Grasshopper

algorithmic modeling for Rhino

Hey guys, I am trying to create a cut sphere with this kind of uv division(as shown in the flat surface) as opposed to the classic ball uv division which is what I get with all the surface tools I've tried so far, does anyone have an idea how I can achieve this?

Rhino solutions would also be welcome. I am really lost on this one. I've tried network of curves but still get the classic ball uv..

Thanks a lot

Tal

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I don't get it... Do you want a partialy cut sphere? 

Here are 2 ways of doing that. It could be also possible to have less than a half of sphere. 

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Hey thanks a lot for your clever solution. The problem is that I want more than half a sphere.. as shown in the newly attached picture. It should be logically possible like the "surface from network of curves" but that doesn't work for it. 

No "problemo", I reuse what I did, put another sphere bigger and shifter it, project control points on the new bigger mesh sphere, use point deform (not a real sphere) and mesh from point (look like a sphere) and it is done.

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may your hands be blessed Laurent:) classic.

I am wondering if there is no "pure" mathematical way of doing such an operation that would give me the true subdivision . something like a Gaussian transformation.

being a mathematician at heart, but only at heart, I lack the knowledge behind it.

There must be a mathematical solution for the isocurve you want. With this equation you calculate the coordinates of "n * n" points which feed Surface from point component, and U = n.

Try to search the equation  on internet.

I have an idea but not yet the equation. I think I must begin with the flat surface, get each coordinate, depending of its distance from the center affect to it a new radius and an new angle.

Here a more mathematic solution. Not clear what you want to control. I wanted to add a S function after range, but dit not did it. 

The control points are on a sphere, but not exactly the surface. The points could be used to make a quad mesh.

I add a control for the angle => -90° = full sphere

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Wow, very cool, thank you.  I reduced the minimum 'UV steps' slider value from ten to two, which gives the fewest number of sub-surfaces.  Affects the shape of one model much more than the other.

The example by Laurent explains it well.

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