"Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
> I recently stumbled upon a web course on CAGD by Leonardo Fernandez-Jambrina and
>
> https://dcain.etsin.upm.es/~leonardo/eindex.html

Nice.  I've seen that page before - I just haven't had time to delve into that
topic again in any meaningful depth.

> What caught my attention was chapter 6, where Coons patches are explained.
>
> I found it interesting that if a Coons patch is made by Bezier curves
> along its edges, then one can make a Bezier control grid for the same
> patch by doing degree elevation on its control grids.

So that you have a subdivided patch . . . It's not instantly obvious why that's
necessary.  Where does one stop subdividing / degree-elevating?

> Once one have such a Bezier control grid, one can use it to find the
> partial derivatives of the surface. The cross product of these gives the
> surface normal.

Excellent.

> When one have the surface normal, one can create offset surfaces. And
> offset surfaces are the foundation for the triangle meshes in this image.

And of course, it's then trivial to calculate the mean and Gaussian curvature of
the surface at any point.

1. This is such an obviously TOK image, that I would be able to instantly pick
it out from a page of image results.  You have a certain style that endures
across decades of work.  :)

2.  I can't tell you how happy I am that (aside from seeing WHY you'd need to
degree-elevate) I can read what you've posted without any trouble whatsoever,
and and feel confident that (given the control grid points) I could even write
the SDL necessary to replicate your result in full.

Thanks for all of your help in guiding me to this point, and always pushing the
envelope a little bit farther.

- BW

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