In general, a smooth curve $C$ in $R^3$ that lies entirely on the boundary of its convex hull, $\mathcal{H}(C)$, is defined to be convex.

- Does any one know of a characterization of a curve in space as convex depending on the sign of its torsion $\tau$?
- Is the projection of a non-singular "short" curve in space to any plane always convex?

Where a "short" curve in space is such that there is a 1-1 correspondence between the space curve and the corresponding projected curve in a plane.

Thanks.

impossiblethat all projections be simple: join two points of the curve by a segment and project in the direction perpendicular to it. The most you can ask is thatalmost allprojections be simple. I guess this only says the curve is planar. $\endgroup$ – alvarezpaiva Jul 30 '13 at 12:38