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The straight-line distance between the central point on the map to any other point is the same as the straight-line 3D distance through the globe between the two points. c. 150 BC: Stereographic: Azimuthal Conformal Hipparchos* Map is infinite in extent with outer hemisphere inflating severely, so it is often used as two hemispheres.
That is (unlike road distance with one-way streets) the distance between two points does not depend on which of the two points is the start and which is the destination. [11] It is positive, meaning that the distance between every two distinct points is a positive number, while the distance from any point to itself is zero. [11]
The slant distance s (chord length) between two points can be reduced to the arc length on the ellipsoid surface S as: [21] = (+) / / where R is evaluated from Earth's azimuthal radius of curvature and h are ellipsoidal heights are each point. The first term on the right-hand side of the equation accounts for the mean elevation and the second ...
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 ...
The distance between sets A and B is the infimum of the distances between any two of their respective points: (,) =, (,). This does not define a metric on the set of such subsets: the distance between overlapping sets is zero, and this distance does not satisfy the triangle inequality for any metric space with two or more points (consider the ...
Thus a point that has an easting of 400 000 meters is about 100 km west of the central meridian. For most such points, the true distance would be slightly more than 100 km as measured on the surface of the Earth because of the distortion of the projection. UTM eastings range from about 166 000 meters to 834 000 meters at the equator.
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d is the distance between the two points along a great circle of the sphere (see spherical distance), r is the radius of the sphere. The haversine formula allows the haversine of θ to be computed directly from the latitude (represented by φ) and longitude (represented by λ) of the two points:
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