The input data is supposed to represent an integrated or averaged property over a certain interval/range (1D) or area/grid cell (2D). Normal point interpolation results in a change of the total/average and artificially smoothens. The current routine is based also on point interpolation, but iteratively improves conservation of the total/average by nudgding the original data until data is conserved (within numerical accuracy). While the algorithm is very simple, the result is a smooth and results in 100% conservative regridding. In addition, the result matches in most cases the underlying (unknown) finer resolution better than normal interpolation (see examples).
Common application area is the Earth sciences where the data can be measured or output from models (see examples). Other application area is that of image interpolation of grayscale pictures, where normal interpolation tends to blur imagery (see conservative_regrid_demo_2D_1.m).
Keywords: regridding, remapping, downscaling, image sharpening, interpolation, pycnophylactic interpolation, area to point, interpolation, oversampling, no anxillary information, cubic spline interpolation, coarse, fine, mass preserving, volume conserving, upsampling, upscaling