Grasshopper

generative modeling for Rhino

# How to create a quadrilateral mesh with planer faces from double curved surface?

Hi
I have a double curved surface, which I would like to divide it into flat rectangular surfaces (Subsrf) or apply quadrilateral mesh with planer faces. I tried Mesh UV (Mesh Surface) and Sub srf, but the faces/subsurfaces are not planer. Any suggestions?

Thanks
Amir

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hei amir,

check the file. a plane is defined by 3 points, therefore a quad does not have to be planar - Srf4Pt creates planar surfaces (100%) only for three points or 4 coplanar points.

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Hi Tudor,
Yes, I agree with you regarding the characteristics of Srf4Pt.
But, is there a way to achieve a subdivision of double curved surface to a planar quads? (Maybe an approximation to the original surface?) The Idea is to manufacture those quads from a solid sheet material... (Something like the attached photo but instead of triangles – flat rectangles)

While talking – Planarize + Equalize commands form Kangaroo just came up to my mind, I will try this option and see what happens
Any other idea?
Thank.
Amir
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Hi

Thanks alot!

Amir

You can also make this:

Make quad curved faces and then move the point number 4 to the other 3 points plane...always 3 points define a plane. Easy and effective. You can messure the deviation of every panel and make a color shader that tells you the gap size.

Yes, this is a good and efficient way to approximate the original surface and see (in colours) the deviation. However, the new sub surfaces (the one that pt #4 moves) will not form a “watertight” shell around the original surface, so I am not sure about how the new panels will fit to each other, I am worried about a gap between the panels...
Any idea of how to approach this issue?
Thanks!
Amir
if you create extrusions/lofts between the planar quads it's going to be watertight.

Try the attached paper....

It's not the best paper I've ever written, but it's a good survey of the different approaches. It was written in 2008, and some things have change since then, but the basics are the same. In order for any optimization technique (Kangaroo especially) to work, you need a good initial guess. Integrating "conjugate curve networks" will provide exactly that gues. For instance, these curve networks (created with the SPM Vector Componets btw.) will flatten nicely:

But most UV subdivision will not.

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Hi Daniel,
Nice to hear from you again!
Thank you very much for the paper – It is VERY useful.
I recommend to anyone interested in the subject to have a look at the paper.
“BTW” – The image above is excellent – I like it...!
Thanks again,

Amir

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