The document presents an overview of octree encoding, a hierarchical data structure used to represent 3D space, particularly beneficial for storage efficiency and object interior representation. Octrees partition the 3D space into octants, building upon the principles of quadtree encoding from 2D images, and are widely used in applications such as 3D graphics, spatial indexing, and collision detection. The presentation is guided by Prof. G. D. Korwar at Vishwakarma Institute of Technology, Pune, and highlights various applications of octrees in computer graphics.

1. Presentation on
Octree Encoding
Presented By:
Aditya Deshpande
Guided By:
Prof. G. D. Korwar
VISHWAKARMA INSTITUTE OF TECHNOLOGY, PUNE

2. Introduction
Octrees are hierarchical tree structures that describe each region of 3D
space as nodes. When compared with the basic voxel representation,
octrees reduce storage requirements for 3D objects. It also provides a
convenient representation for storing information about object
interiors. Octree encoding procedure is an extension of the quadtree
encoding of 2D images

3. • An octree is a tree data structure in which each internal node has
exactly eight children.
• Octrees are most often used to partition a three dimensional
space by recursively subdividing it into eight octants.
• Octrees are the three-dimensional analogue of quadtrees.
• The name is formed from oct + tree, but note that it is normally
written "octree" with only one "t".
• Octrees are often used in 3D graphics and 3D game engines.
• The use of octrees for 3D computer graphics was pioneered by
Donald Meagher at Rensselaer Polytechnic Institute, in a 1980
Octrees - Intro

4. Octrees are hierarchical tree structures
used to represent solid objects
Octrees are particularly useful in
applications that require cross sectional
views
for example medical applications
Octrees are typically used when the
interior of objects is important
Octrees

5. • Octrees are based on a two-dimensional representation scheme
called quadtree encoding
• Quadtree encoding divides a square region of space into four equal
areas until homogeneous regions are found
• These regions can then be arranged in a tree
Octrees & Quadtrees

6. Quadtree Examples 1

7. Quadtree Examples 2

8. • Quadtree encodings provide considerable savings in storage when
large colour areas exist in a region of space
• An octree takes the same approach as quadtrees, but divides a cube
region of 3D space into octants
• Each region within an octree is referred to as a volume element or
voxel
• Division is continued until homogeneous regions are discovered
Octree

9. Octree (cont…)

10. • In 3 dimensions regions can be considered to be homogeneous in
terms of colour, material type, density or any other physical
characteristics
• Voxels also have the unique possibility of being empty
Octree (cont…)

11. Octree Examples

14. Octree Representation of 3D Data
(a) Example 3-dimensional object; (b) its octree block decomposition; and (c) its tree representation.

15. 1. 3D computer graphics
2. Spatial indexing
3. Nearest neighbour search
4. Efficient collision detection in three dimensions
5. View frustum culling
6. Fast Multipole Method
7. Unstructured grid
8. Finite element analysis
9. Sparse voxel octree
10. State estimation
11. Set estimation
Applications