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On a triaxial ellipsoid, there are only three simple closed geodesics, the three principal sections of the ellipsoid given by X = 0, Y = 0, and Z = 0. [7] To survey the other geodesics, it is convenient to consider geodesics that intersect the middle principal section, Y = 0 , at right angles.
An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional scalings, or more generally, ... Geodesics on an ellipsoid;
Vincenty's goal was to express existing algorithms for geodesics on an ellipsoid in a form that minimized the program length (Vincenty 1975a). His unpublished report (1975b) mentions the use of a Wang 720 desk calculator, which had only a few kilobytes of memory. To obtain good accuracy for long lines, the solution uses the classical solution ...
Klein quartic with 28 geodesics (marked by 7 colors and 4 patterns). 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 (non-trivial) intersection of a plane and ellipsoid is an ellipse. Therefore, the arc length, s 12 {\displaystyle s_{12}} , on the section path from P 1 {\displaystyle P_{1}} to P 2 {\displaystyle P_{2}} is an elliptic integral that may be computed to any desired accuracy using a truncated series or numerical integration.
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 reference ellipsoid, customarily chosen to be the same size (volume) as the geoid, is described by its semi-major axis (equatorial radius) a and flattening f. The quantity f = a − b / a , where b is the semi-minor axis (polar radius), is purely geometrical.
Geodesic on an oblate ellipsoid. An ellipsoid approximates the surface of the Earth much better than a sphere or a flat surface does. The shortest distance along the surface of an ellipsoid between two points on the surface is along the geodesic. Geodesics follow more complicated paths than great circles and in particular, they usually don't ...