Hello,

I have modelized a beautiful developable helicoid with the sweep 1 rail command, taking a helix for the rail and a tangent line for the cross-section curve, result looks nice as the Gaussian curvature is null everywhere and isocurves looks close to a line and a helix, result is similar with rail revolve.

So far so good, the problem I encountered is when I tried to unroll this surface, the result is obviously completely wrong, starting by a warning explaining that there is 4.2% in surface increase (which is a little bit too much for one of the purest developable surfaces !), and result looking like a strange portion of a disk with a radius close, but not exactly equal, to the original tangent rule.

The correct result is obviously a disk with a circular hole inside, cut by tangents to this inner circle of lengths exactly equal to the original tangent rule.

A beautiful bug indeed! it should be of course corrected asap, but could it be possible that this whole class of developable surfaces could be affected? (the ones that are neither cylinders nor cones).

Bon courage! I would appreciate to be informed about the resolution of this nice error.

An attempt to unfold with the squish command is giving an even more strange result…

Please find joined a rhino file with the helicoid surface, the Rhino wrong unfold and a another one that I cooked myself from a mesh and looks much better.

Best regards,

JRayHelicoidDevelopable.3dm (123.5 KB)