Another Basis

Choosing another basis for the similarity transformation, for example and , leads to an entirely different computation, but the final results will be the same.

Again Table 1 is our starting point. Now the other control points are the points , , and . We transform the local coordinates of these control points and the free points (, , , and ) with respect to this basis. The results are in a vector def3031. Table 3 shows the results.

Table 3. The transformed coordinates with respect to pt30 and pt31.

We redo the computation for this case.

Here are the final coordinates of pt20, pt21, pt25, and pt32 with respect to the basis pt30 and pt31.