Hello Brian,
could you please send a link to the document- I can't follow you at the moment. Is it a problem with the translator? Maybe you can solve it with a click to the word - then there will displayed alternatives. Maybe Pilou will have a look and switch on the light. The mathematical stuff you are talking about (Dupin???) is out off my mathematical range, but every time a pleasure to see your results.

Have a nice day
Karsten