Algorithms {binary space partitioning} (BSP) can recursively divide space or polygon into two regions using hyperplanes, to make halves, quarters, eights, sixteenths, and so on.
orientation
Hyperplanes can have any orientation, making unequal regions. Hyperplanes that cut at medians make both regions equal.
polygons
Polygons can have angles greater than 180 degrees {reflex angle, polygon} or less than 180 degrees. Dividing polygon recursively makes regions with angles less than 180 degrees {convex set}.
recursion
Recursion steps define trees {BSP tree} and make stored lists {visibility list} that order polygons from front to rear. Convex sets become smaller until they include only point {BSP-tree leaves}.
multiple hyperplanes
Binary space partitioning can use hyperplane pairs or triples for cuts. Hyperplane pair divides space into four regions {quadtree}. Hyperplane triple divides space into eight regions {octree}.
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Date Modified: 2022.0224