  In astrophysical magnetohydrodynamics (MHD) and electrodynamics simulations,
numerically enforcing the divB=0 constraint on the magnetic field has been
difficult. We observe that for point-based discretization, as used in
finite-difference type and pseudo-spectral methods, the divB=0 constraint can
be satisfied entirely by a choice of interpolation used to define the
derivatives of B. As an example we demonstrate a new class of finite-difference
type derivative operators on a regular grid which has the divB=0 property. This
principle clarifies the nature of divB != 0 errors. The principles and
techniques demonstrated in this paper are particularly useful for the magnetic
field, but can be applied to any vector field. This paper serves as a brief
introduction to the method and demonstrates an implementation showing
convergence.
