Create a curved surface on SolidWorks with respect to the center of mass

Hi all

I'm looking for a way to curve a flat surface of a cube relative to its center of mass, on SolidWorks. 

For the moment I managed to curve the surface in a simple way, with the tab "surface --> free form -->control polygon" to curve my face on the x,y,z axis. But I can't make the connection with the center of mass of my piece. 

Anyone have any advice to give me? The goal would be to transform a flat surface into a curved surface with a defined radius of curvature relative to the center of mass of the part.

Thank you in advance. 

Hello;

It is possible to create a point in 3D sketch coinciding with your center of mass (Mass options, display center of gravity).
On the other hand, your CDG (Center of Gravity) will automatically move if you modify a face (your curvature), what type of relationship do you want between your curvatures and this CDG?
You will spend your time rebuilding (CTRL+Q) your part...
Kind regards

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Hello @reyes,

A cube with a curved face...
What is the closest image?

Two questions arise:
- for any surface, the curvature varies at any point on the surface, which is controlled according to the two directions (u, v) of the parameterization. What does the expression "a defined radius of curvature with respect to the center of mass... "? Is it a constant radius, in which case the surface is a sphere (figure on the left), or a shape defined by spline-type guide curves (figure in the foreground)?
- as indicated by Maclane, your idea of defining the surface generates a circular reference: the shape of the surface depends on the position of the center of mass, but the center of mass depends on the shape of the surface. Not sure that a SolidWorks function will accept it...

Can you clarify your intention?

Kind regards...

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