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The To Sphere transformation will give the selection spherical qualities. The Fig. Monkey with increasing sphericity. below shows the results of applying the To Sphere transformation to the monkey mesh.
As can be seen in the below image, the result will be smoother and more spherical when there are more mesh elements available to work with.
The To Sphere transform will generate different results depending on the number and arrangement of elements that were selected (as shown by the below image).