NURBS Fairing by Knot Vector Optimization

The shape of a NURBS curve or patch is defined by the location of its control points, the weights associated with these points, and the parameter intervals, also called the knot vector. Most of the curve and patch design methods assume that the knot vector is constant and the user is allowed to modify only the control points and the weights. The possibility of controlling the shape through the change of the knot vector has shown up recently, but it turned out that this approach is less intuitive than either the control vertex or the weight modification. This paper attacks this problem by setting these knot values automatically, taking into account some goodness measures of the shape. In order to find the global optimum, simulated annealing is selected as the basic mechanism of the optimization. The paper reviews the basics of NURBS and simulated annealing, discusses our approach of setting the knot vector and concludes with the experience gained with this algorithm.