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This is the twice subdivided mesh of a cylinder:

enter image description here

As you can see, the vertices are very close together in horizontal direction but the vertical distance between them is comparatively very large. Is it possible to subdivide only the vertical edges of this object, so that I would get a mesh with edges equidistant in all direction?

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Use the 'ReMesh' modifier on 'Sharp' mode and adjust the Octree depth to match the desired resolution.

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