Given a 3D model that is similar the shape of a cube, how do I map regular gridlines onto the 3D model?

Question

Suppose I have a 3D model that roughly resembles a cube or a cuboid, and I wanted to estimate a regular set of gridlines that lays on top of the 3D model.

Is there an efficient way of doing this?

A brute force way might be to first estimate the 8 corner points, then use the geodesic function in CGAL to link up the corner points to form the initial path lines. Recursively, take the halfway point in each path find the geodesic path to the halfway point of the opposing path.

But that would take up too much computing time.

Is there a faster way to do this via texture mapping texture? I need to code this out so will be thankful if a specific algorithm can be referred to, rather than using a software such as blender, maya, etc.

thanks for any help!