# [Proj] How to obtain (lat, lon ) of a point if I know a reference point and relative distance (km)?

Gerald I. Evenden gerald.evenden at verizon.net
Mon Aug 7 10:46:46 EDT 2006

```On Monday 07 August 2006 12:25 am, Zhuanshi He wrote:
> Dear All,
>
> I want to obtain (lat, lon) of  a serials of points saved in a data
> file. Before do that, I need to know how can I do it for one point.
>
> The pionts came from Mecartor projection. Now, I have a reference
> point (reflat, reflon), and the distance (kilometers) (x,y)
> corresponding to same (reflat,reflon). How to calculate the unkowns
> (?lat.?lon)? Can proj do it?
>
>
>
>  ---(Reflat,reflon)-----------------(x)---------
>
>
>
>
>
> --------- (y)-----------------  ?(lat,lon)---------

Unfortunately, [l]proj does not have a lat_0 option but this can be
compensated for in the following manner:

Assume the reference lat and lon are 45N and 160w respectively.  First
compute the northing for the latitude 45n:

lproj +proj=merc +ellps=intl
0 45

which gives:

0.00    5591388.07

For the remainder of the points, the run line will look like:

lproj +proj=merc +ellps=intl +lon_0=160 +y_0=-5591388.07 -I

For some sample data points (note: y negative south of reference latitude):

0 0
10000 10000
10000 -10000

the results would be:

160dE   45dN
160d5'23.381"E  45d3'49.31"N
160d5'23.381"E  44d56'10.433"N

The above example is the same for program proj.

--
Jerry and the low-riders: Daisy Mae and Joshua
"Cogito cogito ergo cogito sum"
Ambrose Bierce, The Devil's Dictionary
```