I am currently writing a plugin for 3D analysis software and I am working with a data grid where certain values are stored at XYZ coordinates, and I need to find an estimated value of a point that could exist anywhere inside of the grid. I was looking to use Tricubic Interpolation to do so, but I am having a difficult time understanding the concept.
I was wondering if someone could explain the basics to me, or share some resources that give a stellar explanation of Tricubic Interpolation. Most of what I could find online dealt mostly with graphics or image processing, showed results without a why or how, or mostly just went over my head.
Another thing I was wondering if interpolating in "4D" could be a possibility. There is also a time value I need to account for, and being able to add that into my plugin would help greatly since I am currently planning to handle time programmatically, not mathematically.
To give perspective here are the most informational links I could find on the matter: http://www.cds.caltech.edu/~marsden/bib/2005/08-LeMa2005/LeMa2005.pdf http://www.paulinternet.nl/?page=bicubic