[R] computing the radius of an arc

[Hans W Borchers]

Nair, Murlidharan T <mnair <at> iusb.edu> writes:

> 
> Alex Brenning, the developer of the RSAGA package told me that and I quote 
> "the RSAGA package (which uses functions from the free geographical 
> information system [GIS] SAGA GIS) has a curvature function that is designed 
> to calculate the curvature of surfaces, in particular raster (i.e. gridded) 
> digital elevation models. I am not aware of a function in SAGA GIS or other 
> GIS that would calculate curvatures along a line, especially not in 3D"


I have difficulties seeing how you would go about to do this. A surface locally
is characterized by two main curvatures --- this is Gauss' theorem for 2-dim
geometry. The sphere has the same curvature, 1/r, in both directions. So maybe
you can approximate the surface by an ellipsoid, but a strange one as the main
directions may not be orthogonal.

I am not sure this is what you wanted to achieve. As a side remark: The circle
approximating a curve in three dimensions is not uniquely determined.

Regards
Hans Werner


> I shall try to develop it and if I am successful I shall make it available.
> 
> Cheers../Murli
>