  For the IV-VI semiconductor family we derive an exact relation between the
microscopic gap edge wave functions of the bulk insulator and the Dirac-Weyl
topological surface state wave function, thus obtaining a fully microscopic
surface state. We find that the balance of spin-orbit interaction and crystal
field in the bulk, and the band bending at the surface, can profoundly
influence the surface state spin-momentum locking. As a manifestation of this
we predict that the spin texture of the $M$-point Dirac cones of SnTe can be
tuned through an unexpectedly rich sequence of spin textures -- warped helical
with winding number $\pm 1$, $k_x$ linear, hyperbolic, and $k_y$ linear -- e.g.
by tuning the band bending at the surface.
