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In cartography, a map projection is any of a broad set of transformations employed to represent the curved two-dimensional surface of a globe on a plane. [1] [2] [3] In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane.
The two straight-line distances from any point on the map to the two control points are correct. 2021 Gott, Goldberg and Vanderbei’s Azimuthal Equidistant J. Richard Gott, Goldberg and Robert J. Vanderbei: Gott, Goldberg and Vanderbei’s double-sided disk map was designed to minimize all six types of map distortions.
The most common type of occupancy grid maps are 2d maps that describe a slice of the 3d world. If we let m i {\displaystyle m_{i}} denote the grid cell with index i (often in 2d maps, two indices are used to represent the two dimensions), then the notation p ( m i ) {\displaystyle p(m_{i})} represents the probability that cell i is occupied.
A world map is a map of most or all of the surface of Earth. World maps, because of their scale, must deal with the problem of projection. Maps rendered in two dimensions by necessity distort the display of the three-dimensional surface of the Earth. While this is true of any map, these distortions reach extremes in a world map.
The projection found on these maps, dating to 1511, was stated by John Snyder in 1987 to be the same projection as Mercator's. [6] However, given the geometry of a sundial, these maps may well have been based on the similar central cylindrical projection, a limiting case of the gnomonic projection, which is the basis for a sundial. Snyder ...
In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems.
Inset maps may serve several purposes, such as showing the context of the main map in a larger area, showing more detail for a subset of the main map, showing a separated but related area, or showing related themes for the same region. A bar scale or other indication of scale translates between map measurements and real distances.
Cube maps provide a fairly straightforward and efficient solution to rendering stable specular highlights. Multiple specular highlights can be encoded into a cube map texture, which can then be accessed by interpolating across the surface's reflection vector to supply coordinates. Relative to computing lighting at individual vertices, this ...