Dynamic Tessellation - Practical Rendering and Computation with Direct3D 11 - page 445

Figure 9.26. Linear. Figure 9.27. Quadratic.

evaluating the usefulness of it in any tessellation context. This can be seen in Figures 9.26
through Figure 9.28.
In most cases, the mathematical functions employed for higher-order surfaces will be
quadratic (Figure 9.27) or cubic (Figure 9.28); Figure 9.26 is included for reference with
regards to planar triangle/line segments used in conventional rendering.
Individual quadratic or cubic sections are limited in the number of shapes they can
represent, such that any real-world application of higher-order surfaces will want to com-
pose many of these smaller curves into a larger model representing far more complex sur-
faces. How these segments are joined together has strongly impacts the overall appearance
of the surface and is described as geometric continuity. The following figures introduce
four levels of continuity.
Initially, G 2 continuity appears to be the most desirable. While aesthetically it does
result in "perfect" curves, some characteristics of the other continuity levels can be ben-
eficial. The primary motivation for non-G 2 continuity is that of sharp edges, which are
typically required for non-organic or otherwise artificial objects. For example, aspects of a

Figure 9.28. Cubic.