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Driving Range Polygon WGS84 Standard d hav r = hav(φ2 − φ1) + cos(φ1) cos(φ2) hav(λ2 − λ1), where hav is the haversine function defined as 2 θ 1−cos(θ) 2 θ 2 = 1−cos(θ) 2 , hav(θ) = sin 2 = 2 hav(θ) = sin where d is the distance between the two points, r is the radius of the sphere, φ1,φ2: latitude of point 1 and 2, in radians, λ1,λ2: longitude of point 1 and 2, in radians. The distance d could be obtained applying the inverse haversine as follows. −1 √ (h) = 2rarcsin h d = rhav d = 2r arcsin hav(φ2 − φ1) + cos(φ1) cos(φ2) hav(λ2 − λ1) = = 2r arcsin 5.4 WGS84 Standard The World Geodetic System is a standard established in 1984. It allows us to estimate the ellipsoid (in our case the Earth) with a precision of centimeters. This standard is used by GPS and it is implemented in the Haversine formula used in the final source code. This standard defines the coordinates system, geoid, and referenced ellipsoid. It was developed by the U.S. Army. The geoid is defined as an ideal model of the Earth but this model is hard to describe mathematically and it is not suitable for geographical and cartographical tasks. Because of this, it is common to use reference model WGS84 instead. The origin of this standard is meant to be located at the Earth’s center of mass. It is computed with help of satellite measurement and it was last revised in 2004. The coordinate system is based on this standard. Each geographic point is defined with its longitude, latitude and elevation level [Verheijen, 2016]. 13 φ2 −φ1 λ2 −λ1 sin2 + cos(φ1) cos(φ2) sin2 22PDF Image | Driving Range Estimation and Trajectory Planning
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