The parameter business in the API was always a puzzle for me too, but with Michael's pointer to A Programmer's Geometry I'm starting to get a better sense of what's going on. Still have a mental gap between the equations given and MoI though. Relative to parameters, taking the diagram on pg 11, (x0, y0) is somewhere on the line (wherever the normal intersects) and seems from the code to be where t=0 (via algebra), however that does not then sync with parameter values ranging from 0 to 1 to describe the complete line. Makes me wonder if the t parameters are interpreted differently in different forms of equations? My computed tangents do not look correct and are winding up in screwy locations, so I'm still going over my code.

The other puzzlement is how to update the equations and code for the implicit form (section 2) to include the 3rd dimension. Book seems to give hints later on when it gets into lines and planes in space (section 7).

Paging back & forth in the PDF inspired me to order a used copy yesterday. Gotta love bookfinder.com to find good prices on used books, in this case about $7 delivered. Even though I'm in way over my head, I very much appreciate these pearls of wisdom Michael, thank you! Schneider in particular looks to be very worthwhile to better appreciate how these things work...

--Larry