consistent area but deformed shape

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Permalink Reply by McKean Dave on October 7, 2009 at 6:28am

min tian,

i've been trying to do the same thing. did you ever figure it out?

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Permalink Reply by Vicente Soler on October 7, 2009 at 7:28am

What do you mean by morphing a rectangle to a sphere keeping it's volume?
I can think of these options:
1. - A rectangular surface to a sphere (keeping constant surface area)
2. - A box to a sphere (keeping constant volume)
3. - A rectangle to a circle (keeping constant area)

I've done number 3 since it's the easiest :P

There are several ways to morph. If you divide both surfaces or curves into points, find the average position and then interpolate through them a surface or curve, you'll only get an approximation of a circle or sphere. To get a perfect circle or sphere, you should get the control points and their weight and also interpolate their weight (this is my deduction, i could be wrong), but this is not exposed in grasshopper. The next best thing is doing a loft, as i did in the screenshot and extracting sections.

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Permalink Reply by McKean Dave on October 7, 2009 at 3:46pm

Thanks Vicente! But what I am really trying to do is to create a series of curves or surfaces that can change in shape, but share the same area.

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Permalink Reply by Vicente Soler on October 7, 2009 at 4:27pm

Can you be a bit more specific? How does what you are trying to achieve it differ from my example?

If the surfaces are not planar and you are trying to maintain a fixed surface area, it's much more difficult.

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Permalink Reply by McKean Dave on October 8, 2009 at 5:32am

I'm not sure what I'm asking can be done.

The surfaces would be planar. Imagine defining any planar surface from a curve. I want to be able to manipulate the original curve using the control points and have the geometry of the curve react and move in a way that preserves the area of the surface.

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Permalink Reply by Vicente Soler on October 8, 2009 at 6:15am

Sort of like the video i posted in this thread
http://www.grasshopper3d.com/forum/topics/breach-the-bake-gap
(see second page) but with surfaces instead of volumes?

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Permalink Reply by Theunis du Toit on October 8, 2009 at 6:22am

Oh, you posted the same thing while I was writing.

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Permalink Reply by Theunis du Toit on October 8, 2009 at 6:19am

I think what your asking for requires Grasshopper to have an auto bake function. Which it doesn't. But check out these discussion links.

http://grasshopper3d.ning.com/forum/topics/breach-the-bake-gap?id=2...

And this link that Vicente actually posted there that does what I think you are asking for.

http://www.youtube.com/watch?v=Ock0afn-F8c

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Permalink Reply by McKean Dave on October 8, 2009 at 7:06am

Yes, that is exactly what I am trying to do. Except with surface area instead of volume. Thanks for the link.

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