A hyperrectangle is a multidimensional, axis-aligned region formed by choosing a minimum and maximum bound for every coordinate. A point belongs when every coordinate lies within its corresponding interval. section 9.3.6 section 10.2.2
Use hyperrectangles to express range queries over multidimensional data. Unlike hyper-spheres, they can extend farther in some directions than others, matching asymmetric data distributions and often producing tighter bounding regions. section 10.5.1 section 8.3
A region query over a hyperrectangle follows two checks:
- In an R-tree, associate each node with the smallest axis-aligned hyperrectangle containing its entries or child bounding rectangles. section 10.2.2
A two-dimensional range
For a rectangle with x between -2 and 3.5 and y between -4 and 2, return a point only when both inequalities hold. A k-d tree then recursively explores only branches whose split regions intersect that rectangle.
