Arrange selected vertices in a curved shape

I have a cube and by subdividing faces, now I have a bunch of vertices in each face.

How can I arrange some selected vertices in a curved shape (they are now in a straight line shape)?

Then I want to extrude those curved shape vertices.

• This question is still ambiguous, as phrased.. could you illustrate a desired end-result? – Robin Betts Dec 27 '18 at 8:06
• Please show your work as a Blender screen capture for your question above and all future questions. – atomicbezierslinger Dec 27 '18 at 8:42

Another option is:

1. removing the row of vertices you want to make curved

2. adding a Bezier curve in its place.

"Resolution Preview U" should be set to exactly $$N-1$$ where $$N$$ is the number of vertices making a side of your cube.

Also, you might want to make sure that the Bezier curve lays completely on the XY plane

3. converting the curve to mesh

4. joining the curve and the cube

5. reconstructing the faces by selecting the two adjacent rows and doing "Bridge Edge Loops" (must be done once per side)

• Consider Proportional Editing/ Edit Mode Proportional Editing (keyboard shortcut O).

• Consider Loop Tools

There is an Add-On called "Bezier Mesh Shaper" which I use for this exact purpose. Not free, but in terms of usability well worth its asking price.