Standard and Non-standard CAGD Tools for Isogeometric Analysis: A Tutorial

We present a detailed summary of the main CAGD tools of interest in IgA: Bernstein polynomials and B-splines. Besides their well-known algebraic and geometric properties, we give a deeper insight into 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 polynomial spaces. Extensions to the bivariate setting beyond the straightforward tensor-product case are discussed as well. In particular, we focus on the triangular setting.

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