We investigate discrete spin transformations, a geometric framework to
manipulate surface meshes by controlling mean curvature. Applications include
surface fairing -- flowing a mesh onto say, a reference sphere -- and mesh
extrusion -- e.g., rebuilding a complex shape from a reference sphere and
curvature specification. Because they operate in curvature space, these
operations can be conducted very stably across large deformations with no need
for remeshing. Spin transformations add to the algorithmic toolbox for
pose-invariant shape analysis. Mathematically speaking, mean curvature is a
shape invariant and in general fully characterizes closed shapes (together with
the metric). Computationally speaking, spin transformations make that
relationship explicit. Our work expands on a discrete formulation of spin
transformations. Like their smooth counterpart, discrete spin transformations
are naturally close to conformal (angle-preserving). This quasi-conformality
can nevertheless be relaxed to satisfy the desired trade-off between area
distortion and angle preservation. We derive such constraints and propose a
formulation in which they can be efficiently incorporated. The approach is
showcased on subcortical structures.