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How can I move the vertices in the picture in a way that they "stretch" and keep their position relative to each other? I'm interested so that I would end up with a consistent geometry from left to right lets say. I could of course just remove the vertices and create a plane but I'm interested in knowing how to perform the transformation while preserving the grid shape.

enter image description here

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It seems I have figure out one way to do it, and that is by using a lattice and a lattice modifier. By adding the lattice modifier to the scene, then selecting the object to modify > shift and select the lattice > ctrl +p > deform by lattice, this added a lattice modifier to the mesh and used the selected lattice object. By manipulating the object, the mesh is then manipulated while the vertex grid remains uniform.

You can see in this gif how this is done and looks like (https://gph.is/g/Z7G7JAP) The gif was too large to upload it here.

Another thing that could be usefull for anyone, would be proportional editing mode for this too.

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