Is there a variation of trilinear interpolation that works on a "cube" that has been distorted (by moving one or more of its corners by an arbitrary amount into an arbitrary direction)?
I know that I could use the inverse of the distance to each of the 8 corners as weights to get an interpolated point within the distorted cube, but that would involve taking a lot of square roots which would slow my algorithm way down. I like the elegant way of trilinear interpolation but I can't figure out how to adapt it to a distorted cube. Any hint on a fast interpolation method for this situation would be much appreciated.