[Proj] Re: Mercator Problem

[Strebe at aol.com]

Ron's proposal is perfectly sound on a spherical earth. Since the oblique 
Mercator central line runs through the two points of interest, and since the 
scale is constant and correct along that great circle, there's no need for 
integration or scale factor corrections. Obviously it's more problematic on the 
ellipsoid, given that none of the usual oblique formulations carry constant scale 
along the transformed equator (and if I recall correctly, it's not possible 
whilst retaining conformality), but even so, Hotine is close enough to constant 
scale that it might suffice, depending on the accuracy needs and assuming the 
two points are reasonably short of antipodal.

If other calculations that Ron mentions aren't needed then clearly Cliff's 
suggestion is the way to go. Why go out on a... erm... tangent?

Regards,
daan Strebe


In a message dated 10/17/2005 2:42:58 PM 太平洋夏時間, cjmce at lsu.edu writes:

> Ron,
> 
> You're proposing a piecewise-integration along a grid line.  With that,
> you'd also have to include the correction for scale factor at a point, as
> integrated by so many points of choice along the projected line.  Scale
> factor along the Central Line of an Oblique Mercator is not going to
> obviate that need.
> 
> It's far simpler to just call the subroutine in PROJ4 for an ellipsoidal
> geodesic between the two end points.  (Once called the "Principal Problem
> of Geodesy" in the 19th Century).
> 
> Assuming you know how to program the subroutine calls, it's easier done
> than said.
> 
> Clifford J. Mugnier
> Chief of Geodesy and
> Associate Director,
> CENTER FOR GEOINFORMATICS
> Department of Civil Engineering
> LOUISIANA STATE UNIVERSITY
> Baton Rouge, LA 70803
> Voice and Facsimile: (225) 578-8536 [Academic]
> Voice and Facsimile: (225) 578-4474 [Research]
> ================================
> http://www.ASPRS.org/resources/GRIDS
> http://www.cee.lsu.edu/facultyStaff/mugnier/index.html
> ================================
> 
> 
> 
> What about using the Lat and Long of the endpoints to define the central
> line of an Oblique Mercator, with a scale factor of 1.0 on the central
> line?
> Then the distance can be calculated by Pythagoras, and other useful
> operations can easily be calculated - mid point, distance of a third point
> from the line and even the calculation of a buffer zone, all of which seem
> horrendous when working on the ellipsoid. (OK, the mid point is not too
> bad).
> 
> Ron Russell
> Tel : 01823 270308 email : ron at russfam.freeserve.co.uk
> -----Original Message-----
> From: proj-bounces at lists.maptools.org
> [mailto:proj-bounces at lists.maptools.org] On Behalf Of Clifford J Mugnier
> Sent: 17 October 2005 20:52
> To: PROJ.4 and general Projections Discussions
> Subject: Re: [Proj] Mercator Problem
> 
> 

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