An Alternative Cardinal Spline for Cubic B-Spline Interpolation

This paper aims at introducing a special cubic cardinal spline from the GMK-splines, which is able to obtain almost the same interpolation results of the cubic B-spline, but without solving the system of equations for getting control vertices, and exploring its applications in geometric modeling and image processing. The spline involved can be obtained by using a linear combination of several shifted B-splines of the same degree. The spatial and frequency domain comparison demonstrates its superior local support and frequency domain performance. In addition, a number of examples are involved in geometric modeling and digital image processing, compared with a few conventional methods. As shown in this paper, the cubic cardinal spline is an alternative choice instead of the cubic B-spline in the interpolation procedure in order to avoid solving the system of equations over and over again.