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Finding the geodesic between two points on the Earth, the so-called inverse geodetic problem, was the focus of many mathematicians and geodesists over the course of the 18th and 19th centuries with major contributions by Clairaut, [5] Legendre, [6] Bessel, [7] and Helmert English translation of Astron. Nachr. 4, 241–254 (1825).
The Dubins' path gives the shortest path joining two oriented points that is feasible for the wheeled-robot model. The optimal path type can be described using an analogy with cars of making a 'right turn (R)', 'left turn (L)' or driving 'straight (S).' An optimal path will always be at least one of the six types: RSR, RSL, LSR, LSL, RLR, LRL.
Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a). They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than methods that assume a spherical Earth, such ...
Going the "long way round" on a great circle between two points on a sphere is a geodesic but not the shortest path between the points. The map t → t 2 {\displaystyle t\to t^{2}} from the unit interval on the real number line to itself gives the shortest path between 0 and 1, but is not a geodesic because the velocity of the corresponding ...
Altitude is a vertical measurement between a reference datum and an object. Altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context (e.g., aviation, geometry, geographical survey, sport, or atmospheric ...
More generally, a contour line for a function of two variables is a curve connecting points where the function has the same particular value. [2] In cartography, a contour line (often just called a "contour") joins points of equal elevation (height) above a given level, such as mean sea level. [3]
The difference between these two readings equals the change in elevation, which is why this method is also called differential levelling. The procedure is repeated until the destination point is reached. It is usual practice to perform either a complete loop back to the starting point or else close the traverse on a second point whose elevation ...
The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes.Important in navigation, it is a special case of a more general formula in spherical trigonometry, the law of haversines, that relates the sides and angles of spherical triangles.