forward mapping -why is difficult

hi

I am trying to complete a project and it involves forward mapping for images. I have the original image (mxn) pixel locations. I have applied a (moving least squares deformation) transformation to it and obtained new pixel locations 'u' and 'v'.My (u,v) pixels are a non integer numbers..so i need to preform a bi linear interpolation (because the output image grid is a integers numbers).

i need to calculate the distance between the (u,v) pixels to the nearest 4 output grid.

from reading on mathworks web : forward mapping

it is difficult to preform interpolation in the output grid...why? ( i need to find an exploitation why it hard to find the distance between the warped pixels and the output grid for interpolation)

thanks