Lecture 6 B-splines(Uniform and Non-uniform) 6.1 Introduction The formulation of uniform B-splines can be generalized to accomplish certain objectives These include Non-uniform parameterization Greater general flexibility Change of one polygon vertex in a Bezier curve or of one data point in a cardinal(or interpolatory) spline curve changes entire curve(global schemes) Remove necessity to increase degree of Bezier curves or construct composite Bezier curves using previous schemes in order to increase degrees of freedom Obtain a"local "approximation scheme The development extends the Bezier curve formulation to a piecewise polynomial curve with easy continuity controlLecture 6 B-splines (Uniform and Non-uniform) 6.1 Introduction The formulation of uniform B-splines can be generalized to accomplish certain objectives. These include • Non-uniform parameterization. • Greater general flexibility. • Change of one polygon vertex in a B´ezier curve or of one data point in a cardinal (or interpolatory) spline curve changes entire curve (global schemes). • Remove necessity to increase degree of B´ezier curves or construct composite B´ezier curves using previous schemes in order to increase degrees of freedom. • Obtain a “local” approximation scheme. The development extends the B´ezier curve formulation to a piecewise polynomial curve with easy continuity control. 2