geometry – Determining the coordinates of a point in a distorted cube

Is it possible to express the coordinates of a point in a distorted cube? That is, given a distorted cube in 3D space with 8 points (the coordinates of which are not necessarily on the regular positions you’d expect them to be for a non-distorted cube), and a point within that cube, finding a universal way of expressing its position. And if this is possible, is there some established method for determining this alternative expression, so as to transfer it to a differently distorted cube?

The tetrahedron-equivalent of this would be to use a barycentric coordinate system, but that is for 4-point simplexes.