When I google elliptical torus, I get lots of hits for an ellipse (as a cross-section) rotated through a circle. However, I don't see a mention of the converse - a circular cross-section "rotated" through an ellipse in order to give the greatest volume ( although that is slightly ambiguous - I think replacing "circular cross-section" with sphere removes the ambiguity).
More specifically, what would I call the 3D shape formed by a sphere whose center travels around an ellipse.
Or yet more specifically, the union of the volume of all spheres of the same radius whose centers lie on the same ellipse. (is there an equally precise but more succinct way to say this?).
Is there a general term for the shape made from all points at most X units away from any point in another shape? (eg, increasing thickness). Could I call it something like a "thickened" 3D ellipse?
If not, can I dub this shape a torusoid? :)
Pipe surface appears to be the technical term for the "thickening" that I was asking about above.
Therefore, a fairly short name for this shape is "the pipe surface of an ellipse".