SpatialVx (version 0.1-5)

bearing: Bearing from One Spatial Location to Another

Description

Find the bearing from one spatial location to another.

Usage

bearing(point1, point2, deg = TRUE, aty = "compass")

Arguments

point1, point2

two-column numeric matrices giving lon/lat coordinates for the origin point(s) (point1) and the destination point(s) (point2).

deg

logical, should the output be converted from radians to degrees?

aty

character stating either compass (default) or radial. The former gives the standard compass bearing angle (0 is north, increase clockwise), and the latter is for polar coordinates (0 is East, increase counter-clockwise).

Value

• numeric giving the bearing angle.

Details

The bearing, beta, of a point B as seen from a point A is given by

beta = atan2(S,T)

where

S = cos(phi_B) * sin(L_A - L_B), and

T = cos(phi_A)*sin(phi_B) - sin(phi_A)*cos(phi_B)*cos(L_A - L_B)

where phi_A (phi_B) is the latitude of point A (B), and L_A (L_B) is the longitude of point A (B).

Note that there is no simple relationship between the bearing of A to B vs. the bearing of B to A. The bearing given here is in the usual R convention for lon/lat information, which gives points east of Greenwich as negative longitude, and south of the equator as negative latitude.

References

Keay, W. (1995) Land Navigation: Routefinding with Map & Compass, Coventry, UK: Clifford Press Ltd., ISBN 0319008452, 978-0319008454

See Also

atan2, FeatureAxis, rdist.earth

Examples

A <- rbind(c(-105.2833, 40.0167), c(137.65, -33.9333)) # Boulder, Colorado and Wallaroo, Australia.
B <- rbind(c(137.65, -33.9333), c(-105.2833, 40.0167)) # Wallaroo, Australia and Boulder, Colorado.
bearing(A,B)
bearing(A,B,aty="radial")
plot(A, type="n", xlab="", ylab="")
points(A[,1], A[,2], pch="*", col="darkblue")
arrows(A[1,1], A[1,2], A[2,1], A[2,2], col="red", lwd=1.5) # Boulder, Colorado to Wallaroo, Australia.