# Adaptive subdivision: a weakness of the subdivision surface implementation in Section 3.8 is that…

Adaptive subdivision: a weakness of the subdivision surface implementation in Section 3.8 is that each face is always refined a fixed number of times: this may mean that some faces are underrefined, leading to visible faceting in the triangle mesh, and some faces are overrefined, leading to excessive memory use and rendering time. With adaptive subdivision, individual faces are no longer subdivided once a particular error threshold has been reached. An easy error threshold to implement computes the face normals of each face and its directly adjacent faces. If they are sufficiently close to

Adaptive subdivision: a weakness of the subdivision surface implementation in Section 3.8 is that each face is always refined a fixed number of times: this may mean that some faces are underrefined, leading to visible faceting in the triangle mesh, and some faces are overrefined, leading to excessive memory use and rendering time. With adaptive subdivision, individual faces are no longer subdivided once a particular error threshold has been reached. An easy error threshold to implement computes the face normals of each face and its directly adjacent faces. If they are sufficiently close to each other (e.g., as tested via dot products), then the limit surface for that face will be reasonably flat and further refinement will likely make little difference to the final surface. Alternatively, you might want to approximate the area that a subdivided face covers on the image plane and continue subdividing until this area becomes sufficiently small. This approximation could be done using ray differentialssee Section 10.1.1 for an explanation of how to relate the ray differential to the screen space footprint. The trickiest part of this exercise is that some faces that dont need subdivision due to the flatness test will still need to be subdivided in order to provide vertices so that neighboring faces that do need to subdivide can get their vertex one-rings. In particular, adjacent faces can differ by no more than one level of subdivision. You may find it useful to read recent papers by Patney et al. (2009) and Fisher et al. (2009) for discussion of how to avoid cracks in adaptively subdivided meshes.

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