Transforming Cube Surface to Spherical Cube Surface (Generating Spherical Cube)

Question

I have the coordinates of points of an empty cube just like down below:

What I would like to do is transform that cube to something like this:

Ther

Answer 1

Probably one of the most popular solutions to this problem is the Catmull-Clark Subdivision Surface Algorithm which is evulated recursively.

However, that this algorithm "does not approach an actual sphere as a sphere is quadric." Regardless, this algorithm will produce exactly what is in the image you attached. Also note: you would create a simple cube first and then deform it with subdivision, so you would start with 6 faces,

Example of 0 Degree Subdivision

and then a first degree subdivision would give you 24 faces,

Example of 1st degree subdivision

with each of the corner vertices translated towards the center to begin the spherical shape.

Answer 2

Draw grids on the faces cube and project every point that you need radially onto the sphere. Assuming the center of the cube at the origin, transform

(x, y, z) -> (x, y, z) / √(x² + y² + z²)