[Mapserver-users] Map projections

Jan Hartmann jhart at frw.uva.nl
Thu Mar 27 05:53:26 PST 2003


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Krzysztof,

Perhaps the following will make things a bit clearer:

Projections are ways of displaying the three-dimensional globe on an 
two-dimensional map. It is impossible to do this without distortion, so 
many different mathematical models have been developed, each of which 
distorts some aspects of the earth and leaves others correct. MapServer 
uses the PROJ library, which supports more than 100 projections.

Some projections preserve direction (north is upward everywhere) but 
distort the form and area of land and sea masses. Mercator is such a 
projection. It was developed in the seventeenth century in order to 
cross the oceans, so direction was very important. It very much distorts 
the size and form of the continents, especially near the Poles (North 
and South, not your countrymen). Because of this, it is generally not 
thought of as a useful projection for anything but direction based 
transatlantic travel It has been very popular in school atlases and maps 
however, so many people imagine the world as something like a Mercator map.

Other projections preserve the form of continents (e.g. Lambert 
Conformal), others the surface area (e.g. Lambert Equal Area). Both 
distort directions very much. Most projections offer a compromise. They 
distort everything a bit. Most pseudocylindrical projections like the 
sinusoidal are like that.

As to the other parameters:

WSGS84 etc is the ellips on which the projection is based. The earth is 
not a perfect globe, but somewhat elongated at the equator. The 
difference with a perfect globe is minimal: the distance from north-pole 
to south-pole is only about 30 km less than the distance from one point 
on the equator to the other side of the world (on an average radius of 
about 6000 km). This will be only noticeable when comparing topographic 
maps of a very large scale (> 1.1000), e.g. between neighbouring states 
with different projection systems. For you application, you can forget 
about the ellips. Same goes for the k-parameter.

X and Y are mainly used for local grid systems, to displace the origin 
for easier use. In Holland for example, the national projection is 
stereographic, with the center of projection (lon_0,lat_0) at 5.38E 
52.16N, a church tower in Amersfoort, in the middle of the country. If 
we would use this point as the origin for the coordinate system, we 
would have points in all four quadrants, like 100000/-10000 and 
-10000/10000. This is very error prone, so the center has been moved 155 
km to the west and 463 km to the south. That way, all our cordinates are 
positive, and every Dutch X is below 200000, and Y above 300000. In 
general you should not have to set these by hand. There is a 
standardized list of these national projections from EPSG, and you can 
use these in MapServer with the parameter "proj=init:<epsg-number>". The 
EPSG list should be with your MapServer distribution.

lat_0 and lon_0 are the coordinates of the center of projection. Not all 
projections require this, but for Europe this should be somewhere around 
50N 15E, and the US something about  30N 90W.

lat_1 and lat_2 are only used with conic projections like Bonne or 
Lambert Conformal. They specify the latitude where the projection cone 
intersects the globe.  For Europe and the US, numbers between  20N to 
60N are regularly used

For Europe, changing projections doesn't show dramatic differences. For 
routing applications, I would guess that maps should give a correct idea 
of distance, and that directions are less important. That would probably 
make  conformal projections a good choice. If your customers prefer the 
kind of maps they are used to from school, you can just as well use 
something like Mercator. As I said, for Europe it doesn't matter that 
much (it would be different for a road map for the US + Alaska!).


Attached some examples, 5 of the world, 5 of Europe:

- world1.png: Plate Carree (proj=eqc), a rectilinear cylindrical 
projection, much like Mercator
- world2.png: Plate Carree (proj=eqc,lat_ts=60), with true scale at 60 
degrees
- world3.png: Sinusoidal (proj=sinu), pseudocylindrical, compromising 
between direction, distance and area
- world4.png: Lambert Conformal (proj=lcc,lat_0=20,lat_1=20,lat_2=60), a 
popular conic projection
- world5.png: Stereographic (proj=stere,lon0=5), a much used azimuthal 
projection

