Dynamic Tessellation - Practical Rendering and Computation with Direct3D 11 - page 460

Figure 9.45. Splitting a shared vertex.
The original research paper for this algorithm makes a startling claim (with support-
ing proof) that simply splitting a vertex will often generate cracks in the surface of the
object. Chapter 4 introduced the concept of tessellated surfaces being watertight, and this
property of Curved Point Normal Triangles can shatter that!
Since the article proves that with only local information available, this problem can-
not be avoided purely by using the GPU (remember, a key part of this algorithm was
accepting unmodified triangle data without adjacency), a software pre-processing step be-
comes necessary.
Given that we're interested in edges, there are two possible variations—either one, or
both, of the endpoints has differing normals. The software algorithm in use needs to exam-
ine all the vertex data in a given mesh and identify vertices where position information is
the same, but normal vectors are not. Once these are identified, the simplest approach is to
split the offending vertex in two by moving one endpoint very slightly away from the other.
Figure 9.45 shows a simple case of this.
Figure 9.46. Splitting corner geometry.