---
title: "Space partitioning representation"
subject: "Computer Graphics"
chapter: 6
key: "semester_5/computer_graphics:space-partitioning-representation"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/space-partitioning-representation
site: BCT Engineering
---

# Space partitioning representation

Computer Graphics · Chapter 6: Surface Modeling

- Asked in: 2082 Kartik (new course), 3 marks
- Video: [3D Object Representation: Boundary vs. Space Partitioning, Polygon Surfaces, and Meshes](https://www.youtube.com/watch?v=Pwsp6ONTlRI) — OPengineer
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/space-partitioning-representation
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-6

## Question

Illustrate space partitioning representation in brief.

## 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.

## Answer

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.

```text
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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Space-partitioning represents an object by:
   A. Listing its surfaces
   B. Dividing its space into non-overlapping cells and marking which belong to it
   C. Combining primitives
   D. Storing vertices only
   Answer: B. The solid is the union of cells. (Key point: Idea)

2. In an octree, a partial octant is:
   A. Subdivided further until a minimum size
   B. Discarded
   C. Marked empty
   D. Marked full
   Answer: A. Partial octants are refined. (Key point: Octree)

3. A BSP tree splits space with:
   A. Planes into front and back half-spaces
   B. Eight cubes
   C. Voxels only
   D. Vertices
   Answer: A. It yields depth ordering. (Key point: BSP)

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- [State space model of vertical two-mass system](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Ass-mech-m1-m2-k-b) — Control Systems, chapter 8
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