<p>More of an extended comment than an answer:</p>

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

<p>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.</p>

<p>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 <em>specific</em> application in mind, with specific requirements, we may be better able to help you navigate your options.</p>

CC BY-SA 3.0
2015-09-17T21:21:30.903Z
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
CC BY-SA 3.0
2015-09-16T06:05:56.157Z
2015-09-16T06:05:56.157Z
Etienne
<p>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?</p>

CC BY-SA 3.0
2015-08-05T03:21:46.453Z
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
CC BY-SA 3.0
2015-08-09T21:22:15.260Z
These comments sound like the perfect material for someone to write a summarising answer.
trichoplax is on Codidact now
CC BY-SA 3.0
2015-08-10T01:04:58.047Z
@Rahul Would you mind turning your comments and any other information you might have into an answer?
J Sargent
CC BY-SA 3.0
2015-08-10T08:12:12.877Z
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
CC BY-SA 3.0
2015-08-16T11:58:54.183Z
Since [the wikipedia page](https://en.wikipedia.org/wiki/Subdivision_surface) 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 is on Codidact now
CC BY-SA 3.0
2015-08-16T12:06:31.653Z
I've [raised this on meta](http://meta.computergraphics.stackexchange.com/questions/82/is-this-question-too-broad) to see what people think.
trichoplax is on Codidact now
<subdivision>
What subdivision algorithm advances have occurred since Catmull-Clark?
J Sargent
# What subdivision algorithm advances have occurred since Catmull-Clark?

(Asked by: username_0 on 2015-08-04)

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?

**Tags:** subdivision

> **Comments:**
> **username_1**: 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!  
> **username_2**: These comments sound like the perfect material for someone to write a summarising answer.  
> **username_0**: @Rahul Would you mind turning your comments and any other information you might have into an answer?  
> **username_3**: 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  
> **username_2**: Since [the wikipedia page](https://en.wikipedia.org/wiki/Subdivision_surface) 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.  
> **username_2**: I've [raised this on meta](http://meta.computergraphics.stackexchange.com/questions/82/is-this-question-too-broad) to see what people think.  

---

## 1 answers

### Answer by username_4 on 2015-09-16. Score: 5 | Accepted answer

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.

> **Comments:**
> **username_5**: 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.  

---

