  Translations or, more generally, coordinate transformations of scalar fields
arise in several applications, such as weather, accretion disk and magnetized
plasma turbulence modeling. In local studies of accretion disks and magnetized
plasmas these coordinate transformations consist of an analytical mapping and
enter via sheared-shift boundary conditions. This work introduces a
discontinuous Galerkin algorithm to compute these coordinate transformations or
boundary conditions based on projections and quadrature-free integrals. The
procedure is high-order accurate, preserves certain moments exactly and works
in multiple dimensions. Tests of the proposed approach with increasing
complexity are presented, beginning with translations of one and two
dimensional fields, followed by 3D and 5D simulations with sheared
(twist-shift) boundary conditions. The results show that the algorithm is
(p+1)-order accurate in the DG representation and (p+2)-order accurate in the
cell averages, with p being the order of the polynomial basis functions.
Quantification of the algorithm's diffusion and, for shearing boundary
conditions, discussion of aliasing errors are provided.
