Degree Reduction of Interval B-Spline Curves

An algorithmic approach to degree reduction of interval B-spline curve is presented in this paper. The curves that are useful in geometric modeling should have a relatively smooth shape and should be intuitively connected with the path of the sequence of control points. One family of curves satisfying this requirement is represented by the B-spline curves. The four fixed Kharitonov's polynomials (four fixed Bspline curves) associated with the original interval B-spline curve are obtained. The control points of the four fixed Kharitonov's polynomials (four fixed B-spline curves) with lower degree are obtained by solving a set of linear equations. Finally, the interval control points of the required reduced interval B-spline curve are obtained from the fixed control points of the four reduced fixed Kharitonov's polynomials (four fixed reduced B-spline curves). An illustrative example is included in order to demonstrate the effectiveness of the proposed method.