Summary of Analysis Results

In the previous chapters we have seen how, given a mask, we can analyse various aspects of the behaviour of a subdivision scheme. We now address the much more interesting topic of how to invent a subdivision scheme which has some combination of desirable properties. 

We do this by looking at the space of all possible schemes, to see how the properties analysed above are distributed within it, and how, given a desirable property, what the subspace is containing all schemes with that property. 

Then all we have to do is to take the intersection of the required subspaces. This sounds easy, but, as usual in a design context, there are trade-offs to be made. Often the requirements are conflicting. However, the following approach allows it to be visible when this is the case. 

Finally we look at what can be achieved by changing the rules fundamentally, by considering non-stationary subdivision, in which the mask changes from step to step. In particular we consider geometry-sensitive schemes where the mask is itself determined locally and at every step from the geometry of the polygon. 

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