Patches VS Faces

[樊林旭]

Hey：

This question may sounds naive but anyone got an idea of what's the difference between a patch and a face? In the tutorial 5.1, a pyramid is refined one level. The number of patch is 13 but the number of faces is 16.  Thanks.

Regards

Linxu

[David G Yu]

Hi,

Have you had a chance to read through the overview documentation at: Subdivision Surfaces

One way to think of the difference is that a face is a discrete topological entity while a patch is a parametric function. For a subdivision surface the base mesh is a collection of polygonal faces while the subdivision limit surface is computed from the collection of parametric patches determined by the base mesh.

The distinction is contextual, e.g. a simple triangle can be considered a face, but it can also be considered to be a triangle patch, e.g. if you are interpolating values across the triangle using barycentric weights.

For a Catmull-Clark subdivision surface we often talk about a polygonal base mesh (the control mesh) and a parametric limit surface where each base mesh face is associated with one or more bicubic bspline patches. Additionally, the parametric limit surface might be tessellated where the positions and derivatives are evaluated on the limit surface parametric patches at the corners of the tessellated triangle faces.

The pyramid mesh in far_tutorial_5_1 illustrates an additional consideration related to irregular faces. The pyramid has five base mesh faces (4 triangle sides and 1 quad base). After one level of uniform subdivision the resulting mesh has 16 quad patches, each triangle is split into 3 quads while the base quad is split into 4 quads (16=3*4+1*4). So where does the 13 come from? Each triangle face is considered an irregular face because CatmullClark is a quad based subdivision scheme. The 13 base faces are accounting for the quadrangulation of each irregular triangle face (13=3*4+1).

-David