How to generate clusters with a given degree of separability for each feature?

Question

data mining

Generation of Random Clusters with Specified Degree of Separaion (Qiu, W.-L. and Joe, H. (2006a), Journal of Classification, 23(2), 315-334) shows how to generate clusters with a given degree of separability between cluster and its closest neighbors in the entire feature space.
It is necessary to generate clusters with a given degree of separability for each feature.

Answer 1

It's impossible. Clusters strictly separated from each other in N-dimensional space can be projected into a continuous segment along one of the dimensions.
For clarity: Let's present here 2 initial features - these are our measurements on the plane. For example, these concentric circles for each individual feature (dimension) are continuously dense, nevertheless they are separate clusters on the plane.