## What subdivision algorithm advances have occurred since Catmull-Clark?

16

In 1978 Edwin Catmull and Jim Clark defined the recursive subdivision process that bears their names, and although those principles are applicable still today, what advances have occurred as far as optimization and accuracy?

These comments sound like the perfect material for someone to write a summarising answer. – trichoplax – 2015-08-09T21:22:15.260

@Rahul Would you mind turning your comments and any other information you might have into an answer? – veryRandomMe – 2015-08-10T01:04:58.047

Sorry, I'm at SIGGRAPH and have absolutely no free time (except to write this comment). Someone else should feel free to write an answer using the links in my comments. – Rahul – 2015-08-10T04:17:38.400

2

Apologies to @NoviceInDisguise for also not having time, but WRT to Catmull-Clark, perhaps one of the reasons for it still being very much in use was DeRose et al's extensions to it to include, e.g. sharpness factors in the tessellation to allow creases etc. http://www.cs.rutgers.edu/~decarlo/readings/derose98.pdf
IIRC those extensions weren't initially free to use (but some commercial tools licensed it from Pixar) however, unless I'm mistaken, it now seems to be free e.g. http://graphics.pixar.com/opensubdiv/docs/subdivision_surfaces.html#arbitrary-topology

– Simon F – 2015-08-10T08:12:12.877

Since the wikipedia page lists a number of different improvements over the intervening time (almost 4 decades), and branching into several different types (approximating/interpolating, quads/triangles), I suspect this question may be too broad to be a good fit for this site.

– trichoplax – 2015-08-16T11:58:54.183

1

I've raised this on meta to see what people think.

– trichoplax – 2015-08-16T12:06:31.653

At SIGGRAPH 2014, in advances in real-time rendering, there was talk of subdivision used in call of duty. I don't remember the specifics but there is probably some good info there for you! – Alan Wolfe – 2015-08-05T03:21:46.453

@trichoplax I'll keep an eye on it, thanks – veryRandomMe – 2015-08-16T21:29:33.483

4

This sounds like a question best answered by a survey paper on subdivision surfaces, and indeed, searching Google for "subdivison surfaces survey" brings up a number of relevant publications. For example, "Algorithms for direct evaluation [Sta98, ZK02], editing [BKZ01, BMBZ02, BMZB02, BLZ00], texturing [PB00], and conversion to other popular representations [Pet00] have been devised and hardware support for rendering of subdivision surfaces has been proposed [BAD+01, BKS00, PS96]" —Boier-Martin et al., 2005.

– Rahul – 2015-08-05T07:09:06.853

1

"We also examine the reason for the low adoption of new schemes with theoretical advantages, [and] explain why Catmull–Clark surfaces have become a de facto standard in geometric modelling" —Cashman, 2011.

– Rahul – 2015-08-05T07:12:13.487

Note that the idea of "accuracy" for a subdivision scheme is not well-posed. Different schemes will have different limit surfaces, but there is no canonical way of declaring one limit surface to be "more accurate" than any another. One can pose some constraints on the type of limit surface one desires, but these constraints are again very application-dependent: one person might ask for $G^n$ everywhere, the next will complain because this precludes preserving sharp creases.
What is $G^n$ ? Didn't you mean $C^n$ i.e. $n$-times continuously differentiable? Actually I would be interested if there is subdivision algorithm which gives higher smoothness than Catmul-Clark. Catmul-Clark gives you $C^1$ at extraordinary vertices and $C^2$ everywhere else. People making 3d models for living are actually quite concerned about minimizing number of those extraordinary vertices in their meshes. – tom – 2015-09-17T21:21:30.903