Geometric Theory

A definiton of geometric theory is the study of geometric objects. Modelling with the geometric theory includes the basic object used in mesh modelling which is a vertex, a point in three demensional space.

Vertices is the plural of ‘vertex‘ which is the meeting point(corners) of at least two straight lines. A triangle for example has three vertices. In geometric theory it is possible for two vertices to have two distinct edges connecting them. Also it is possible for two vertices to exist at the same spatial coordinates, or two faces to exist at the same location. A group of polygons which are connected by shared vertices is referred to as a mesh.

In order for a mesh to appear attractive when rendered, it is required that it be non-self-intersecting, meaning that no edge passes through a polygon. Another way of looking at this is that the mesh cannot pierce itself. It is also best that the mesh not contain any errors such as doubled vertices, edges, or faces. For some purposes it is important that the mesh be a manifold – that is, that it does not contain holes or singularities (locations where two distinct sections of the mesh are connected by a single vertex).

This is a self-intersecting polygon. This is what you want to avoid when creating models in 3Ds Max.

More complex polygons can be created out of multiple triangles, or as a single object with more than 3 vertices. Four sided polygons (May also be referred to as quads) and triangles are the most common shapes used in polygonal modeling. A group of polygons, connected to each other by shared vertices, is generally referred to as an element. Each of the polygons making up an element is called a face.