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 the parameter space and internally. Let's look at each of these individually:

• Outer level 0 (OL0): This is the number of subdivisions along the v direction where u = 0
• Outer level 1 (OL1): This is the number of subdivisions along the u direction where v = 0
• Outer level 2 (OL2): This is the number of subdivisions along the v direction where u = 1
• Outer level 3 (OL3): This is the number of subdivisions along the u direction where v = 1
• Inner level 0 (IL0): This is the number of subdivisions along the u direction for all internal values of v
• Inner level 1 (IL1): This is the number of subdivisions along the v direction for all internal values of u

The following diagram represents the relationship between the tessellation levels and the areas of parameter space that are affected by each. The outer levels define the number of subdivisions along the edges, and the inner levels define the number of subdivisions internally:

The six tessellation levels described some time back can be configured via the gl_TessLevelOuter and gl_TessLevelInner arrays. For example, gl_TessLevelInner[0] corresponds to IL0, gl_TessLevelOuter[2] corresponds to OL2, and so on.

If we draw a patch primitive that consists of a single quad (four vertices), and use linear interpolation, the triangles that result can help us to understand how OpenGL does quad tessellation. The following diagram shows the results for various tessellation levels:

When we use linear interpolation, the triangles that are produced represent a visual representation of parameter (u, v) space. The x axis corresponds to the u coordinate and the y axis corresponds to the v coordinate. The vertices of the triangles are the (u,v) coordinates generated by the tessellation primitive generator. The number of subdivisions can be clearly seen in the mesh of triangles. For example, when the outer levels are set to 2 and the inner levels are set to 8, you can see that the outer edges have two subdivisions, but within the quad, u and v are subdivided into eight intervals.

Before jumping into the code, let's discuss linear interpolation. If the four corners of the quad are as shown in the following figure, then any point within the quad can be determined by linearly interpolating the four corners with respect to the u and v parameters:

We'll let the tessellation-primitive generator create a set of vertices with appropriate parametric coordinates, and we'll determine the corresponding positions by interpolating the corners of the quad using the preceding equation.