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A common way to approach a subdivision surface is to imagine a polygon mesh (the control mesh) which undergoes a local averaging (or smoothing) at every vertex, creating a new set of vertices which have a smoother appearance than the original mesh. One application of this averaging operator everywhere on a mesh is a single subdivision step. If we could take an infinite number of subdivision steps, eventually we will converge to a limit surface, which has a set of guaranteed smoothness properties depending on the type of subdivision being used.
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Like most other types of geometry, a subdivision mesh is described by its control mesh. Unlike NURBS, the control mesh is not confined to be rectangular, so in this respect, the control mesh is very similar to polygonal surface. But where polygonal surfaces require large numbers of points to appear smooth, a subdivision mesh's limit surface is guaranteed to be smooth - meaning that polygonal artifacts or faceting are never present, no matter how the surface animates, or how closely it is viewed.
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- Catmull-Clark subdivision surfaces are the industry standard. It is a quadrilateral based subdivision scheme, and work best with control meshes that is comprised mostly of quads - any non-quad geometry is immediately converted to quadrilaterals on the very first subdivision step. They generally good for most situations and have no special concerns when it comes to texture filtering.
- Loop subdivision surfaces (Not Supported in XPU) is a triangle based scheme, which is optimized for control meshes that are entirely triangles: they tend to require less memory than Catmull-Clark scheme. However, due to the nature of triangles, derivatives can be discontinuous from face to face, which may lead to texturing artifacts that require extra effort to solve.
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