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

[Harry Kim]

Hey Tom!

     It's great to hear from you :).  I did think about using a UTM
projection but the region of interest (Turkey) is too big. It requires
6 UTM zones to cover it and if the point is around the boundary i
thought that it would create some problems. I wasn't aware of other
distance/area preserving projections. I will take a look at the zip
file on your website. For some reason radicalcartography website isn't
working for me.

Thanks again for the detailed code tom!
Hope things are going well for you.

P.S: The pyramids were awesome but i thought Petra was better :-D.
http://www.facebook.com/cardboy?ref=profile#/album.php?aid=2477670&id=1204683&op=6
http://www.facebook.com/cardboy?ref=profile#/album.php?aid=2481932&id=1204683&op=6

On Wed, Oct 7, 2009 at 1:36 AM, Tomislav Hengl
<hengl at spatial-analyst.net> wrote:
>
> 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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