Isogeometric Analysis Based on a Set of Truncated Interpolatory Basis Functions

Abstract

This paper presents some results on isogeometric analysis (IGA) using a new class of basis functions, named truncated interpolatory basis function (TIBF). While much work in IGA has been done based on approximating basis functions, such as B-splines, NURBS and T-splines, little work is reported so far using interpolatory schemes. In this article, a truncated interpolatory basis function is proposed for isogeometric analysis. The basis function has many nice properties which are desirable for both modeling and isogeometric analysis. It has also the potential to be used as an alternative basis for interpolatory subdivision schemes whose basis functions are often not explicitly available. Based on TIBF, a cut-off rule is also proposed for handling shapes with boundaries. The proposed interpolatory scheme based on TIBF exhibits modeling qualities that are pretty close to the Kobbelt subdivision scheme for a regular control mesh. Several examples on IGA based on TIBF are also presented in this article. Both the modeling and simulation examples show that TIBF provides a good alternative option for isogeometric analysis.