic'' come from '' geodesy'', the science of measuring the size and shape of Earth, though many of the underlying principles can be applied to any ellipsoidal geometry. In the original sense, a geodesic was the shortest route between two points on the Earth's surface. For a spherical Earth, it is a segment of a great circle (see also great-circle distance). The term has since been generalized to more abstract mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph. In a Riemannian manifold or submanifold, geodesics are characterised by the property of having vani ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Video Game Development
Video game development (or gamedev) is the process of developing a video game. The effort is undertaken by a developer, ranging from a single person to an international team dispersed across the globe. Development of traditional commercial PC and console games is normally funded by a publisher, and can take several years to reach completion. Indie games usually take less time and money and can be produced by individuals and smaller developers. The independent game industry has been on the rise, facilitated by the growth of accessible game development software such as Unity platform and Unreal Engine and new online distribution systems such as Steam and Uplay, as well as the mobile game market for Android and iOS devices. The first video games, developed in the 1960s, were not usually commercialised. They required mainframe computers to run and were not available to the general public. Commercial game development began in the '70s with the advent of first-generation video gam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geodesic Grid Gcrm Atmosphere Vorticity 4096x4096
In geometry, a geodesic () is a curve representing in some sense the shortest path ( arc) 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. It is a generalization of the notion of a "straight line". The noun ''geodesic'' and the adjective ''geodetic'' come from ''geodesy'', the science of measuring the size and shape of Earth, though many of the underlying principles can be applied to any ellipsoidal geometry. In the original sense, a geodesic was the shortest route between two points on the Earth's surface. For a spherical Earth, it is a segment of a great circle (see also great-circle distance). The term has since been generalized to more abstract mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph. In a Riemannian manifold or submanifold, geodesics are characterised by the property of having vanishing ge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyhedral Map Projection
A polyhedral map projection is a map projection based on a spherical polyhedron. Typically, the polyhedron is overlaid on the globe, and each face of the polyhedron is transformed to a polygon or other shape in the plane. The best-known polyhedral map projection is Buckminster Fuller's Dymaxion map. When the spherical polyhedron faces are transformed to the faces of an ordinary polyhedron instead of laid flat in a plane, the result is a polyhedral globe. Often the polyhedron used is a Platonic solid or Archimedean solid. However, other polyhedra can be used: the AuthaGraph projection makes use of a polyhedron with 96 faces, and the myriahedral projection allows for an arbitrary large number of faces. Although interruptions between faces are common, and more common with an increasing number of faces, some maps avoid them: the Lee conformal projection only has interruptions at its border, and the AuthaGraph projection scales its faces so that the map fills a rectangle without inter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadrilateralized Spherical Cube
In mapmaking, a quadrilateralized spherical cube, or quad sphere for short, is an equal-area polyhedral map projection and discrete global grid scheme for data collected on a spherical surface (either that of the Earth or the celestial sphere). It was first proposed in 1975 by Chan and O'Neill for the Naval Environmental Prediction Research Facility. This scheme is also often called the COBE sky cube, because it was designed to hold data from the Cosmic Background Explorer (COBE) project. A related projection called the S2 projection was created at Google for the purpose of defining a discrete global grid scheme. It is similar to the quad sphere but is not equal-area. Elements The quad sphere has two principal characteristic features. The first is that the mapping consists of projecting the sphere onto the faces of an inscribed cube using a curvilinear projection that preserves area. The sphere is divided into six equal regions, which correspond to the faces of the cube. The ve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Design
A spherical design, part of combinatorial design theory in mathematics, is a finite set of ''N'' points on the ''d''-dimensional unit n-sphere, ''d''-sphere ''Sd'' such that the average value of any polynomial ''f'' of degree ''t'' or less on the set equals the average value of ''f'' on the whole sphere (that is, the integral of ''f'' over ''Sd'' divided by the area or Measure (mathematics), measure of ''Sd''). Such a set is often called a spherical ''t''-design to indicate the value of ''t'', which is a fundamental parameter. The concept of a spherical design is due to Delsarte, Goethals, and Seidel, although these objects were understood as particular examples of cubature formulas earlier. Spherical designs can be of value in approximation theory, in statistics for experimental design, in combinatorics, and in geometry. The main problem is to find examples, given ''d'' and ''t'', that are not too large; however, such examples may be hard to come by. Spherical t-designs have also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Global Grid
