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Space partitioning representation

Short answer

Space partitioning divides a 3D object into small non-overlapping solid cells and marks which belong to the object. A common method is the octree, which recursively splits a cube into eight octants, classifying each as full, empty or partial until a minimum cell size.

Illustrate space partitioning representation in brief.

In space-partitioning representation, a 3D object is described by dividing the space it occupies into small, non-overlapping solid cells and marking which cells belong to the object. The solid is the union of these cells.

Common methods

  1. Octree: the cube enclosing the object is divided into 8 equal octants. Each octant is classified as full (inside the object), empty (outside) or partial. Partial octants are subdivided again until a minimum size is reached. Each node of the tree has 8 children.
  2. BSP (binary space partitioning) tree: space is split recursively by planes into two half-spaces (front and back). Objects are stored in the tree, and it gives an easy depth ordering for hidden surface removal.
  3. Voxel / cell decomposition: space is divided into a regular grid of voxels.
Octree: the cube is split into 8 octants (front face shown)
 +-----+-----+
 |  4  |  5  |
 +-----+-----+   -> tree: root with children 0..7;
 |  0  |  1  |      partial children are split further
 +-----+-----+

Uses: medical (CT) data, volume rendering, collision detection, and fast set operations (union, intersection). The costs are high memory use for fine detail and approximate (stair-stepped) boundaries.

✓ Answer checked by Claude Opus 5.5 (high effort)

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