Folded Paper - updated with picture

Hi All,

Thanks for the amazing resource you have here

I am not sure which tools to utilize in order to create a particular shape from a plane or curve.

My end goal is to some how apply this geometry to a poly surface, or at least to a curve - for example -a circle centred on the apex of this shape

Do I create a curve (circle) on a square surface, group the two, then manipulate the control points so that the surface and the circle curve end up approximating shape of the picture I have attached?

Do I have to drag each individual control point on the circle in such a way to approximate the surface shape in question, or is there a more elegant way to accomplish this?

Essential I want to raise the centre of a square plane (or planar curves), but with creases diagonally across (square), such that the crease lines remain straight and the rest of the surface sags creating a curved surface. Imagine a square sheet loosely secured at corners with diagonal lengths of rope supporting underneath, then raise the centre point with sheet anchored only at corners.

If I can apply this to a a group of planar curves, by by spliting the group diagonally, then have it conform to surface I have described, as though it were drawn uponit , then I could join the parts into a closed curve and I would have the shape I am trying to model.

Ideally I would want to be able to fine tune and tweak the distance the centre has been raised from its original planar position.

Could someone please point me in the right direct of which tools to use to approach this in rhino?

And if there is a better or different way to ahieve this please let me know.




1 Like

Hi Nathan,
I think your image attachment didn’t work, can you try uploading it again?

If you do not want to use relaxation methods.
(kangaroo2 and fold angle goal on seams of triangulated quad mesh)

You can just draw 4 lines, and 4 arcs. Then sweep them.

It would also work by loft bunch of straight lines at eavh quarter of your form.

take 3 curves use EdgeSrf and mirror/rotate/join the resulting surfaces.

Thanks for the helpful replies.

I am new to Rhino and to the particular commands suggested but will give it a try.

However, the end goal is to manipulate a curve to conform to this surface.

For example, a circle drawn upon the paper:

When the surface is folded in a particular way, the circle would appear almost like a square when viewed front on. This is the effect I am trying to acheive.

The actual curves I want to manipulate are more complex and aysymetrical than a simple circle, thus the idea of having the curves conform to a surface and manipulating the surface seems like it would be a better way than directly maniuplating the curves themselves. Maybe I am overthinking this.

I know I can simply project the curves onto the surface created by one of the suggestions above, but I want to create this model such that I can then manipulate the distance(height) of the centre point of the the square (plane)


The shape of the curve will be the easy part—because you can always project that (or indeed any) shape you’d like onto any surface you want.

What I’m not sure about however is if it’s possible to bake that outline into the surface itself.

From what I can tell… the curve still remains an independent curve after the project command is used… and ideally for you’d want the curve to become baked onto the paper surface so that it move together with the paper surface and according to is base geometry. And not with any external influence of it’s own set of control points (which it has as an independent object).

So I’m not sure how this bake process might work in Rhino.

But as a workaround… I’d suggest that you use the curve in combination with the split command… and that will in turn create a cutout in the paper surface, which will move along with any changes you make to the paper surface.

That will at least give you the basics of your curve shape, and you’ll be able to see the changes it will undergo as you play around with modifying the main surface geometry underneath it.

you’ll still be left with having to fill in the hole you cut if you didn’t want that, but there would be ways to get around that. One of them could be that you have two side by side models which get manipulated in the same manner. One is there to provide the outside field shape (i.e. the negative space), and other to supply the cutout shape that will fill in the hole you made. and you just combine the two together when you’re done.

Finding a way to bake that curve shape into the surface itself will of course eliminate the need for this sort of workaround. I think it’s possible… I just don’t know how it happens.

The other part of this it that you’ll probably need to use the rebuild command (or something similar)… so that you can have control points in the places where you need them in order to get the paper to fold that way you want it to.

the PointsOn commands makes these visible… and you can start selecting a few of them to modify the surface shape.

Thanks for the detailed response.

If I understand correctly, the workaround you are suggesting involves splitting the surface with the curve and then manupulating the surface to the desired shape. So I could end up with the desired surface shape that is split along the curve. However, I am not sure how I would then create a curve from the split surface. Does this require some kind of boolean function? As I understand it the split has no volume, so how do generate the positive (curve) from the negative (split surface) ?

This is a simplified version of what I was trying to write about. I know I made it sound harder than what I was actually thinking about. But in illustrated form it would go like the following:

2 version of the same object…

Modified in the same way…

Should hopefully be able to reconnect…

But there are probably limits to how far you can go with this approach.

Rhino keeps the base structure intact… so even the smaller positive shape is still influenced by the same set of control points… and that’s why I thought you could take advantage of this and be able to end up with matching pieces when the changes are all over.

But of course I haven’t tested this too heavily,… so I’m afraid I don’t know where all of the limits are.

I’ll play around with you idea for the next couple of days and will come back to reply if I find anything good.

… and Finally the Light Bulb turns on:

Having said everything above… There is a better way to reverse the actions of the split command. You could always just use the Untrim command. and that will restore your object back to it’s original pre-Split command) condition.

That would probably be the Smart Thing to do, and the Wise Thing to do… and I’m not sure why I couldn’t think of that command earlier… so don’t bother asking me that question.

I have a general curse where I tend to do things the hard way before I remember there was an easy way. This is a pretty good example of that… but rest assured there are many others which I could also talk about.