[Proj] How to Scale a Mercator projection?

Christopher Barker Chris.Barker at noaa.gov
Wed Jul 26 16:40:42 EDT 2006


Thanks for your helpful comments -- I think I'm slowly starting to get this.

Gerald I. Evenden wrote:
> I use the term "scale factor" to mean a factor to multiply the annotated scale 
> of the map to arrive at the true scale at a particular point.  For example: 
> k_0=0.9996 is the scale factor along the CM of a Transverse Mercator map and 
> means that the true scale is determined by 0.9996 x map-scale.

OK - got it. Can i assume that proj is outputting meters, then?

> By "true" they mean that the scale at that latitude matches the scale 
> annotated in the margin of the map (1:xxx,xxx).

That's what I thought.

> Internally, proj does not allow simultaneous use of lat_ts and k_0.  Such use 
> would grossly confuse usage.
> Proj does *not* determine the scale of the projection in the general sense.  
> That is determined by either scaling the major axis/radius (a=) or scaling 
> the x/y output by the application.  Any map making application that uses proj 
> should consider the map scale as the application's duty.

That's key. Thanks for clarifying that for me. I was looking to have 
Proj do the whole thing for me -- now that I know that It's not supposed 
to to that, I know what to do.

But just in case, I think this is what I need to do:


proj=merc +lat_ts=29.1333 +lon_0=-89.583333 +ellps=WGS84 +datum=WGS84 

That will give me the coordinates in meters.

Then I need to multiply this by the scale (1/80000) and divide the 
pixels per meter (10,000), to get pixels. then I need to shift to get 
the coordinates to (0,0) at the appropriate place.

Another alternative is to set the false easting and false northing to 
get (0,0) in the right place. I think those are set in meters.

Is that about right?

I should be able to give this a try tomorrow.



Christopher Barker, Ph.D.
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Chris.Barker at noaa.gov

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