Smooth curve interpolation with generalized conics (Q1912859)

A local algorithm using piecewise generalized conic segments is proposed for shape preserving curve interpolation. It is proved that there exists a smooth piecewise generalized conic curve which not only interpolates the data points, but also preserves the convexity of the data. It is also shown that the approximation order is \(h^6\). An efficient algorithm for the simultaneous computation of points on the curve is derived so that the curve can be easily computed and displayed. The numerical complexity of the algorithm for computing \(N\) points on the curve is about \(2N\) multiplications and \(N\) additions. Some numerical examples are provided and comparisons with both quadratic and cubic spline interpolants are also given. A number of figures illustrates the results.