Ruled Surface returns surfaces with <0 Gaussian Curvature

I am being a bit picky here, but wondering why I am able to get Ruled surfaces (built in Grasshopper) which return Gaussian curvature results of just slightly less than 0.

Correct me if I am wrong - these ruled surfaces are by definition developable which by definition should return 0 Gaussian curvature throughout their extents?

I have attached some images - I can attach the definition if necessary but it seems to be the case with any random nurbs curve defined ruled surface.

Thanks!

Attachments:

GaussianCurvature_lessThan0.JPG, 43 KB
GaussianCurvature_lessThan0_ghop.JPG, 102 KB

Replies to This Discussion

Permalink Reply by David Rutten on September 7, 2017 at 2:44pm

As far as I know a ruled surface is not necessarily developable. Ruled surfaces are made by connecting two curves using only straight lines, however for a surface to be developable adjacent straight lines need to be either exactly parallel or they must intersect. I'm pretty sure ruled surfaces create lines that merely cross.

Permalink Reply by Paul Mecomber on September 7, 2017 at 3:29pm

David - thanks for you reply - yes it seems you are right - see a more detailed discussion here:

ruled vs developable surfaces:

http://web.mit.edu/hyperbook/Patrikalakis-Maekawa-Cho/node190.html

Given either your definition or the definition in the MIT article - how might you begin to use grasshopper to make developable surfaces between arbitrary NURBS curves. I know Evolute Tools has a piece of software as a purchase which does this already but I'm interested in the geometry / logic.

Any help in the right direction would be greatly appreciated!!

Permalink Reply by Paul Mecomber on September 7, 2017 at 3:39pm

Hi David - already found another discussion from Daniel Piker on the subject:

http://www.grasshopper3d.com/forum/topics/developable-surface

Thanks again for pointing out my misunderstanding of ruled surfaces - very interesting topic!

RSS