By definition a Canal Surface, $\mathcal{C}_u$, is an envelope of the one-parameter pencil of spheres. However, I can make surfaces with a pencil of ellipsoids instead. Are these new surfaces (with elliptical cross-sections) considered as canal surfaces as well, or there is another name/group for them?
Update:
I am working on (canal) surfaces with elliptical and even arbitrary cross-section and I want to find proper references. As cited by @Steve Kass I looked into the book: "An Introduction to differential geometry" and I realize that the term used for such surfaces is developable surfaces. But at the same time by definition, the directrix of the developable surfaces is a straight line not a curve.