Degree Reduction of Interval WB Curves

Wang-Ball (WB) curve is one of the generalized cubic Ball basis which was first put forward in CONSURF system by Ball. Wang extended it to arbitrary odd and even degrees. An algorithmic approach to degree reduction of interval Wang-Ball curve is presented in this paper. The four fixed Kharitonov's polynomials (four fixed WB curves) associated with the original interval WB curve are obtained. These four fixed WB curves are transformed into four fixed Bezier curves. The degree of the four fixed Bezier curves is reduced based on the matrix representations of the degree reduction process. The process of degree reductions times are applied to the four fixed Bezier curves of degree to obtain the four fixed Bezier curves of degree without changing their shapes. The four fixed reduced Bezier curves are converted into WB curves of the same degree. Finally the reduced interval WB control points are obtained from the four fixed reduced WB control points. An illustrative example is included in order to demonstrate the effectiveness of the proposed method. Index Term— Image processing, CAGD, degree reduction, interval Wang-Ball (WB) curve, interval Bezier curve.