The way I was thinking about was that the curvature is named undefined because it has discontinuities in it, which result from the fact that the object is const

The way I was thinking about was that the curvature is named undefined because it has discontinuities in it, which result from the fact that the object is constructed by sticking pieces together, and the joints aren't entirely smooth. Is there something deeper to its 'undefined curvature'? Or I guess that's just more important than it seems to me: like it being amenable to classification by curvature type is the essential thing here. And I guess it must be something deeper than not being smooth at the joints, since there are probably applicable smoothing algorithms.