Neighbor-finding algorithm using a kd-tree. The example demonstrates the process of finding neighboring points within a radius of r = 2 around a point (8, 9), denoted by a green circle. The left panel displays the plane divisions created by the points on the kd-tree. The dashed yellow and dotted purple lines divide the plane vertically and horizontally, respectively. The shaded yellow area represents the region within a radius of r = 2 from the point (8, 9). The right panel illustrates the kd-tree structure employed to identify neighboring points around the point (8, 9). The red circles indicate points that are not traversed, and the other circles represent points that are traversed. The purple points highlight the neighboring points found within the radius of r = 2.