[NB: I think this question may have been asked and answered before, but in doing a search of the archived questions and answers, using what I though would have been words contained, I did not come up with any matches.]
Consider this set of images,
and assume that I have made a mesh of any one of them in Blender. Is there a simple way to create the other two from the mesh I made, so that I could change the width of the border around the figure? I want to change the width of the part of the mesh shown in black, while leaving the part of mesh shown in white relatively unaffected. Using the scale function seems to change the width of the border at the outer most points of the mesh by a different amount than the border of the elements that cross nearest to the center.