Blossoming
A good labeling scheme can provide a lot of information about an algorithm, but till now we have avoided labeling the interior nodes in de Casteljau’s algorithm. Here we shall introduce a labeling scheme for these nodes suggested by a probabilistic interpretation of the de Casteljau diagram. This labeling scheme will lead us to the notion of blossoming, an extremely powerful technique for analyzing the properties of Bezier curves and surfaces. Blossoming is a particularly effective tool for deriving change of basis algorithms. In Section 6.3 and 6.5 we will see that formulas for degree elevation, subdivision, and conversion from monomial to Bezier form are easily derived from blossoming. We shall also apply blossoming in ...
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