Mesh data structure & file format GI127 陳勁宇

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

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

Object File Format(OFF)

Object File Format(OFF)

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

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 models Quick traversal between faces, edges, vertices Linked structure of the network Assume there is no holes in each face

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.

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

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

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

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