[OSRS-PROJ] Re: projection formula?

[Strebe at aol.com]

Chris Jessee <jessee at virginia.edu> writes:

> Yes, perhaps too elaborate. I'm experimenting with different 
> projections in hopes of finding one that offers limited visual 
> difference from Lambert conformal Conic but allows point plotting in 
> cartesian coordinates without much compute overhead.

If you really are limiting your subject area to New England, then I suggest 
forgetting about ellipsoids and even the Lambert conformal conic. You can get 
low distortion for such a limited area from a simple equirectangular projection 
with the standard parallel set to the central parallel of your map:

x = R * (longitude - central meridian) * cos (standard parallel)
y = R * (latitude - standard parallel)

The parallels will not be curved like the Lambert conformal conic, but the 
amount of curvature across a region that small is quite minimal anyway. 
Obviously the inverse projection is just as simple. This projection is not accurate 
enough for geodetic work but it should be imminently suitable for your project.

Regards,

daan Strebe
Geocart author
http://www.mapthematics.com

Original:
_____
On Wednesday, October 22, 2003, at 01:59  PM, Strebe at aol.com wrote:

>
> Chris Jessee <jessee at virginia.edu> writes:
>
> >User mouse movement gives realtime lat lon readout.
> >A measure tool provides distance and angle measure between two points.
>
> I'm curious what you want the "angle" for. If you intend to measure 
> direction with it then you will fail. There is no projection on which 
> you can measure correct directions between any two points. If it is 
> direction you want, then you need to calculate the azimuth from the 
> first point to the second. Gerald Evenden mentioned Snyder's "Map 
> Projections - A Working Manual". That reference includes azimuth 
> calculation formulae.

You are correct, we need the azimuth.

>
> >The trouble begins when we try to use a base map in a
> >Lambert_Conformal_Conic projection. The specifics of the projection 
> are
> >at the end of this email. To implement the functionality noted above I
> >have 2 choices: re-project the map into a Geographic Coordinate system
> >or dynamically calculate the difference between rectilinear screen
> >space and the conic projection. On the first option I'm also
>
> What you really want is the inverse projection. Inverse projections 
> compute latitude and longitude given the cartesian coordinates x and 
> y. The same Snyder reference provides inverse formulae for the Lambert 
> conformal.

Yes, correct again.

>
> Since Snyder's volume may be hard to find in a hurry, you may also 
> look at:
>
> http://mathworld.wolfram.com/LambertConformalConicProjection.html
> http://www.codeguru.com/algorithms/GeoCalc.html

Thank you, these links are very helpful. Fortunately I work in the 
university library and Snyder's volume was available just down the hall!

> This all seems very elaborate for your project! It looks very good, 
> though.

Yes, perhaps too elaborate. I'm experimenting with different 
projections in hopes of finding one that offers limited visual 
difference from Lambert conformal Conic but allows point plotting in 
cartesian coordinates without much compute overhead.

Thank you,

Chris Jessee
jessee at virginia.edu


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