Is it possible to subdivide without vertex displacement?

Hello, i’m new to blender and i try to figure out how to make wooden ships hull.
Trying to subdivide curve between frames.
Lower image shows what’s the problem - subdivision makes vertex displacement. Higher image shows my hand made correction which takes enormous amount of time of 10 minutes and i feel totally discouraged for know.
Catmull- clark subd is a great tool for making organic shapes, but in this example doesn’t work.
I searched the web up and down and didn’t find an answer, but maybe one of You blender artists and veterans has some solution?

Subdivide always does somekind of smoothing, but there is a difference between subdiv modifier (changing orig vertices, smooth between tjem) and subdivide in edit mode (not changing orig vert, smoothing arround them) with smoothness factor 0.0-1.0. You may have a look.

I think the subdiv on simple mode with a smooth modifer will give you the bend more exact at your desired location.

Usually the unsub should be a little larger than the form you anticipate to combat this change.