Dynamic Tessellation - Practical Rendering and Computation with Direct3D 11 - page 448

substantial code changes. It also didn't require different geometry to be created by artists.
This would have been prohibitively difficult, due to targeting multiple types of hardware,
and to not suiting the commonly used tools of the period.
The mathematics of the algorithm therefore only require a conventional triangle com-
prised of three positions and three normal vectors. Even with Direct3D 11, where adjacency
(up to 32 control points per primitive) is relatively easy to provide, this simple property can
be quite convenient. Most importantly, allows for an "upgrade" path of sorts—existing art
assets can be rendered via Direct3D 11 using this algorithm without any changes, while
developers still have the option to use more complex modeling formats and algorithms
when the resources support it.
Curved Point Normal Triangles also neatly map on to the Direct3D 11 tessellation
pipeline. The first stage is to take the incoming triangle and generate a more detailed con-
trol mesh —a hull shader program that amplifies. After sample locations are generated (by
the fixed-function tessellation unit) the mathematical surface is evaluated using the de-
tailed control mesh—a classic Direct3D 11 Domain Shader program.
Geometric Components
Tessellation of the geometry that actually makes up the final rasterized surface is done on
a cubic basis, requiring an additional seven control points.
Looking back at Figure 9.27 and Figure 9.28, it becomes clear that a quadratic function
cannot represent a full range of surface variations. However, a cubic function can capture
surface inflections, resulting in a more accurate and aesthetically pleasing representation.
Figure 9.36 shows the locations of the additional seven control points (green) as well
as the original three vertex positions (blue), as provided by the application. These seven
control points, two per side and one in the middle, are evenly distributed across the surface
of the triangle.
Figure 9.36. Additional control points.