Whether you model using polygons, nurbs, voxels or some other method, the goal of creating 3D models is to define the surface shape of an object displayed in 3D space.
General modeling guides suggests that you should model in all quads. Generally speaking it is much easier to maintain equidistant topology (the distance between edges and vertices in your model) if you use quads. Animation concerns should be at the forefront of the chosen modeling technique. Due to deformation, it is not desirable to have any triangles in a model (if it will be deformed when animated). At some point you will have to include a triangle (or 2) in order to make the model work. The key will be hiding the location of the triangles so that it does not impact aspects further down the line in the production process. It should be noted that a render engine reduces polygons to their simplest forms (triangles). To get the most out of your models, this fact should come into play at some point, most often when baking model information from a high poly to a low poly model. That process is covered in a later section.
See Articulation for a reference to good topology. You may also check out William Vaughn's Pushing Points Topology Workbook or Topology in this reference.
Example of face topology for Pixar Animation Studios' feature film The Incredibles. Notice the split additional polygons in the cheaks and the polygon direction flow change around the lips.
Subdividing is the process of taking one polygon and dividing it into four (1 subdivision level) or more. Subdivisions are used to smooth a mesh. Subdividing is useful for adding detail or areas that you can more easily add detail too. Below is an explanation of the Catmull-Clark subdivision process (Turbosmooth and Mesh Smooth in 3DS Max and Maya respectively).
The hierarchy of importance is a color coding system that helps a modeler establish the relative visual importance of various features on a mesh to the player. The high the level of importance, the lower on the pyramid it appears. Generally, important elements take up more space overall on the mesh than less important elements.
