Polygonal Meshes 3D Object Representation -Tyler Abrams

What are Polygonal Meshes?  A 3D object is a set of surface polygons that enclose an objects interior.  Polygon Mesh – collection of edges, vertices, and polygons where each edge is connected to form the “skin” of the object.  A closed object: when all polygonal faces fit together to form a closed space.

Meshes and Polygons  Meshes are a list of polygons with information about their respective facial direction.  This directional information is provided by describing the “normal” vector to a given polygon’s face.

Properties of Meshes  Solidity: if an object’s faces enclose a finite and positive amount of face  Connectedness: an unbroken path between two vertices of a polygon edge must exist  Simplicity: a mesh is simple if it represents a solid object and contains no holes  Planarity: all faces of the mesh must remain a planar polygon. In other words, the vertices of each face must lie in the same plane

Mesh Features  A mesh should include these following functions: Ability to choose individual polygons Ability to determine all edges of an individual polygon Determine any polygons that share edges Retrieval of vertices from any given polygon Ability to change the mesh Ability to display the mesh

Mesh Representations  Two different basic types of mesh representation: Explicit Polygons Mesh Explicit Edges Mesh

Explicit Polygons Mesh  Each vertex is stored (once) as a number triple in a table  Polygons are composed of by multiple sequences of these vertices

Visualization of Explicit Polygons Mesh

Explicit Polygons Mesh (2)  Advantages: Takes up little amount of storage Modifying the mesh is simple Deleting and adding of polygons is easy  Disadvantages Finding shared edges Finding shared vertices All shared edges drawn twice

Explicit Edges Mesh  An alternative to the explicit polygons mesh  Rids most of the problems of polygons mesh

Explicit Edges Mesh (2)  Consists of the following Table of all vertices Linked list record of all edges  Edge – two vertices that connect  Pair of pointers consist of an edge  Also contains pointers to a “polygon list”  A counter Polygon List  Pointers into the edge list  Traversal Mesh is traversed by edge list

Explicit Edges Mesh (3)  Advantages: Shared edges are specified All edges of a specific polygon can be determined No side effects when manipulating vertices  Disadvantages Addition and deletion of vertices is more complicated Does not contain information about vertices that are designated to edges

In Conclusion  A need for more efficient structures  More well designed structures exist today