Snapping points of a roughly spherical mesh exactly onto a sphere I have a mesh whose points ought to lie on a sphere.  They don't, but are roughly close.  Is there a convenient way to nudge them all along their radii to "snap" each to some fixed R?

I've been nudging each vertex by hand, for a simple demo model, but this isn't practical when I get to more elaborate cases.  I tries extrude-scaling the mesh toward the center point, then using a boolean intersection with a sphere, but that cut off all the intricate surface topology, leaving hollow shapes like oddly tapered cookie cutters.
To sphere:

You could try AltShiftS>To Sphere:

From the wiki:


  The To Sphere transformation will give the selection spherical qualities.


Example:



Shrinkwrap:

Or using the Shrinkwrap modifier to shrink your mesh to a sphere object.

From the wiki:


  The Shrinkwrap modifier allows an object to “shrink” to the surface of another object. It moves each vertex of the object being modified to the closest position on the surface of the given mesh (using one of the three methods available).


You could add a shrinkwrap modifier to your mesh and set the Target to a sphere: