C2 interpolation T-splines

Abstract In this work, we construct a class of C 2 interpolation T-spline (called IT-spline) basis functions over regular T-meshes. A new rule for determining the local knot vectors of the IT-spline basis functions is designed. The resulting IT-spline basis functions are always linearly independent for regular T-meshes. In order to guarantee the partition of unity and compact support properties of the IT-spline basis functions, several modified schemes are developed. An iteration adjustment algorithm for adjusting the points on IT-spline surface to the targeted points is proposed. Some applications of the new IT-spline basis functions in fitting bivariate functions and open 3D meshes, solving numerical PDEs and IGA are given.