[OSRS-PROJ] Re: projection formula?

[Ed McNierney]

Chris -
 
This is a good idea, especially if you're in central/western Mass - the
length of a degree of longitude differs by less than 0.5% or so from the
central parallel, since the state's less than three-quarters of a degree
north-south (except for the eastern portion).
 
            - Ed
 
 
Ed McNierney
President and Chief Mapmaker
TopoZone.com
ed at topozone.com
 
-----Original Message-----
From: Strebe at aol.com [mailto:Strebe at aol.com] 
Sent: Wednesday, October 22, 2003 4:20 PM
To: osrs-proj at remotesensing.org; cj8n at virginia.edu
Subject: [OSRS-PROJ] Re: projection formula?
 

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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