  When using the black hole exclusion (horizon boundary condition) technique,
$K$ is usually nonzero and spatially variable, so none of the special cases of
York's conformal-decomposition algorithm apply, and the full 4-vector nonlinear
York equations must be solved numerically.
  We discuss the construction of dynamic black hole initial data slices using
this technique: We perturb a known black hole slice via some Ansatz, apply the
York decomposition (using another Ansatz for the inner boundary conditions) to
project the perturbed field variables back into the constraint hypersurface,
and finally optionally apply a numerical 3-coordinate transformation to (eg)
restore an areal radial coordinate.
  In comparison to other initial data algorithms, the key advantage of this
algorithm is its flexibility: $K$ is unrestricted, allowing the use of whatever
slicing is most suitable for (say) a time evolution.
  We have implemented this algorithm for the spherically symmetric scalar field
system. We present numerical results for a number of Eddington-
Finkelstein--like initial data slices containing black holes surrounded by
scalar field shells. Using 4th order finite differencing with resolutions of
$\Delta r/r \approx 0.02$ (0.01) near the (Gaussian) perturbations, the
numerically computed energy and momentum constraints for the final slices are
$\ltsim 10^{-8}$ ($10^{-9}$) and $\ltsim 10^{-9}$ ($10^{-10}$) in magnitude.
  Finally, we briefly discuss the errors incurred when interpolating data from
one grid to another, as in numerical coordinate transformation or horizon
finding. We show that for the usual moving-local-interpolation schemes, even
for smooth functions the interpolation error is not smooth.
