Catmull-Clark subdivision surfaces: holes and boundaries

Posted: 12 Jun 2011 10:37
Tags: catmull clark subdivision surface

As promised, this post describes the remaining features in Catmull-Clark subdivision surfaces: holes and boundaries. This is going to be a lot more straightforward than the previous posts


A hole is a face or a group of faces that will not generate geometry to be drawn. You could say, why bother and specify data that will not be seen? Remember that a face depends on its 1-neighbourhood. Therefore, when a subdivision iteration occurs, a face next to a hole is influenced by it even if it is not to be seen.

Putting it all together
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crease, hole and two corners


So far, so good but for faces abutting the boundary of an open mesh, their 1-neighbourhood is not complete and smooth subdivision rules as defined in this post do not apply. There are three possible interpolation strategies to handle this particular case:

  • no interpolation: boundary faces are treated like holes and will not be rendered
  • edge interpolation: boundary edges are tagged as infinitely sharp creases (which do not require a 1-neighbourhood for subdivision). All boundary vertices become implicitely crease vertices.
  • full interpolation: boundary edges are tagged as infinitely sharp creases and boundary vertices of valence 2 (in general, these correspond to geometric corners) are tagged as infinitely sharp corners. If you have abutting control meshes, you get abutting limit surfaces but they are only C0-continuous.

Let's have a quick example to illustrate all of these:

No interpolation
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Edge interpolation
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Full interpolation
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Not yet ready …

This ends the series of posts on Catmull-Clark but it does not mean I am ready for delivery. Although I have made good progress with the implementation, there are still rough edges to be ironed out, the biggest one being the lack of texturing support for this primitive.

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