Algorithm for homogenization of non-equidistant 1-D grid

I am looking for proper algorithm for so called "delta-homogenization" of 1-D non-equidistant grid.

Definition: The sorted monotonically changing vector x is delta-homogeneous if for specified , the differences ratio

satisfy to the condition:

, for , where

Problem: In a case of non delta-homogeneous vector x, how to find minimum number of additional points , to be vector delta-homogeneous?

The problem is motivaded by proper design of non-equidistant grids, which are able to guarantee numerical stability of PDEs solution.

Example:

> x = (1:4).*(1:4)
1     4     9    16 

>d = 1.5;

ratioviolationIdx =

  1×2 logical array

   0   1


ratios =

    1.6667    1.4000


deltalimits =

    0.6667    1.5000
    

So, x is not delta-homogeneous for delta = 1.5. But , the x is delta-homogeneous for delta = 2

>> [~,ratioviolationIdx,ratios,deltalimits] = isdeltahomog([x],2)

ratioviolationIdx =

  1×2 logical array

   1   1


ratios =

    1.6667    1.4000


deltalimits =

    0.5000    2.0000

An finaly, when I add several points to the vector x for delta = 1.5, I have delta-homogeneous vector

>> [~,ratioviolationIdx,ratios,deltalimits] = isdeltahomog([x 2.5 6 12],1.5)

ratioviolationIdx =

  1×5 logical array

   1   1   1   1   1


ratios =

    1.0000    1.3333    1.5000    1.0000    1.3333


deltalimits =

    0.6667    1.5000
    

See attached code...

Thanks in advance for any help.