One of the best ways to understand OpenGL's hardware tessellation is to visualize the tessellation of a 2D quad. When linear interpolation is used, the triangles that are produced are directly related to the tessellation coordinates (u,v) that are produced by the tessellation primitive generator. It can be extremely helpful to draw a few quads with different inner and outer tessellation levels, and study the triangles produced. We will do exactly that in this recipe.
When using quad tessellation, the tessellation primitive generator subdivides (u,v) parameter space into a number of subdivisions based on six parameters. These are the inner tessellation levels for u and v (inner level 0 and inner level 1), and the outer tessellation levels for u and v along both edges (outer levels 0 to 3). These determine the number of subdivisions along the edges of parameter space and internally. Let's look at each of these individually: