Nice construction. Took me a little while to figure out that by oriented ellipse you really mean a fixed curve in 3d, not just a fixed direction of the normal t

Nice construction. Took me a little while to figure out that by oriented ellipse you really mean a fixed curve in 3d, not just a fixed direction of the normal to the plane of the ellipse, which was my first reading. That way orientation takes 3 (real) dimensions + 1 dimension for eccentricity, which gives the 4 real dimensions in CP^2. How accessible it is to intuition is debatable though :P