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.)
I assume that your texture is deemed to belong to the plane of the trajectory.

Looking at the unprojected ellipse, you can map the circle to it by an anisotropic scaling. If necessary, rotate the texture first if there is any orientation requirement.

To achieve this first mapping, you will compute the four corners of a rectangle, presumably related to the frame formed by the ellipse axis.

Then transform those vertices to the global scene coordinates, the same way to transform the ellipse.