# Project quad onto ellipse in 3D

I have three points P0, P1, P2, which are located on an arbitrarily oriented ellipse in 3D space. I have a square texture map with a circle on it. I would like to render a textured quad (with the obvious UV mapping) so that the circle in the texture map projects onto the ellipse that P0, P1, P2 are on.

How do I calculate the vertices of the quad to project the ellipse correctly?

(Alternately, in addition to P0, P1, P2, I have the Keplerian elements of an elliptical orbit, if that's more straightforward.)

• Isn't this slightly under-constrained? If you only have 3 coplanar(?), non-colinear points, won't that allow you to have a circle? (Or do you also have the centre?) Dec 1, 2015 at 13:20
• Are the three points any particular points on the ellipse? e.g. if one is guaranteed to be one end of the major axis, and another is one end of the minor axis, then the problem is trivial. Dec 1, 2015 at 15:16
• Yeah, someone elsewhere pointed out it's underconstrained, and the Keplerian elements are probably more usable. That said, I can arrange for the points to be the end of the major and minor axes if that trivializes the problem. Dec 1, 2015 at 16:43
• If you have the center and major/minor axis vectors, then the corners of the quad will just be center ± major ± minor. Dec 2, 2015 at 1:10