Hi Jon:
Ive thought a lot about what the generalization of monotonicity to nD
coordinates must be. It turns out the monotonic 1d coordinate values are
necessary and sufficient to make the coordinate function invertible. The
condition we want on nD coordinates is that these are invertible as
functions from index space to coordinate space. I havent been able to
formulate a simple algebraic test for that, but i have a simple
geometric one. If you draw a mesh connecting the coordinate values (eg a
2d curvilinear case), the lines of the mesh must not cross. I think in
topology they call this a "conformal mapping", where you get to distort
a rubber sheet (contianing the mesh) as much as you want, but cant tear
or fold the sheet over on itself.
i wrote this up some years ago, though my math is a bit limited:
http://www.unidata.ucar.edu/staff/caron/papers/CoordMath.htm
Jonathan Blower wrote:
> Yes, I agree too that axis values should be monotonic.
>
> I wonder if this requirement can/should be extended to two-dimensional
> coordinate variables?
> (http://cf-pcmdi.llnl.gov/documents/cf-conventions/1.4/cf-conventions.ht
> ml#id2984605) It seems much more difficult in this case because in
> certain convoluted cases, values that are next to each other in grid
> space are not necessarily close in real space.
>
> Jon
>
> -----Original Message-----
> From: cf-metadata-bounces at cgd.ucar.edu
> [mailto:cf-metadata-bounces at cgd.ucar.edu] On Behalf Of Jonathan Gregory
> Sent: 13 April 2010 08:13
> To: John Caron
> Cc: cf-metadata at cgd.ucar.edu
> Subject: Re: [CF-metadata] longitude wrapping creates
> non-monotoniccoordinate values
>
> Dear John
>
> I agree with you and Steve, and that is the approach I too have taken in
> analysis software. "Monotonic" means the numbers must uniformly increase
> or
> decrease, and some of them will have to be wrapped round to achieve
> this.
> The CF checker should give an error for the file as it stands, because
> monotonicity is a requirement in section 5 of
> http://cf-pcmdi.llnl.gov/conformance/requirements-and-recommendations/1.
> 4/
>
> Best wishes
>
> Jonathan
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Received on Tue Apr 13 2010 - 07:54:53 BST
