Regridding

regridding

We often have an image $\bold h_0$on a coarse mesh that we would like to use on a refined mesh. This regridding chore reoccurs on many occasions so I present reusable code. When a continuum is being mapped to a mesh, it is best to allocate to each mesh point an equal area on the continuum. Thus we take an equal interval between each point, and a half an interval beyond the end points. Given n points, there are n-1 intervals between them, so we have

          min = o - d/2
          max = o + d/2 + (n-1)*d

which may be back solved to

          d = (max-min)/n
          o = (min*(n-.5) + max/2)/n

which is a memorable result for d and a less memorable one for o. With these not-quite-trivial results, we can invoke the linear interpolation operator lint2. It is designed for data points at irregular locations, but we can use it for regular locations too. Operator refine2 defines pseudoirregular coordinates for the bin centers on the fine mesh and then invokes lint2 to carry data values from the coarse regular mesh to the pseudoirregular finer mesh. Upon exiting from refine2, the data space (normally irregular) is a model space (always regular) on the finer mesh. refine2refine 2-D mesh Finally, here is the 2-D linear interpolation operator lint2, which is a trivial extension of the 1-D version lint1 . lint22-D linear interpolation