distance: Vincenty Direct Calculation of Distance and Direction

In SDMTools: Species Distribution Modelling Tools: Tools for processing data associated with species distribution modelling exercises

Description

distance estimates the distance given a starting & ending latitude and longitude.

For general information on Vincenty's formula, see e.g., http://en.wikipedia.org/wiki/Vincenty's_formulae. It states:
Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of an spheroid, developed by Thaddeus Vincenty in 1975. They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than methods such as great-circle distance which assume a spherical Earth.

Note: this method assumes a locations are lat & lon given in WGS 84.

Direction, if requested, is the the initial bearing (sometimes referred to as forward azimuth) for which one would follow as a straight line along a great-circle arc from start to finish.

Note: this will fail if there are NA's in the data.

Usage

distance(lat1, lon1 = NULL, lat2 = NULL, lon2 = NULL, bearing = FALSE)

Arguments

lat1	a single value or vector of values representing latitude in decimal degrees from -90 to 90 degrees. Alternatively, a data.frame or matrix can be used here with each column representing lat1, lon1, lat2, lon2 (in that order).
lon1	a single value or vector of values representing longitude in decimal degrees from -180 to 180 degrees. If NULL, lat1 is assumed to be a matrix or data.frame.
lat2	a single value or vector of values representing latitude in decimal degrees from -90 to 90 degrees. If NULL, lat1 is assumed to be a matrix or data.frame.
lon2	a single value or vector of values representing longitude in decimal degrees from -180 to 180 degrees. If NULL, lat1 is assumed to be a matrix or data.frame.
bearing	boolean value as to calculate the direction as well as the distance.

Value

Returns a data.frame with:

lon1	the original longitude
lat1	the original latitude
lon2	the destination longitude
lat2	the destination latitude
distance	the distance used
bearing	if requested, the bearing between the two points

Author(s)

Jeremy VanDerWal [e-mail]

Source

The source code for the distance algorithm here was modified from http://www.movable-type.co.uk/scripts/latlong-vincenty.html.

Distances were validated against Geoscience Australia calculations (http://www.ga.gov.au/geodesy/datums/vincenty_inverse.jsp).

Bearings were from multiple sources including http://williams.best.vwh.net/avform.htm#Crs.

References

Vincenty, T. 1975. Direct and Inverse Solutions of Geodesics on the Ellipsoid with application of Nested Equations. Survey Review, vol XXII no 176. http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf

See Also

destination

Examples

#get the distance of 1 degree longitude at each 5 degrees latitude from -90 to 90
distance(lat1=seq(-90,90,5),lon1=rep(0,37),lat2=seq(-90,90,5),lon2=rep(1,37),bearing=TRUE)

Example output

   lat1 lon1 lat2 lon2  distance  bearing
1   -90    0  -90    1      0.00 90.50000
2   -85    0  -85    1   9734.15 90.49810
3   -80    0  -80    1  19391.28 90.49240
4   -75    0  -75    1  28895.14 90.48296
5   -70    0  -70    1  38171.07 90.46985
6   -65    0  -65    1  47146.67 90.45316
7   -60    0  -60    1  55752.52 90.43302
8   -55    0  -55    1  63922.76 90.40958
9   -50    0  -50    1  71595.61 90.38303
10  -45    0  -45    1  78713.83 90.35356
11  -40    0  -40    1  85225.05 90.32140
12  -35    0  -35    1  91082.08 90.28679
13  -30    0  -30    1  96243.05 90.25000
14  -25    0  -25    1 100671.60 90.21131
15  -20    0  -20    1 104336.93 90.17101
16  -15    0  -15    1 107213.84 90.12941
17  -10    0  -10    1 109282.75 90.08683
18   -5    0   -5    1 110529.68 90.04358
19    0    0    0    1 110946.26 90.00000
20    5    0    5    1 110529.68 89.95642
21   10    0   10    1 109282.75 89.91317
22   15    0   15    1 107213.84 89.87059
23   20    0   20    1 104336.93 89.82899
24   25    0   25    1 100671.60 89.78869
25   30    0   30    1  96243.05 89.75000
26   35    0   35    1  91082.08 89.71321
27   40    0   40    1  85225.05 89.67860
28   45    0   45    1  78713.83 89.64644
29   50    0   50    1  71595.61 89.61697
30   55    0   55    1  63922.76 89.59042
31   60    0   60    1  55752.52 89.56698
32   65    0   65    1  47146.67 89.54684
33   70    0   70    1  38171.07 89.53015
34   75    0   75    1  28895.14 89.51704
35   80    0   80    1  19391.28 89.50760
36   85    0   85    1   9734.15 89.50190
37   90    0   90    1      0.00 89.50000

SDMTools documentation built on Jan. 11, 2020, 9:23 a.m.