Islamic pattern on a dome with no deformation

Hello there
i am trying to model an islamic geometric pattern on a dome interior but whenever i make the pattern using parakeet and then project the pattern on the dome interior it gets deformed
what is the correct way to do it ?
image for the result i am trying to model

Hello
it seems you choose something difficult. What is you exact aim ?
To replicate the exact geometry ?
To make something approaching ?
For the second you have surely many choices to make, on the number of symmetries, the patterns … You certainly must read some documentations on the subjects. I don’t think there is a Magic plugin.

@Esmaeil_Mtghi have you some ideas on this subject ?

Are you trying to create a flat pattern and then put the pattern onto the dome? It is not possible to put a flat pattern on a dome without distortion with one exception. That exception is if the dome is made up of multiple segments and each segment has single curvature, ie is “developable” and each segment can be unrolled flat without distortion. Then the flat pattern can be flowed onto each segment without distortion although the pattern may not align between segments.

The alternative is to create the pattern in place directly on the dome surface.

Thank you for your reply sir
i am not trying replicate the exact same geometry
what i am trying to achieve is creating a (mainly) 10 point rosette seamless pattern on an interior of a dome
i am also trying to achieve the radial effect in the pattern meaning that the central rosette is bigger in scale then the other rosettes change in scale
i have been researching this problem for couple of days now what i understood thats a non euclidean geometry so the normal euclidean pattern will get distorted when projected on the dome
also from what i collected i understood (thats maybe very wrong :sweat_smile:)that a hyperbolic pattern is an already distorted pattern that if it is projected on a sphere or a dome it will be projected in a correct manner with no distortion
so what i am searching for now is how to turn my 10 rosette seamless pattern into hyperbolic patter to try this theory (again thats maybe so wrong )

Hyperbolic distorsion is not so difficult. See there




To change a bit the patter just move the slider and the graphmapper
2020403_hyperbolic_pattern.gh (41.3 KB)

Here is the same way to transform a Pattern, here from Parakeet

The idea is the same it is to project on a sphere with an angle depending on the distance from a center point.





In order to make it work, the flat pattern must be as square (on a circle indeed) as possible. You can bake the result if you want a certain pattern to be on the top of the sphere. The plug the center point in the point component.
islamic pattern on sphere.gh (23.9 KB)

And if you move the sphere in Z, you can have more projection on it and more deformation.

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Thank you so much for your effort i really appreciate it
thats by far the closest result for what i wanted to achieve (no deformation at all) and i have learned alot during this process
thank you again and hope you are having a great day

No problem. Parakeet is doing a big part of the work.

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Hello
I posted some images on Instagram. The pattern I used seems “bad” or not respecting some rules. I searched a bit and on Parakeet script you can find the reference of the work
Star Pattern II

a Geometrical method for designing Islamic Patterns (Based on a method presented by Hankin Lee & Craig S. Kaplan &; http://www.cgl.uwaterloo.ca/csk/) in order to get a heterogenous Pattern, inpute various parameters (A and D) for each Cell

http://www.cgl.uwaterloo.ca/csk/phd/

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hi guys,
i need some help here with how to do this pattern and controlling that dome on it? i tried so many ways but just couldn’t figure out this…i am open to any suggestions?

spherical-sri-yantra