Degree Reduction of Interval SB Curves

Ball basis was introduced for cubic polynomials by Ball, and was generalized for polynomials of higher degree by Said. An algorithmic approach to degree reduction of interval Said-Ball (SB) curve is presented in this paper. The four fixed Kharitonov's polynomials (four fixed SB curves) associated with the original interval SB curve are obtained. These four fixed SB 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 SB curves of the same degree. Finally the reduced interval SB control points are obtained from the four fixed reduced SB 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 Said-Ball (SB) curve, interval Bezier curve.