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
Remaining points from the initial list
Demonstration of increasing the number of nearby points
[b][i]Example[/i][/b]. After moving the "[i]moving point[/i]" of the [color=#ff7700][b]initial list[/b][/color] to the area of the [b][color=#cc0000]TestPoint[/color][/b], the number of [color=#ff00ff][b]remaining[/b][/color] particles decreased by 3: [b][color=#ff00ff]104[/color][/b] [b]→[/b][b][color=#ff00ff]101[/color][/b], and the [b][color=#980000]filtered[/color][/b] particles increased accordingly to [b][color=#980000]122[/color] → [color=#980000]125[/color][/b]. The number of [i][b]nearby[/b][/i] points at the [b][color=#cc0000]TestPoint[/color][/b] has increased to [b][color=#cc0000]13[/color][/b] [b]→[/b][b][color=#cc0000]14[/color][/b].

Information: A method for filtering nearby points in a list