Surface with singularities

Hi everybody, I have a question regarding surfaces with curvature-singularities.

As you can see in the image I've got a 3d mesh relying on formfinding methods (using Kangaroo) and I want to generate a Nurbs-surface from mesh-vertices and a planar square boundary.

The Patch command works fine but generates a surface with horizontal tangents (like a skyjump) on the corners. I know that if I want to avoid horizontal tangents the surface must have singularities in curvature (see the British Museum image below).

The question is: how can I get a surface with curvature-singularities on the corner starting from a point-cloud and a planar square boundary?

Thank you in advance.

Attachments:

formfinding.jpg, 305 KB

Replies to This Discussion

Permalink Reply by nikos tzar on October 4, 2015 at 12:18pm

Hello Davide,

Try to partition the list of vertices so that each branch contains one "row" of points and then use [Interpolate Curve] on them. Finally Flatten your tree and use [loft] to create the surface. Hopefully this should get you what you are after.

Cheers,

Nikos

Permalink Reply by nikos tzar on October 4, 2015 at 12:32pm

Ok, my bad, I just realised this doesn't solve your problem. Sorry about that.

Permalink Reply by Davide on October 4, 2015 at 2:48pm

The problem is that I need a surface with singularities in curvature (not continuos) but NURBS geometries are inherently continuous.

Permalink Reply by Riccardo Majewski on October 5, 2015 at 2:51am

What you want to do must be done with a single surface?

A patchwork of more surfaces would be easier...maybe...

Btw, a "solution" could be moving more control points to the same location to have a "singularity" (as same with nurb curves), but this will mess up the topology and probably cause other problems.

(here in pic, 8 point moved to the central one, degree 3 require 3 points for a singularity in both U and V so 3x3=9 , 8+1)

Also, in your first pic (the red GH preview), the corners are "flat" and not smooth because of the low mesh quality, with a higher one it should be like you need.

Why you need a single surface with "singularities"?

I'm curious, keep us updated :D

Permalink Reply by Davide on October 5, 2015 at 3:38am

The following image explains (I hope) what I wan to get. The corner singularities avoid the horizontal tangent (sky jump) and this is crucial for a shell structure.

Permalink Reply by Daniel Piker on October 5, 2015 at 3:52am

What is the reason for wanting a NURBS surface rather than a mesh if the built shell is going to be panelized anyway?

..or if it is going to be a continuous surface such as a concrete shell, surely you don't want these ridge discontinuities?

Permalink Reply by Davide on October 5, 2015 at 4:13am

Hi Daniel, I need the NURBS for some reasons (e.g. I have to create a pattern on it and I need NURBS-tools in order to do that).

Basically my problem is similar to the definition of British Museum roof, where the designers used an equation (image above) to generate the surface with ridge discontinuities.

RSS