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i'm currently working a lot with tessellation and have one specific question about the spacing parameter:

I know that fractional spacing leads to much smoother transitions between different tessellation values than equal spacing. But why are there two different types of fractional spacing (odd and even)? Is one type not enough?

Many thanks

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Each kind of fractional tessellation is a different compromise:

Odd spacing lets you use a factor of 1 (meaning no tessellation) and smoothly transition from the base mesh.

Even spacing requires you to use a factor of at least 2 (each edge is split at least once). However, the new vertex stays in the same position as two new vertices are introduced. This can greatly reduce "crawling" artifacts caused by vertices sliding across the surface, particularly for highly curved surfaces.

There are some useful images that illustrate this on the OpenGL wiki page for Tesselation.