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A method for filtering nearby points in a list

I propose a method for filtering points so that only one point remains from each group of nearby points.

Points from the initial list

Points from the initial list

Remaining points from the initial list

Remaining points from the initial list

Demonstration of increasing the number of nearby points

Demonstration of increasing the number of nearby points
Example. After moving the "moving point" of the initial list to the area of the TestPoint, the number of remaining particles decreased by 3: 104 101, and the filtered particles increased accordingly to 122125. The number of nearby points at the TestPoint has increased to 13 14.