A discrete global grid (DGG) is a mosaic that covers the entire Earth's surface. Mathematically it is a space partitioning: it consists of a set of non-empty regions that form a partition of the Earth's surface. 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. When each cell of a grid is subject to a recursive partition, resulting in a "series of discrete global grids with progressively finer resolution", forming a hierarchical grid, it is called a hierarchical DGG (sometimes "global hierarchical tessellation" or "DGG system"). Discrete global grids are used as the geometric basis for the building of geospatial data structures. Each cell is related with data objects or values, or (in the hierarchical case) may be associated with other cells. DGGs have been proposed for use in a wide range of geospatial applicati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grid Reference
A projected coordinate system, also known as a projected coordinate reference system, a planar coordinate system, or grid reference system, is a type of spatial reference system that represents locations on the Earth using cartesian coordinates (''x'',''y'') on a planar surface created by a particular map projection. Each projected coordinate system, such as "Universal Transverse Mercator WGS 84 Zone 26N," is defined by a choice of map projection (with specific parameters), a choice of geodetic datum to bind the coordinate system to real locations on the earth, an origin point, and a choice of unit of measure. Hundreds of projected coordinate systems have been specified for various purposes in various regions. When the first standardized coordinate systems were created during the 20th Century, such as the Universal Transverse Mercator, State Plane Coordinate System, and British National Grid, they were commonly called ''grid systems''; the term is still common in some domai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geographic Coordinate System
The geographic coordinate system (GCS) is a spherical or ellipsoidal coordinate system for measuring and communicating positions directly on the Earth as latitude and longitude. It is the simplest, oldest and most widely used of the various spatial reference systems that are in use, and forms the basis for most others. Although latitude and longitude form a coordinate tuple like a cartesian coordinate system, the geographic coordinate system is not cartesian because the measurements are angles and are not on a planar surface. A full GCS specification, such as those listed in the EPSG and ISO 19111 standards, also includes a choice of geodetic datum (including an Earth ellipsoid), as different datums will yield different latitude and longitude values for the same location. History The invention of a geographic coordinate system is generally credited to Eratosthenes of Cyrene, who composed his now-lost ''Geography'' at the Library of Alexandria in the 3rd century ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geodesics On An Ellipsoid
The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth is well approximated by an ''oblate ellipsoid'', a slightly flattened sphere. A ''geodesic'' is the shortest path between two points on a curved surface, analogous to a straight line on a plane surface. The solution of a triangulation network on an ellipsoid is therefore a set of exercises in spheroidal trigonometry . If the Earth is treated as a sphere, the geodesics are great circles (all of which are closed) and the problems reduce to ones in spherical trigonometry. However, showed that the effect of the rotation of the Earth results in its resembling a slightly oblate ellipsoid: in this case, the equator and the meridians are the only simple closed geodesics. Furthermore, the shortest path between two points on the equator does not necessarily run along the equator. Finally, if the ellipsoid is further perturbed to b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Grid
In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. It has Schläfli symbol of meaning it has 4 squares around every vertex. Conway called it a quadrille. The internal angle of the square is 90 degrees so four squares at a point make a full 360 degrees. It is one of three regular tilings of the plane. The other two are the triangular tiling and the hexagonal tiling. Uniform colorings There are 9 distinct uniform colorings of a square tiling. Naming the colors by indices on the 4 squares around a vertex: 1111, 1112(i), 1112(ii), 1122, 1123(i), 1123(ii), 1212, 1213, 1234. (i) cases have simple reflection symmetry, and (ii) glide reflection symmetry. Three can be seen in the same symmetry domain as reduced colorings: 1112i from 1213, 1123i from 1234, and 1112ii reduced from 1123ii. Related polyhedra and tilings This tiling is topologically related as a part of sequence of regular polyhedra and tilings, extending ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaussian Grid
A Gaussian grid is used in the earth sciences as a gridded horizontal coordinate system for scientific modeling on a sphere (i.e., the approximate shape of the Earth). The grid is rectangular, with a set number of orthogonal coordinates (usually latitude and longitude). At a given latitude (or ''parallel''), the gridpoints are ''equally'' spaced. On the contrary along a longitude (or ''meridian'') the gridpoints are ''unequally'' spaced. The spacing between grid points is defined by Gaussian quadrature. By contrast, in the "normal" geographic latitude-longitude grid, gridpoints are equally spaced along both latitudes and longitudes. Gaussian grids also have no grid points at the poles. In a ''regular'' Gaussian grid, the number of gridpoints along the longitudes is constant, usually double the number along the latitudes. In a ''reduced'' (or ''thinned'') Gaussian grid, the number of gridpoints in the rows decreases towards the poles, which keeps the gridpoint separation approx ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
