[Algorithms] Tangential Curvature of terrain

[Klaus H. <k_h...@os...>]

Hi,

I'd like to enhance my texture synthesizer for terrain. In particular, I'd
like to make my ecosystem-classification depend on the tangential curvature
of the terrain. I guess that may require some explanation.

I have a set of ecosystem definititions. Such definitions include things
like:
[1] the upper elevation limit at which the ecosystem can exist
[2] the minimum and maximum slops at which the ecosystem can exist
[3] elevation skewing
[4] etc...

Now, for each data point in the height field, I go through the set of
ecosystems, and determine which ecosystem exists at this data point. Such a
system is very useful for 'realistic' texture synthesis, and it's also great
to create a natural distribution of trees.
However, there's one thing I haven't been able to implement, yet. I'd like
to make my ecosystem classification depend on the concavity/convexity of the
terrain. I know that this requires me to compute the tangential curvature of
the terrain (which is usually stored in an extra curvature field).

To make it easier for you to understand, you can have a loot at the
following web-site:
http://www2.gis.uiuc.edu:2280/modviz/

The fifth terrain image (from above) shows the tangential curvature of some
terrain. This is exactly what I'd like to do. I know how I need to use the
information from curvature field to modify my ecosystem classification, but
I have no idea how I to compute the tangential curvature field itself. In
know that there's a paper on the above mentioned web-site, and I also know
that there's an implementation in the GRASS package. However, I don't know
enough about the math here to understand the paper, and the implementation
in the GRASS package is, well, ... have a look at it, and you'll know what I
mean.

Finally, my question is this. Does anyone know of a more detailed and
I-don't-expect-you-know-everything resource on calculating the tangential
curvature? Or maybe some readable source? Or even better... can someone
explain this to me?

Again, I've reached a point, where I wished that my math skills were better.
At least I hope that the answer to my question is not too easy, so that
maybe some math guys are interested. I cannot even promise that I'll be able
to follow your replies, but I'm sure someday I will (after re-reading,
re-re-reading, ... :)

Thanks,
Niki