A new variant of Lane–Riesenfeld algorithm with two tension parameters

Abstract

We present a generalization of Lane–Riesenfeld algorithm with two tension parameters for curve design. The generalization incorporates existing families as special cases: Hormann–Sabin's family, Romani's family, J-spline family, and Siddiqi's improved binary four-point family. The new family also has common members with dual de Rham-type approximating schemes when n is even. Analysis of the new family indicates that there are parameter choices that provide higher continuity and higher generation degree than available with any of those existing families.