Search results
Results from the WOW.Com Content Network
The exponential map of the Earth as viewed from the north pole is the polar azimuthal equidistant projection in cartography. In Riemannian geometry, an exponential map is a map from a subset of a tangent space T p M of a Riemannian manifold (or pseudo-Riemannian manifold) M to M itself. The (pseudo) Riemannian metric determines a canonical ...
exponential map (Lie theory) from a Lie algebra to a Lie group, More generally, in a manifold with an affine connection , X ↦ γ X ( 1 ) {\displaystyle X\mapsto \gamma _{X}(1)} , where γ X {\displaystyle \gamma _{X}} is a geodesic with initial velocity X , is sometimes also called the exponential map.
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 two-point equidistant projection or doubly equidistant projection is a map projection first described by Hans Maurer in 1919 and Charles Close in 1921. [1] [2] It is a generalization of the much simpler azimuthal equidistant projection. In this two-point form, two locus points are chosen by the mapmaker to configure the projection ...
If the azimuthal equidistant projection map is centered about a point whose antipodal point lies on land and the map is extended to the maximum distance of 20,000 km (12,427 mi) the antipode point smears into a large circle. This is shown in the example of two maps centered about Los Angeles, and Taipei.
It is the exponential map of a canonical right-invariant affine connection on G. This is usually different from the canonical left-invariant connection, but both connections have the same geodesics (orbits of 1-parameter subgroups acting by left or right multiplication) so give the same exponential map.
AOL
Composition of (r,φ) with the inverse of the exponential map at p is a polar coordinate system. Polar coordinates provide a number of fundamental tools in Riemannian geometry. The radial coordinate is the most significant: geometrically it represents the geodesic distance to p of nearby points.