Multiple Degree Reduction of Interval DP Curves

O. Ismail, Senior Member, IEEE Abstract— Fixed DP curve is a recent representation of the polynomial curves, proposed by Delgado and Pena in 2003. They introduced a new curve representation with linear computational complexity. An algorithmic approach to degree reduction of interval DP curve is presented in this paper. The four fixed Kharitonov's polynomials (four fixed DP curves) associated with the original interval DP curve are obtained. These four fixed DP 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 reduction 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 DP curves of the same degree. Finally the reduced interval DP control points are obtained from the four fixed reduced DP control points. An illustrative example is included in order to demonstrate the effectiveness of the proposed method.