4 ms·
The infinite layering of corrugations is required regardless, because the "true" surface has undefined curvature. They are doing an approximation to that of arb
by tjradcliffe 12y ago
The infinite layering of corrugations is required regardless, because the "true" surface has undefined curvature. They are doing an approximation to that of arbitrary precision.
This is a really delightful peice of work. The existence of surfaces with the curvature undefined everywhere is an easily described concept that comes up fairly frequently in topology, but I'd always assumed it was just impossible to visualize them.
- westoncb 12y agoThe 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.
- darkmighty 12y agoI'd like to see this answered by someone knowledgeable too. From my limited knowledge I would guess the function being C2 gives the curvature a "global" domain; while if the function is only C1 the curvatures will have limited influence, and you can use that to enforce other curvatures "prohibited" under C2. Anyway, I might be completely wrong, just the idea I got from the article :)