An adaptive configuration method of knots and data parameters for NURBS curve interpolation

Abstract

The shape of an interpolated NURBS curve depends on the configuration of knot vectors, and the parameterization of data points and the weights. Based on the geometric features reflected by the data points, we present a method for computing the corresponding tangents of discrete data points using piecewise quadratic Bezier curve interpolation. Then, a new method is proposed to guarantee strict NURBS curve interpolation and approximation tangent vectors constraint via combining the optimization principle of genetic algorithm, freeing the data point parameters and knots of NURBS curve, and considering the tangent vector and other conditions. Compared to traditional methods, this method makes full use of degree of freedom of the NURBS curve such that the resulting interpolation curve is more natural and a desired shape can be better achieved. It is effective for interpolating NURBS curves with any degree and its feasibility is validated to a certain degree.