Need help creating a non-convex hexagon mesh on a catenoid

Hello everyone,

I am trying to design a small scale temporary pavillion shaped like the half of a catenoid. The principle is shown in the image at the bottom of my post taken from the book "Architectural Geometry". I hope to recreate the mesh with nearly planar bow-tie-like non-convex hexagon faces.

I have been using Kangaroo and Weaverbird to create the minimal catenoid surface with a quad mesh. But I have yet to figure out how to create the non-convex hexagon faces.

Any suggestions as where to start, what to read or how to do it would be greatly appreciated!

/peter

Replies to This Discussion

Permalink Reply by Damon on July 14, 2014 at 10:19am

If you have a quad mesh, get the vertices in row-column order (each branch is one row of points, for example). Then it is a connect-the-dots exercise. It will require shifting the branches and lists a few times. For your bowtie, it is a 3-row, 3-column pattern. If you call the columns A, B, and C and the rows 0, 1, and 2 (like in Excel), you'd want to create two panels: A0-A2-C2-B1-C0 and A0-B1-A2-C2-C0. Once you've connected those points to make panels, you'll have a bunch of overlapping panels. So you cull.

There are easy ways, but they are usually a mess on the canvas.

There are the smart ways, but they usually require a really good understanding of the Relative Item and/or Path Mapper components.

Paneling Tools would also be helpful, but I'm not familiar with those.

Hope this gives you a place to start!

Permalink Reply by Peter Vejrum on July 15, 2014 at 1:03am

Thanks Damon!

I will try out your method.

Just to clarify, because maybe I am not understanding your method completely, but will the panels not cease to be planar if they are overlapping and then culled?

Permalink Reply by Damon on July 15, 2014 at 5:40am

Planarity is based on the geometry of the surface and the way you subdivide. Even if your surface is a developable surface, I don't think this pattern breaks it down into planar surfaces. This is a different topic, although related, to how to form the pattern in Grasshopper that you are showing.

Permalink Reply by Damon on July 15, 2014 at 6:27am

It might be easier to build the bow tie panels, planar or not, then rebuild them as planar. You could build a plane from three points from the bow tie, then project the other two points to the plane and rebuild the surface.

This would mean, however, that not every corner of the panel met the adjacent panels' corners.

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