I am using this article: http://www.gamasutra.com/view/feature/131389/b%C3%A9zier_triangles_and_npatches.php?print=1 and this topic: http://www.gamedev.net/topic/624397-bezier-triangle-partial-derivatives/

So far, I have first-order derivates of bezier triangle patch. But hot to calculate second one?

In some article, I have found this:

[attachment=25227:Clipboard02.png]

But I am not sure, if it is correct - for example, third sum in Fuu seems incorrect with (i - 1).

It is difficult to write the entire derivation here in the forum, but AFAIK the second order derivatives should be the following ones:



EDIT: To arrive at this result you have to use the observation at the end of Shnoutz post in the discussion you have linked. You first derivate the Bernestein polynomials and then change the indices.
EDIT2: The derivatives in the gamasutra article are clearly wrong since partial derivatives are vectors while that formula defines a point. In the formulas above each "control point" is a vector since it is a linear combination of point whose coefficients sum to zero. In computer graphics we usually use vectors and points interchangeably, but they are different mathematical objects and it is sometimes useful to consider their differences when verifying an equation.

Thanks.. I have come to similar conclusion, based on Shnoutz post, so I guess, it is correct one :-)