Neither ternary schemes

It is also possible for the mask of a ternary scheme to have an even number of entries. In this case exactly the same algorithm tells us that the range of an original control point can lie one quarter of the way between point images. The end of the influence of one control point is no longer at the same place as the start of the influence of another. 

This can be seen in the basis function of the ternary scheme [l,3,5,5,3,l]/6 with the control points after one step from cardinal data. 

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An example has these vertices defined by weight combinations [5/6, 1/6], [1/2,1/2] and [1/6, 5/6]. This is a paradoxical scheme whose limit curve has strange properties that we shall deduce as examples later in the book. We call it just the ternary neither scheme , as its main function is to illustrate that possibility. 

This is a fairly tough question. Because the ternary neither scheme does not have unit eigenrows for the vertices and mid-spans as it stands, we have to take its square, thus creating a both scheme. 

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