1. Mesh data structure & file format
GI127 陳勁宇

2. Content Object File Format(OFF) Polygon File Format(PLY)
The Winged-Edge Data Structure
The Half-Edge Data Structure

3. Object File Format(OFF)
Storing a description a 2D or 3D object
Simple extension can handle 4D objects
4D: (x,y,z,w)
OFF File Characteristics
ASCII (there is also a binary version)
Color optional 3D
No compression

4. Object File Format(OFF)

5. Object File Format(OFF)

6. Polygon File Format Stanford Triangle Format
Store 3-d data from 3D scanners
Properties can be stored including
color and transparency
surface normals
texture coordinates
data confidence values

7. Stanford 3D Scanning Repository (url)
Cyberware 3D Scanners (url)
Large models also avaiable at GeogiaTech

8. Polygon File Format PLY structure Header Vertex List Face List
(lists of other elements)

9. Polygon File Format

10. The Winged-Edge Data Structure
Commonly used to describe polygon models
Quick traversal between faces, edges, vertices
Linked structure of the network
Assume there is no holes in each face

11. The Winged-Edge Data Structure
vertices of this edge
its left and right faces
the predecessor and successor when traversing its left face
the predecessor and successor when traversing its right face.

12. The Winged-Edge Data Structure
Vertices
Faces
Left Traverse
Right Traverse
Name
Start
End
Left
Right
Pred
Succ a X Y 1 2 d b c e
Edge Table

13. The Winged-Edge Data Structure
Vertices
Faces
Left Traverse
Right Traverse
Name
Start
End
Left
Right
Pred
Succ a A D 3 1 f e c b B 4 d 2 C

14. The Winged-Edge Data Structure
the vertex table and the face table
multiple choices of edges
Vertex Name
Incident Edge A a B b C d D c
Face Name
Incident Edge 1 a 2 c 3 4 b

15. The Winged-Edge Data Structure
For a face with inner loops are ordered clockwise.
Adding an auxiliary edge between each inner loop and the outer loop

16. The Half-Edge Data Structure
Doubly connected edge list

17. Euler-Poincare Formula (url)
V: the number of vertices
E: the number of edges
F: the number of faces
G: the number of holes that penetrate the solid, usually referred to as genus in topology
S: the number of shells. A shell is an internal void of a solid. A shell is bounded by a 2-manifold surface, which can have its own genus value. Note that the solid itself is counted as a shell. Therefore, the value for S is at least 1.
L: the number of loops, all outer and inner loops of faces are counted.
Then, the Euler-Poincaré formula is the following:
V - E + F - (L - F) - 2(S - G) = 0