Rune Allnor <

[email protected]> writes:

> Hi all.

>

> I am working with some data that contain UTM positions.

> The problem is that I need the UTM coordinates on centimeter

> precision, which means I need some 8 or 9 significant digits

> in the UTM coordinates; a few digits too many to make the

> coordinates fit into a single-precision floating point number.

> ...
As Tim already said: there should be no big problem. I dealt with

transformations between geographical and Gauß-Krüger (UTM up to

normalizations) coordinates about a decade ago and found the math

quite easy for someone familar with complex analysis. Here is what I

remember:

Given geographical coordinates on the ellipsoid. Then first problem

is calculating the length of an arc of an ellipse which gives you GK

(Gauß-Krüger Koordinaten) for the middle of the zone. Integration is

done by expanding the integrand.

The characteristic requirement for GK is that they are obtained by a

conformal (theory of functions!) mapping from geographical

coordinates. This means, the mapping is complex differentiable and

thus it is sufficient to know it on the middle meridian of the zone,

which we have already got. Thus seems clear you can use local

coordinates for the inner calculations and transform between these and

UTM.

I remember that you need ten or twenty terms of the powerseries

expansion of the mapping to get it up to a centimeter. Calculating

the coefficients is messy and has been done and published in a paper

by the US Airforce.

--

hw