# Moving each point of a surface in direction of corresponding normal

So let assume that I have some convex smooth and unclosed surface. I'm moving each point of it in a normal direction by some constant factor (This factor is same for all points on surface).

Can I replace this operation by Uniform or Non-uniform Scaling + Translate?

Will resulting surfaces be mathematically identical in these cases?

For example, I want to transform this surface (side view):

The issue is that the amount a section of the curve/surface grows depends on its curvature, not its orientation in space. Notice here that the circular arc grows uniformly in all directions (by a factor of $3/2$) whereas the length of the horizontal segments remains unchanged at a length of $2$.