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Subdivision is selected as Catmull-Clark by default. However, the Blender development team still includes the Simple subdivision in Blender 2.72. Does it serve a purpose? Why should I use the Simple subdivision instead of the Catmull-Clark subdivision?

Here is a picture of the Subsurface panel. You can clearly see the options Catmull-Clark and Simple.

Subsurf panel

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    $\begingroup$ Simple subsurf just subdivides all faces without moving any geometry. Catmull-Clark subdivides the mesh and moves the geometry around to smooth the look. Specifically I believe each vertex gets moved to the average position of itself and its neighbors with its own position being weighted twice. Simple is usually used just to add more geometry for another modifier like displace to use. $\endgroup$
    – PGmath
    Commented Nov 23, 2014 at 15:33

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One can use the simple Subsurf Subdivision Modifier when additional geometry is required without the deformation that occurs when Catmull-Clark algorithm is used. Simple subsurf can create the geometry for a Displacment Modifier . See this image its underlying geometry is a default torus. But has two subsurf modifiers and a displacement modifier.

enter image description here

Without the 2nd simple subsurf it would look like:

enter image description here

This technique is call UV-sculpting and a tutorial was posted at this BA thread.

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As an example of a case where simple is might be preferred over Catmull-Clark, say you have a large plane which you want to subdivide non-destructively for use with the displace modifier.

When subdivided with Catmull-Clark, it becomes nearly a circle:

enter image description here

But with Simple it maintains the original square shape:

enter image description here

This is just one example. There are probably many such use-cases where Catmull-Clark subdivision doesn't provide the desired result without extra things like edge-creases.

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About Simple Subdivision from the wiki:

Only subdivides the surfaces, without any smoothing (similar to W → Subdivide, in Edit mode). Can be used, for example, to increase base mesh resolution when using displacement maps or textured emitters with indirect lighting.

I think it's a suitable example. It's just an option to programmatically subdivide your object's geometry. It can be used to add more detail to your geometry very quick without e.g. manually placing new edge loops. The main advantage is that the modifier have no effect on the appearance of the object itself (non-destructive) unlike the catmull-clark algorithm.

For illustration purposes here is a simple test environment. I've selected the real edges of the geometry to better see the difference between both modifiers.

enter image description here Example geometry without Subsurf

enter image description here Example geometry with Simple Subsurf

enter image description here Example geometry with Catmull Subsurf

Note: There is a interesting wikipedia article about the Catmull algorithm.

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