Standard and non-standard CAGD tools for isogeometric analysis: a tutorial

We present a short summary of CAGD tools of main interest in isogeometric analysis, namely Bernstein polynomials and B-splines. Besides their well-known algebraic and geometric properties, we provide a deeper insight why these representations are so popular and efficient by proving that they are optimal bases for the corresponding function spaces. Moreover, we review some generalizations of the B-spline structure in function spaces which extend classical polynomials. Extensions to the bivariate case beyond the straightforward tensor-product case are also presented.