CINPACT-splines: A Class of C∞ Curves with Compact Support

Recently, Runions and Samavati [7] proposed Partion of Unity Parametrics (PUPs), a generalization of NURBS which replaces B-spline basis functions with arbitrary Weight-Functions (WFs) while preserving affine invariance. A key problem identified by Runions and Samavati was the identification of classes of weight-functions which are well-suited to geometric modeling. In this paper, we propose a class of WF based on bump-functions, which arise in the study of smooth, non-analytic manifolds. These give rise to a class of C∞ curves with compact-support, which we call CINPACT splines. The WFs are similar in form to B-spline basis functions, and are parameterized by a degree-like shape parameter. We examine the approximating and interpolating curves created using the proposed class of WF. Furthermore, we propose and demonstrate a method to specify the tangents and higher order derivatives of the curve at control points for CINPACT and PUPs curves.