I've seen many discussions online and in papers on how circles can be wrapped onto spheres. However, if I wanted to, say, wrap an ellipse so that it perfectly covers the top half on an ellipsoid (thus an semi-ellipsoid, sorry I don't know if there's an official word for this) without overlapping, what cutouts/petal designs would need to be used so that this can be done?
And, how could the cutout shapes be described mathematically?
For more detail of the 3D shape I'm describing to wrap; it's the intersection of an elliptic paraboloid with a cylinder. Here's an image of everything I'm trying to do:
You can see the dimensions of the elliptic paraboloid and the cylinder (and an idea of the y height, which can be ignored), plus the output ellipsoid and the question of what the cutout looks like. For the sake for making sure there's a common idea of what the answer could be, let's set f to an arbitrary value of 330.