Determining Knots by Minimizing the Second Derivative

Abstract

In constructing a parametric curve interpolating a set of data points, one of the key problems is to specify a parameter value node for each data point. A new method of choosing knots is presented. For each data points, the new method constructs a quadratic polynomial curve by three adjacent data points. The node parameters of the quadratic curve are determined by minimizing the second derivative of the quadratic curve. And the knot interval between two adjacent data points is determined by two quadratic curves associated with the two adjacent data points. Experiments showed that the curves constructed using the knots by the new method generally have better interpolation precision.