Contents
VDIST - Using the WGS-84 Earth ellipsoid, compute the distance between two points
within a few millimeters of accuracy, compute forward azimuth, and compute backward azimuth, all using a vectorized version of Vincenty's algorithm.
s = vdist(lat1,lon1,lat2,lon2) [s,a12] = vdist(lat1,lon1,lat2,lon2) [s,a12,a21] = vdist(lat1,lon1,lat2,lon2)
- s = distance in meters (inputs may be scalars, vectors, or matrices)
- a12 = azimuth in degrees from first point to second point (forward)
- a21 = azimuth in degrees from second point to first point (backward) (Azimuths are in degrees clockwise from north.)
- lat1 = GEODETIC latitude of first point (degrees)
- lon1 = longitude of first point (degrees)
- lat2, lon2 = second point (degrees)
Original algorithm source:
T. Vincenty, "Direct and Inverse Solutions of Geodesics on the Ellipsoid with Application of Nested Equations", Survey Review, vol. 23, no. 176, April 1975, pp 88-93. http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf
Notes:
- lat1,lon1,lat2,lon2 can be any (identical) size/shape. Outputs will have the same size and shape.
- Error correcting code, convergence failure traps, antipodal corrections, polar error corrections, WGS84 ellipsoid parameters, testing, and comments: Michael Kleder, 2004.
- Azimuth implementation (including quadrant abiguity resolution) and code vectorization, Michael Kleder, Sep 2005.
- Vectorization is convergence sensitive; that is, quantities which have already converged to within tolerance are not recomputed during subsequent iterations (while other quantities are still converging).
- Vincenty describes his distance algorithm as precise to within 0.01 millimeters, subject to the ellipsoidal model.
- For distance calculations, essentially antipodal points are treated as exactly antipodal, potentially reducing accuracy slightly.
- Distance failures for points exactly at the poles are eliminated by moving the points by 0.6 millimeters.
- The Vincenty distance algorithm was transcribed verbatim by Peter Cederholm, August 12, 2003. It was modified and translated to English by Michael Kleder. Mr. Cederholm's website is http://www.plan.aau.dk/~pce/
- Distances agree with the Mapping Toolbox, version 2.2 (R14SP3) with a max relative difference of about 5e-9, except when the two points are nearly antipodal, and except when one point is near the equator and the two longitudes are nearly 180 degrees apart. This function (vdist) is more accurate in such cases. For example, note this difference (as of this writing): >>vdist(0.2,305,15,125) 18322827.0131551 >>distance(0.2,305,15,125,[6378137 0.08181919]) 0
- Azimuths FROM the north pole (either forward starting at the north pole or backward when ending at the north pole) are set to 180 degrees by convention. Azimuths FROM the south pole are set to 0 degrees by convention.
- Azimuths agree with the Mapping Toolbox, version 2.2 (R14SP3) to within about a hundred-thousandth of a degree, except when traversing to or from a pole, where the convention for this function is described in (10), and except in the cases noted above in (9).
- No warranties; use at your own risk.