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General idea: The user defines two regions on a mesh:
A support region which should be affected by the modeling.
A handle region inside the support region which the user can transform freely. The support region between the handle and the rest of the mesh should interpolate smoothly.

Solution: Fix all vertex positions except those of the support region.
For the support region vertices, solve

i.e. compute a smooth interpolating surface.

Problem: Smoothly interpolated surface loses detail.

Detail Preservation
Input mesh .
Fix vertex positions in the handle and the non-support regions and compute smooth surface .
Compute detail offset mesh .
Let the user transform the handle region and compute a new smoothed mesh .
Re-add the detail information:
.

For rotations: Store normal offsets instead of absolute position offsets.