====== Coordinates ======

This note is a continuation of [[:notes:match|Displaying incomplete data on the map]].

===== How to display only a selected part of the map? =====

First we have to display the coordinates.
<code>
> plot(SI,axes=TRUE)
</code>

{{:pics:notes:SIaxes.png}}

We select a port of the picture by specifying the parameters ''xlim'' and ''ylim''. Let us display the neighborhood of Ljubljana:
<code>
> plot(SI,col=pal[ci],xlim=c(430000,500000),ylim=c(84000,129000),bg="lightyellow")
</code>

{{:pics:notes:SIlj.png}}

===== How to draw the given points? =====

Assume that we have the some position on the map, for example [[http://en.wikipedia.org/wiki/Ljubljana|Ljubljana]]:  46°03'20”N 14°30'30”E . How to position it on the picture? The coordinates X_C and Y_C are the centers of communes - they are useless.

The **first solution** is to get the information about the [[http://en.wikipedia.org/wiki/Geography_of_Slovenia|extreme points of Slovenia]]
<code>
    North: 46°52'36”N 16°13'59”E, Šalovci,
    South: 45°25'19”N 15°10'0”E,  Črnomelj,
    East:  46°28'11”N 16°36'38”E, Lendava,
    West:  46°17'53”N 13°22'32”E, Kobarid.
</code>
and the corresponding picture coordinates using the ''bbox'' function
<code>
> bbox(SI)
        min      max
x 375209.19 624065.3
y  30853.18 193270.4
</code>
From these data we can determine the linear mappings of map coordinates (xM, yM) to picture coordinates (xP, yP):\\  xP = A*xM + B  and yP = C*yM + D .

<code>
> NN <- 46+(52+36/60)/60; NE <- 16+(13+59/60)/60 # North: Šalovci,
> SN <- 45+(25+19/60)/60; SE <- 15+(10+ 0/60)/60 # South: Črnomelj,
> EN <- 46+(28+11/60)/60; EE <- 16+(36+38/60)/60 # East:  Lendava,
> WN <- 46+(17+53/60)/60; WE <- 13+(22+32/60)/60 # West:  Kobarid.
> LjN <- 46+(3+20/60)/60; LjE <- 14+(30+30/60)/60
> E <- c(NE,SE,EE,WE,LjE); N <- c(NN,SN,EN,WN,LjN)
> E
[1] 16.23306 15.16667 16.61056 13.37556 14.50833
> N
[1] 46.87667 45.42194 46.46972 46.29806 46.05556
> (bb <- bbox(SI))
        min      max
x 375209.19 624065.3
y  30853.18 193270.4
> my <- bb[2,1]; My <- bb[2,2]; mx <- bb[1,1]; Mx <- bb[1,2]
> A <- (Mx-mx)/(EE-WE); B <- mx - A*WE 
> C <- (My-my)/(NN-SN); D <- my - C*SN
> (co <- cbind(A*E+B,C*N+D))
> co
         [,1]      [,2]
[1,] 595025.7 193270.41
[2,] 512992.5  30853.18
[3,] 624065.3 147835.76
[4,] 375209.2 128669.47
[5,] 462349.4 101594.77
> plot(SI)
> points(co,pch=16,col=c(rep("blue",4),"red"))
</code>

{{:pics:notes:SIpts.png}}

The **second solution** is to get the information about the meaning of the picture coordinates. In Europe some variant of the Gauss-Krüger projection is usually used. After some searching on the WWW it seems that the current system used in Slovenia is //**MGI 1901 Slovene National Grid**// with EPSG number 3912 (see also 2170, 3787, 3794, and others for locally more precise conversions). The units in this system are meters. A support for projections is available in the package ''rgdal''.

<code>
> library(rgdal)
> (cP <- cbind(E,N))
            E        N
[1,] 16.23306 46.87667
[2,] 15.16667 45.42194
[3,] 16.61056 46.46972
[4,] 13.37556 46.29806
[5,] 14.50833 46.05556
> cP_sp <- SpatialPoints(cP,proj4string=CRS("+proj=longlat +ellps=WGS84"))
> (MGI <- spTransform(cP_sp, CRS("+init=epsg:3912")))
SpatialPoints:
            E         N
[1,] 593975.6 193226.56
[2,] 513041.4  30837.61
[3,] 623670.8 148520.60
[4,] 374871.0 129464.57
[5,] 461960.4 101350.22
Coordinate Reference System (CRS) arguments: +init=epsg:3912 +proj=tmerc +lat_0=0
+lon_0=15 +k=0.9999 +x_0=500000 +y_0=-5000000 +ellps=bessel +units=m +no_defs 
> plot(SI)
> points(coordinates(MGI),pch=16,col=c(rep("blue",4),"red"))
</code>

The precision of the results is in the range of 1km.
<code>
> coordinates(MGI)-co
               E          N
[1,] -1050.10041  -43.84313
[2,]    48.96126  -15.56588
[3,]  -394.46432  684.84265
[4,]  -338.21666  795.09904
[5,]  -388.98495 -244.55146
</code>
http://www.e-prostor.gov.si/si/zbirke_prostorskih_podatkov/drzavni_koordinatni_sistem/


===== URLs =====

  * R-help: [[http://r.789695.n4.nabble.com/Gauss-Kruger-coordinates-system-td792826.html|Gauss-Krüger coordinates system]] 
  * GIS: [[http://gis.stackexchange.com/questions/1179/how-to-convert-coordinates-from-gauss-krueger-to-longitude-latitude|How to convert coordinates from Gauss-Krueger to Longitude/Latitude?]]
  * R-sig-Geo: [[https://stat.ethz.ch/pipermail/r-sig-geo/2010-November/009833.html|Projections and Transformations with Garmin GPS Coordinates?]]
  * Tomislav Hengl: [[http://spatial-analyst.net/wiki/index.php?title=Special:AllPages|Wiki]]; [[http://spatial-analyst.net/wiki/index.php?title=MGI_/_Balkans_coordinate_systems|Balkans coordinate systems]]
  * Microimages: [[http://www.microimages.com/documentation/Tutorials/CoordRef.pdf|Coordinate
Reference Systems]]
  * [[http://icaci.org/documents/ICC_proceedings/ICC2011/Poster%20Presentations%20PDF/POSTERS%20SESSION%203/P-153.pdf|Conversion of coordinates between the Gauss-Krüger and UTM]]
  * http://armypubs.army.mil/eforms/pdf/a7288_r.pdf
  * GRASS 6.0: [[http://www.gdf-hannover.de/lit_html/grass60_v1.2_en/node22.html|Coordinate systems]]
  * OGP: [[http://www.epsg.org/guides/docs/G7-2.pdf|Coordinate Conversions and Transformations including Formulas]]
  * Alexander Kolesnikov: [[http://cs.joensuu.fi/pages/koles/sis/Lecture_03.ppt|Map Projections]]
  * http://trac.osgeo.org/proj/
  * CRAN: [[http://cran.r-project.org/web/packages/sp/|sp]], [[http://cran.r-project.org/web/packages/rgdal/index.html|rgdal]]
  * [[http://www.geopedia.si/#T105_x500000_y100000_s9_b4|Geopedia]]
  * [[http://spatialreference.org/ref/epsg/?page=4|EPSG]]: [[http://spatialreference.org/ref/epsg/2170/|2170 MGI/Slovenia]]; [[http://spatialreference.org/ref/epsg/3787/html/|3787 MGI/Slovene National Grid]]: [[http://georepository.com/crs_3912/MGI-1901-Slovene-National-Grid.html|3912]];[[http://www.epsg-registry.org/|EPSG registry]] (name: Slovenia)