Facts which will be Relevant to Other Analyses

3 Facts which will be Relevant to Other Analyses 

Once we know how much of the curve is influenced by each original control point, we can determine how many control points influence a given part of the limit curve. This is a key parameter to some of our other analyses. 

Call the parameter value at which the zero and non-zero parts of the basis function meet an end-point. 

We have to consider two cases such a point may be either at the ends of two different control points supports, which will be the case if the support width is integral, or at the end of only one, which will be the case if the support width is fractional. 

Consider first the case of integer support width. If the support width is even, the end-point will have an integer label and correspond to an original control point. If the support width is odd, the end-point will have a halfinteger label and correspond to a midedge of the original polygon. 

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