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Distance formula, Algebraic expression that gives the distances between pairs of points in terms of their coordinates (see coordinate system).
A zone of width ω on the unit sphere is defined as the set of points within spherical distance ω/2 of a given great circle.
was computed for each spherical distance.
Considering Bruns's formula, Stokes's integral formula for geoid determination is given as (Stokes, 1849; Heiskanen and Moritz, 1967), (12) where N is the geoid undulation, ψ is the spherical distance between the running and the computation points, R is the mean radius of the Earth, and S is the Stokes's kernel.
The optimal spherical distance was evaluated empirically by comparing gravimetric and GPS/leveling geoid undulations at various spherical distances.
In this case, the circular distance is equal to the spherical distance, since.
Therefore, a method to personalize the distance formula is proposed.
The optimal spherical distance was evaluated empirically by comparing gravimetric and GPS/levelling geoid undulations at spherical distances ranging from 18 km to 72 km.
Notice that the relation in above lemma does not hold for spherical distance, since for spherical distance maybe larger than as shown in Figure 4(b).
In this paper, we will use three different distances as the route metric in routing algorithm: Euclidean distance, spherical distance and circular distance.
Distances between two customers are calculated using the Euclidean distance formula.
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