Cubic B-Spline Functions and Their Usage in Interpolation

摘要

Here we investigate the use of cubic B-splines in interpolating functions and data generated from real objects. First, we derive the cubic B-spline functions, then we use these functions for interpolation. We consider two types of boundary conditions, namely natural and clamped conditions. Examples with numerical results are presented for the natural and the clamped boundary conditions. Numerical results indicate that the clamped cubic B-splines give better interpolation than the natural cubic B-splines near the end points. Also, the cubic B-spline method creates unique cubic polynomials at each sub-interval, regardless of the value of the number of intervals.