Ok, I wil put the generation of the four 16 by 16 matrices
on my todo list. It may be a few days before I have some time
to do it. If you have access to Matlab it will be even easier,
then I could send you some of my scripts.

Further down on my list will be to create some macros for
the conversion and even further down to create some
tutorial pages on bicubic patches in POV and how to convert
from one representation to the other (unless someone already
did that of course).

	Andrel

Sascha Ledinsky wrote:

> As I was able to compute all but the four inner bezier controlpoints (or 
> the hermite twist vectors) I searched the internet again and found the 
> following equation to convert from bezier to hermite (or vice versa):
> 
> d^2P/dudv(0,0) = 9(P00-P011+P10-P11)
> 
> I'll have to try it, but it looks promising.
> 
> Anyway, thanks a lot for your help!
> -Sascha
> 
> 
> andrel wrote:
> 
>> Have you solved your ploblem yet.
>>
>> Today in the train I realized that my suggestion
>> is correct, but that it is too much influenced by
>> the fact that I do have a program to solve the inverse
>> of a 16 by 16.
>>
>> Rethinking it from the perspective of: 'how would
>> I solve this by hand?' often gives better results.
>> - there are only three types of points in the (realized)
>>  patch: corner points (4), side points (8) and center
>>  poinys (4)
>> - cornerpoints are in all representations the same, so
>>  we do not have to apply any interpolation.
>> - sidepoints are only influenced by the two cornerpoints
>>  on that side and in case ot the bezier patch the control
>>  points on that side, and in the hermite case by the
>>  2 derivatives along the side. All in all we need 4
>>  numbers only to do the conversion from one representation
>>  to the other. We use symmetry to apply the same 4 to
>>  every sidepoint of course.
>> - For the center points we need only 16 numbers to
>>  describe the conversions.
>> All in al we need compute only 4+16 numbers to do
>> all conversions. so the 16 by 16 matrix is a bit overkill
>> (I will keep using it because it greatly somplifies
>>  my code but that is another issue).
>>
>>   Andrel
>> Sascha Ledinsky wrote:
>>
>>> I've got to delve into that.
>>> Thanks a lot for your help!
>>> -Sascha
>>
>>
>>

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