Distance between points on sphere or ellipsoid
[
computes the lengths, arclen,az] = distance(lat1,lon1,lat2,lon2)arclen, of the great circle arcs
connecting pairs of points on the surface of a sphere. In each case, the shorter
(minor) arc is assumed. The function can also compute the azimuths,
az, of the second point in each pair with respect to the
first (that is, the angle at which the arc crosses the meridian containing the
first point).
Using pt1,pt2 notation, find the distance from Norfolk,
Virginia (37°N, 76°W), to Cape St. Vincent, Portugal (37°N, 9°W), just outside the
Straits of Gibraltar. The distance between these two points depends upon the
track value selected.
arclen = distance('gc',[37,-76],[37,-9])
arclen = 52.3094
arclen = distance('rh',[37,-76],[37,-9])
arclen =
53.5086The difference between these two tracks is 1.1992 degrees, or about 72 nautical miles. This represents about 2% of the total trip distance. The tradeoff is that at the cost of those 72 miles, the entire trip can be made on a rhumb line with a fixed course of 90º, due east, while in order to follow the shorter great circle path, the course must be changed continuously.
On a meridian and on the Equator, great circles and rhumb lines coincide, so the distances are the same. For example,
% Great circle distance
arclen = distance(37,-76,67,-76)
arclen =
30.0000
% Rhumb line distance arclen = distance('rh',37,-76,67,-76)
arclen =
30.0000The size of nonscalar latitude and longitude coordinates,
lat1, lon1,
lat2, and lon2, must be
consistent. When given a combination of scalar and array inputs, the
distance function automatically expands scalar inputs to
match the size of the arrays.
To express the output arclen as an arc length in either
degrees or radians, omit the ellipsoid argument. This is
possible only on a sphere. If ellipsoid is supplied,
arclen is a distance expressed in the same units as the
semimajor axis of the ellipsoid. Specify ellipsoid as
[R 0] to compute arclen as a distance
on a sphere of radius R, with arclen
having the same units as R.
Distance calculations for geodesics degrade slowly with increasing distance and may
break down for points that are nearly antipodal, as well as when both points are very
close to the Equator. In addition, for calculations on an ellipsoid, there is a small
but finite input space, consisting of pairs of locations in which both the points are
nearly antipodal and both points fall close to (but not precisely
on) the Equator. In this case, a warning is issued and both arclen
and az are set to NaN for the “problem
pairs.”
Distance between two points can be calculated in two ways. For great circles (on the sphere) and geodesics (on the ellipsoid), the distance is the shortest surface distance between two points. For rhumb lines, the distance is measured along the rhumb line passing through the two points, which is not, in general, the shortest surface distance between them.
When you need to compute both distance and azimuth for the same point pair(s), it is
more efficient to do so with a single call to distance. That is,
use
[arclen az] = distance(...);
arclen = distance(...) az = azimuth(...)