[R-sig-Geo] Determining a coordinate given another coordinate, a great circle distance, and an angle

[Tomislav Hengl]

Hi Harry,

The key issue is that you need to select the (Euclidean) coordinate system. For example, to
represent the whole world, there are many possiblities
(http://www.radicalcartography.net/?projectionref). If you are working with the great circle
distance, make sure that the geographic coordinate system uses a sphere. Say if you want to use some
equidistant coordinate system with center at 0,0 longlat (Lambert Azimuthal Equal-Area), you could
then get the coordinates by using:

> P1 <- data.frame(E=35, N=25)
> lambda <- 60  # azimuth!
> dist12 <- 300000
> coordinates(P1) <- ~E+N
> proj4string(P1) <- CRS("+proj=longlat +datum=WGS84")
> P1.xy <- spTransform(P1, CRS("+proj=laea +lat_0 +lon_0 +x_0 +y_0"))
> P2.xy <- data.frame(E=P1.xy at coords[1,1]+dist12*sin(lambda),
N=P1.xy at coords[1,2]+dist12*cos(lambda))
> coordinates(P2.xy) <- ~E+N
> proj4string(P2.xy) <- P1.xy at proj4string
> P2 <- spTransform(P2.xy, CRS("+proj=longlat +datum=WGS84"))
> P12 <- rbind(P1, P2)
> P12
SpatialPoints:
            E      N
[1,] 35.00000 25.000
[2,] 33.55488 22.554
Coordinate Reference System (CRS) arguments:
+proj=longlat +datum=WGS84 +ellps=WGS84 +towgs84=0,0,0

> load(file=url("http://spatial-analyst.net/DATA/worldborders.RData"))
> spplot(worldborders["NAME"], colorkey=FALSE, col.regions=rep(grey(0.5),
length(levels(worldborders$NAME))), sp.layout=list("sp.points", P12, pch="+", col="red", cex=3))

But I would consider using the UTM or which ever coordinate system is of your interest; then you
also need to convert the GCD to distance in the local system. For example, to represent the whole of
USA (contiguous 48-state area) I typically use:

+proj=aea +lat_1=29.5 +lat_2=45.5 +lat_0=23 +lon_0=-96 +x_0=0 +y_0=0 +ellps=GRS80 +datum=NAD83
+units=m +no_defs

See also:

http://spatial-analyst.net/DATA/usgrids5km.zip 

cheers,

T. Hengl
http://spatial-accuracy.org/FromGEOSTAT2009 

PS: I never got any photos from your trip to the Pyramids!




> -----Original Message-----
> From: r-sig-geo-bounces at stat.math.ethz.ch [mailto:r-sig-geo-bounces at stat.math.ethz.ch] On Behalf
> Of Harry Kim
> Sent: Tuesday, October 06, 2009 7:23 PM
> To: r-sig-geo at stat.math.ethz.ch
> Subject: [R-sig-Geo] Determining a coordinate given another coordinate,a great circle distance,
> and an angle
> 
> Dear R-sig-geoers,
> 
>       I am stuck with a problem and i was hoping if you could help me.
> Suppose i am given a coordinate in lat/long (say 25 lat 35 long) and a
> great circle distance (say 10km). Also assume that i am given an angle
> with respect to latitude (an angle from the x-axis say 30 degrees).
> What would be the best way to determine a coordinate 10kms away from
> 25 lat 35 long with a given angle (30 degrees)?
> 
>      I think in euclidean space, I can use tangent of the given angle
> and combine with the Pythagorean theorem to find the target
> coordinate.
> 
> Thank you very much in advance,
> Harry
> 
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