In many cases it is desirable for the interpolating forms \phi_i^k to pick the field's strength on particular grid elements without interference from other \phi_j^k. This allows one to assign field values to specific grid elements, which can then be interpolated in-between. A common case is linear interpolation for which the interpolating functions (0-forms) are zero on all nodes except on one, where the interpolating function is one. A similar construct can be applied to mimetic interpolation
