Something like Houdini's bulge node

something like “bulge” node of houdini would be nice, I still cant do it. By the way if you can do it please tell me how.

bulge

One way is to use the Cast Modifier with a plane and a sphere…

Or as you asked…in GN

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in addition to that, using map range with blur attribute node helps softness of “bulge” in close proximity.

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You can also use the warp modifier for it.

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tested teh methods, they seem to be working on a plane but not exactly working as I expected. In any case I think you got the right ideas. Thanks.