- eur1.png: Lambert Conformal (proj=lcc,lon_0=-5, lat_0=5, 
lat_1=45,lat_2=75), conformal conic
- eur2.png: Lambert Conformal (proj=lcc,lon_0=-5,lat_0=0,lat_1=15, 
lat_2=20), same as 1, but more rectilinear, showing the effect of 
changing lat_1 and lat_2
- eur3.png: Lambert Equeal Area (proj=lea,lat_0=-1,lat_1=85): conic 
equal area, showing the difference with a conformal projection like 1 and 2
- eur4.png: Plate Carree: Cylindrical
- eur5.png: Good old Mercator


To get descriptions and examples of all projections, please download the 
PROJ manual at http://www.remotesensing.org/proj


Hope this helps,

Jan




Krzysztof Chodak wrote:
> Hello again dear mapserver professionals,
> 
> I would be grateful if someone could clear my mind in projections subject. (I'm sorry for such inquiries but it is too difficult for me to solve these problems and maybe they would be simple for some of you)
> 
> 
> I got all geographic data in WGS84 projection. As I have made some "investigation" I think that Mercator is proper projection for my target users and theirs needs (I need to show all Europe road network for routing purposes). Am I correct that it is most suitable for such area and planned usage?
> 
> Is there any significant difference in ellipsoid used with Mercator projection? In EPSG guide Bessel is used in an example. Is it suggested ellps for Mercator (SP1) or may I simple stay with WGS84 one? Should I recompute false easting and northing given in example when switching to WGS84 ellps? Maybe they are constants, aren't they?
> 
> I also cannot catch the difference between one and two standard parallels. Which one is more suitable for my case in your opinion?
> 
> Another thing is a k0 parameter (scale factor at natural origin). When I'm doing following transformation (using PROJ library):
> from "+proj=latlong +datum=WGS84"
> to "+proj=merc +ellps=bessel +lat_ts=0N +lon_0=110E +k_0=0.997 +x_0=3900000 +y_0=900000"
> 	or the same with ellps=WGS84
> the k0 parameter is replaced by 1.0 (and practically skipped in next computations as it is used as multiplier) after initiating target projection (pj_init). Is it correct way of PROJ transformation and would it have any influence on my projected maps when k0 factor would be skipped and not set to 0.997?
> 
> Maybe you can also give some advices for lat_ts and lon_0 - should I change them to any other values to project my area more precisely?
> 
> 
> I got also a polite question to Jan Hartmann [jhart at frw.uva.nl] if he could publish his world map projections images in our discussion group - maybe they would help me and other people with understanding projections stuff?
> 
> Best regards,
> 
> Krzysztof Chodak
> 
> ...lost in projections world :)
> 
> 
> PS. Example from EPSG guide:
> "2. Mercator (1SP) (EPSG coordinate operation method code 9804)
> For Projected Coordinate Reference System: Makassar / NEIEZ
> Parameters:
> Ellipsoid: Bessel 1841 a = 6377397.155metres 1/f = 299.15281
> then e = 0.081696831
> Latitude of natural origin ϕO     0°00'00"N = 0.0 rad
> Longitude of natural origin λO 110°00'00"E = 1.91986218 rad
> Scale factor at natural origin kO 0.997
> False easting FE 3900000.00 metres
> False northing FN   900000.00 metres
> Forward calculation for:
> Latitude ϕ =     3°00'00.00"S = -0.05235988 rad
> Longitude λ = 120°00'00.00"E = 2.09439510 rad
> gives Easting E = 5009726.58 metres
> Northing N =   569150.82 metres
> Reverse calculation for same easting and northing first gives:
> t = 1.0534121
> χ = -0.0520110
> Then Latitude ϕ =    3°00'00.000"S
> Longitude λ = 120°00'00.000"E"
> 
> 
> _______________________________________________
> Mapserver-users mailing list
> Mapserver-users at lists.gis.umn.edu
> http://lists.gis.umn.edu/mailman/listinfo/mapserver-users
> 
Jan Hartmann
Department of Geography
University of Amsterdam
jhart at frw.uva.nl

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