Illustration of an isotropic range search using the k-d tree. Panels a, b, and c show the partitions of the data points (black dots) during the k-d tree construction, the resulting minimum axis-aligned bounding box of leaf nodes and their parents, and the diagram of the tree structure, respectively. In particular, non-leaf nodes in panel (c) are indicated by the corresponding dividing lines in panel a. The red point and circle in panel b indicate the reference point and radius for a range search. The grey regions in panel c and the yellow areas in panels b and c highlight the visited non-leaf and leaf nodes during this query. The retrieved data points are shown in pink in panel d.