I want to get the exact definition of ‘the displacement vector’ in the documentation.

Suppose I have a vector field \vec{v}(\vec{x}) defined on a domain \Omega. Does this filter add the displacement vector \vec{v}(\vec{x})-\vec{x} at each point \vec{x}. So literally it just relocates each point \vec{x}\in\Omega at \vec{v}.

I have a circular domain and vector field on it as below. But somehow after ward the domain becomes much larger, which should be a little smaller if I understand… Can you tell how this happens? Or it actually adds \vec{v} instead of \vec{v}-\vec{x} to every points. The first figure is the original, the second is the warped.

I think the function of this filter is to displace the points by the assigned vector. That is to relocate each point \vec{x} by \vec{x}+\vec{v}. To get the ‘displacement’ in the context of elasticity theory, one has to use the calculator to create the displacement vector first, then warp.