How to compare B Spline Surfaces?

Question

We can define b spline surfaces over a set of points. However, is it possible to compare two set of b-spline surfaces fitted over different set of points ? The objective is to identify if the curves are similar.

Answer 1

A B-spline surface is defined by

1) degree in u and v direction,
2) knot sequence in u and v direction,
3) m x n (weighted) control points.

So, to compare two B-spline surfaces, you can check if these data are the same in the order they are listed above (i.e., degree, then knot sequence, then control points). If any of of them is different, then you can say the two B-spline surfaces are different.

Please note that two B-spline surfaces could be geometrically identical but have different data for degree, knot sequence and/or control points. For example, given any B-spline surface, we can always perform degree elevation to generate another B-spline surface that has higher degree and more control points. But these two surfaces are in fact geometrically identical. The "data-wise" comparison method mentioned above is certainly not suitable for such special cases.