Three Dollar Quill

I was a little out of it today, but I just now ran the calculations for perspective-projecting a sphere. There are two parts to this. One is determining the center, radius, and orientation of the outer circle according to the camera. This is nearly as straightforward as the calculations for projecting a line. The other part is projecting that circle, which brings me back to whatever is going on with projecting an arbitrary ellipse. (Keeping in mind that the hard part, broadly speaking, is not "arbitrary", but "ellipse".)

Actually, now that I think about it, I haven't actually worked out the whole thing. I've gotten as far as "formal determinant of six by six matrix", but that just gets me as far as "generalized conic coefficients". I need to take those and convert them into center, major axis, minor axis, and rotation about the center. I think that's easier, but on the other hand, I hadn't anticipated just how gnarly it will be to solve for the generalized coefficients, so really, any unpleasant outcome is possible. In any case, I just installed SymPy, and it looks like it can handle what I want, so I'll see about running the numbers later. Right now, I want to get to bed.

Good night.