Direct Degree Elevation of Nurbs Curves

In this paper we provide the guidelines for the direct degree elevation of NURBS curves. Through the analysis of linear equation systems of quartic and lower degree splines we derive a direct relation between the knot vector of a spline and the degree elevation coefficients. We also present a direct degree elevation scheme and several algorithms based on the discovered relation. Experimental results indicate that the direct degree elevation algorithms are up to twice more time-efficient than Piegl and Tiller’s degree elevation method. This proves the inefficiency of Bspline calculation schemes based on blossoming that involve redundant operations with control points. It also negates Piegl and Tiller’s claim about the inefficiency of linear equation system solving method for quartic and lower degrees.