We now turn to a discussion of the triangle mesh, the most widely used representation of shape in graphics. Triangle meshes consist of many triangles joined along their edges to form a surface (see Figure 8.1). Other meshes, in which the basic elements are quads (quadrilaterals), or other polygons are sometimes used, but there can be problems associated with them. For instance, it’s easy to create a quadrilateral whose four vertices do not all lie in a plane; how should the interior be filled in? For triangles, this is not a problem: There’s always a plane containing any three vertices. Because triangle meshes are so widespread, we concentrate on them in this chapter.