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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?

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  • $\begingroup$ 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! $\endgroup$ – Alan Wolfe Aug 5 '15 at 3:21
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    $\begingroup$ 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. $\endgroup$ – Rahul Aug 5 '15 at 7:09
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    $\begingroup$ "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. $\endgroup$ – Rahul Aug 5 '15 at 7:12
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    $\begingroup$ 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. 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. graphics.pixar.com/opensubdiv/docs/… $\endgroup$ – Simon F Aug 10 '15 at 8:12
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    $\begingroup$ I've raised this on meta to see what people think. $\endgroup$ – trichoplax Aug 16 '15 at 12:06
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More of an extended comment than an answer:

What do you mean by "optimization and accuracy"? Do you mean computational efficiency for some particular application, like ray tracing, physical simulation, CAD modeling, ....?

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.

Catmull-Clark (and Loop, for triangle meshes) remains popular because of its simplicity, which in many cases outweigh its weaknesses (no handling of sharp features; loss of regularity at extraordinary vertices). Countless alternative schemes (which may or may not be improvements over Catmull-Clark, depending on the specific application) have been proposed -- if you have a specific application in mind, with specific requirements, we may be better able to help you navigate your options.

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    $\begingroup$ 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. $\endgroup$ – tom Sep 17 '15 at 21:21

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