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In the first part of the book, Chapters 1 and 2 covers the geoid, the geographic coordinate system of latitudes and longitudes, and the measurement of distance and location. Chapter 3 concerns data structures for geographic information systems, data formatting based on raster graphics and vector graphics , methods for buffer analysis , [ 3 ...
The longitude on the ellipsoid and the distance along the geodesic are then given in terms of the longitude on the sphere and the arc length along the great circle by simple integrals. Bessel and Helmert gave rapidly converging series for these integrals, which allow the geodesic to be computed with arbitrary accuracy.
Map algebra is an algebra for manipulating geographic data, primarily fields.Developed by Dr. Dana Tomlin and others in the late 1970s, it is a set of primitive operations in a geographic information system (GIS) which allows one or more raster layers ("maps") of similar dimensions to produce a new raster layer (map) using mathematical or other operations such as addition, subtraction etc.
Bird's-eye views can be an aerial photograph, but also a drawing, and are often used in the making of blueprints, floor plans and maps. [ 1 ] Before crewed flight was common, the term "bird's eye" was used to distinguish views drawn from direct observation at high vantage locations (e.g. a mountain or tower), from those constructed from an ...
In many branches of mathematics, the term map is used to mean a function, [5] [6] [7] sometimes with a specific property of particular importance to that branch. For instance, a "map" is a "continuous function" in topology, a "linear transformation" in linear algebra, etc.
In taxicab geometry, the distance between any two points equals the length of their shortest grid path. This different definition of distance also leads to a different definition of the length of a curve, for which a line segment between any two points has the same length as a grid path between those points rather than its Euclidean length.
Proximity analysis is a class of spatial analysis tools and algorithms that employ geographic distance as a central principle. [1] Distance is fundamental to geographic inquiry and spatial analysis, due to principles such as the friction of distance, Tobler's first law of geography, and Spatial autocorrelation, which are incorporated into analytical tools. [2]
Many large-scale maps use conformal projections because figures in large-scale maps can be regarded as small enough. The figures on the maps are nearly similar to their physical counterparts. A non-conformal projection can be used in a limited domain such that the projection is locally conformal. Glueing many maps together restores roundness.