Mesh data structure & file format

GI127 陳勁宇

Content

Object File Format(OFF)Polygon File Format(PLY)The Winged-Edge Data StructureThe Half-Edge Data Structure

Object File Format(OFF)

Storing a description a 2D or 3D objectSimple 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

Object File Format(OFF)

Object File Format(OFF)

Polygon File Format

Stanford Triangle FormatStore 3-d data from 3D scannersProperties can be stored including color and transparency surface normals texture coordinates data confidence values

Stanford 3D Scanning Repository (url)

Cyberware 3D Scanners (url)

Large models also avaiable at GeogiaTech

Polygon File Format

PLY structure Header Vertex List Face List (lists of other elements)

Polygon File Format

The Winged-Edge Data Structure

Commonly used to describe polygon modelsQuick traversal between faces, edges, verticesLinked structure of the network

Assume there is no holes in each face

The Winged-Edge Data Structure

vertices of this edgeits left and right facesthe predecessor and successor when traversing its left facethe predecessor and successor when traversing its right face.

The Winged-Edge Data Structure

Edge Vertices Faces Left Traverse Right Traverse

Name Start End Left Right Pred Succ Pred Succ

a X Y 1 2 d b c e

Edge Table

The Winged-Edge Data Structure

Edge Vertices Faces Left Traverse Right

Traverse

Name Start End Left Right Pred Succ Pred Succ

a A D 3 1 f e c b

b A B 1 4 a c d f

c B D 1 2 b a e d

d B C 2 4 c e f b

e C D 2 3 d c a f

f A C 4 3 b d e a

The Winged-Edge Data Structure

Vertex Name Incident Edge

A a

B b

C d

D c

the vertex table and the face tablemultiple choices of edges

Face Name Incident Edge

1 a

2 c

3 a

4 b

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

The Half-Edge Data Structure

Doubly connected edge list

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