Finding the index number on a stretched cartesian grid

[jonasboy]

Imagine I have a set of discrete points equally spaced out and indexed from 1 to n (a 1D grid). On a cartesian grid if the spacing, dx, is constant the index can be obtained simply by:

i = floor(x/dx)

That was pretty simple, now if the cartesian grid is stretched (i.e. dx is not constant), it is not clear to me how to go about finding the index analytically. I am guessing that since we know the grid analytically we should be able to find the index analytically regardless if the grid is stretched or not. Any thoughts?

Thanks in advance.

 

[haruspex]

Not entirely certain of the question but...
Suppose the grid points are given by x_i = f(i), some suitably nice function f. Wouldn't the grid point next below x be floor(f^-1(x))?