Divide dome surface with same areas in grasshopper

Hello,
I am trying to divide dome surface like photo with same areas. But I couldn’t. Do you know how can I do it?

This may help

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Thank you, I will check.

Equal height slices of a sphere have equal surface areas


So if you make the spacing between your slices the same as the number of radial divisions for that slice, the areas of the resulting patches will be equal

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Equi-area sphere sections.gh (17.0 KB)

… just a tiny step (or “math gimmick”) past Daniel’s concept.

Edit:
see this page translated Della sfera e del cilindro - Wikipedia
or Archimedes and the area of sphere | Mathematics@CUHK

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Thank you for answer. But I don’t understand exactly. I am newer on grasshopper. You said “Equal height slices of a sphere have equal surface areas” but I divide sphere with contour with same height and split it. And I checked the areas. They were different. In the second picture heights are different. I am confused. Can you explain more simply please?

Can you post a model showing what you did so we can help clear up the confusion?

Ok. I use contour to split surface. But areas are different.

LOL
Necmettin, I think you got us all.

Probably everyone (me included) here thought about a sphere, a spherical dome (every point at the same distance from a center point).
That’s what your first picture suggested.

But your second picture shows you are working with a generic, non-spherical dome.
If so, everything is different.

So, spherical or non-spherical dome?

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for arbitrary shape you can use this brute force method :slight_smile:


same_area_dome.gh (63.2 KB)
(not as elegant as @maje90 solution)

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Oo ok, I misunderstand that sorry. Actually its not spherical dome. You are right. I am trying to create Hagia Sophia’s dome like a masonry dome technique with bricks. This is my mistake sorry sir.

Actually sir, I created a dome with flat bricks. I searched a lot. And finally I did it. But on this model, all the elements (bricks) come to the upper elevations, they start to get smaller. I wanted to fix it. Because of that I asked how dome surface divide with same areas. I am trying to understand of main logic. I started simple sphere. But you are right. It is not a spherical. Firstly I create surface and later convert a mesh. This code works like that. I talked too much sorry. But this is the main idea. Thank you again.

If you are not insistent on absolutely equal areas and your dome is symmetrical round the z axis, then you could use one of the solutions here for a hemisphere, pull the corners of each panel to your dome, and create a 4 point surface. ,

From the link

-Create disk with the same area of the hemisphere.
-Create series of circles or use offset, than project the new circles on the hemisphere (with spheres and intersections) or maybe there is a mathematic method.

hemisphere_equal-areas.gh (24.1 KB)

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Once again: tweaking @Gijs’s idea now.

equi-area revolved srf divisions.gh (35.8 KB)
Galapagos’s Simulated Annealing seems faster for this… :face_with_raised_eyebrow:

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This is a different way from the paper (the link above)

hemisphere_equal-area_cells.gh (15.3 KB)

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I didn’t think like that. Thank you. It’s cool.

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