How does interpolationCellPoint work?
 

Hi,

I am doing lagrangian particle simulation and was kinda curious to how does interpolationCellPoint work? I understand that it is used to interpolate something that is at an arbitrary location in a cell based on the link below:
http://openfoamwiki.net/index.php/In..._%28by_cell%29

The link also explained that it works by:

• breaking each face down into triangles;
• defining tetrahedra using these triangles and the cell centre-point;
• cycling through all tetrahedra to find which encloses the arbitrary point; and
• using inverse distance weights to perform linear interpolation.

However, I still don't get how does it work. Is there a theoretical explanation behind it? Are there any mathematical explanation to this?

Thanks.

Cheers,
Ahcai