hzar.map.greatCircleDistance: The distance between two points on the Earth's surface.
In hzar: Hybrid Zone Analysis using R

Description Usage Arguments Details Value Author(s) References Examples

The distance along a great circle between two points on a spheroid approximation of the Earth's surface.

1	hzar.map.greatCircleDistance(lat1, long1, lat2, long2, units = "Km", degrees = TRUE)

`lat1`	The latitude of point 1.
`long1`	The latitude of point 1.
`lat2`	The latitude of point 2.
`long2`	The latitude of point 2.
`units`	The units of distances returned. Only the case sensitive values `"Km"` for kilometers, `"miles"` for miles, and `"nautical"` for nautical miles are valid.
`degrees`	Are the latitude and longitude in degrees?

The Lambert formula is the approximation used to calculate the distance, due to its high accuracy and robustness.

Geometry of Earth R = 6371.009 #Earth radius in kilometers earthSphd.r = 298.257223563 #WGS84 earthSphd.ep= (2*earthSphd.r -1)/(earthSphd.r-1)^2

dLat=p2$lat.rad-p1$lat.rad; dLong=p2$long.rad-p1$long.rad; dLong=ifelse( dLong>pi, dLong-2*pi, ifelse(-dLong>pi, dLong+2*pi, dLong));

mLat=(p2$lat.rad+p1$lat.rad)/2;

reLat1=atan((earthSphd.r -1)*tan(p1$lat.rad) /earthSphd.r ) reLat2=atan((earthSphd.r -1)*tan(p2$lat.rad) /earthSphd.r ) cenNum=sqrt((cos(reLat2)*sin(dLong))^2+(cos(reLat1)*sin(reLat2)-cos(reLat2)*sin(reLat1)*cos(dLong))^2); cenDen=sin(reLat1)*sin(reLat2)+cos(reLat2)*cos(reLat1)*cos(dLong); central <- atan2(cenNum,cenDen); lFP <- (reLat1+ reLat2)/2 ; lFQ <- (-reLat1+ reLat2)/2 ; lFX <- (central-sin(central))*sin(lFP)^2*cos(lFQ)^2/cos(central/2)^2; lFY <- (central+sin(central))*cos(lFP)^2*sin(lFQ)^2/sin(central/2)^2;

lambertFormulaeD <- ifelse(central==0,0,R*(central-(lFX+lFY)/(2*earthSphd.r)));

The great circle distance between points 1 and 2.

Graham Derryberry asterion@alum.mit.edu

Lambert formula, published on the web somewhere.

hzar.map.greatCircleDistance(89.5,60,89.5,390)
# 28.87587
hzar.map.greatCircleDistance(-89.5,-90,89.5,90)
# 19981.56
hzar.map.greatCircleDistance(-89.5,90,89.5,90)
# 19869.99
hzar.map.greatCircleDistance(0,90,89.5,90)
# 9934.996
hzar.map.greatCircleDistance(0,90,0,-90)
# 20015.12
hzar.map.greatCircleDistance(0,90,0,180)
# 10007.56

Loading required package: MCMCpack
Loading required package: coda
Loading required package: MASS
##
## Markov Chain Monte Carlo Package (MCMCpack)
## Copyright (C) 2003-2018 Andrew D. Martin, Kevin M. Quinn, and Jong Hee Park
##
## Support provided by the U.S. National Science Foundation
## (Grants SES-0350646 and SES-0350613)
##
Loading required package: foreach
[1] 28.87587
[1] 19981.56
[1] 19869.99
[1] 9934.996
[1] 20015.12
[1] 10007.56