Degree reduction and multiple degree reduction for the DP curves

DP curve is a recent representation of the polynomial curves, proposed by Delgado and Pena in 2003. This curve has been claimed for its normalized totally positive (NTP) property and requires only the linear time computation. These properties indicate the shape preservation and the efficiency of evaluating the points on DP curves. Among several important properties of a non-rational curve, the degree reduction of a curve from n into n-1 degrees is very useful for many applications to decrease the complexity of the polynomials. The shape of the curve remains the same although the numbers of control points has been reduced. In this work, the degree reduction and the multiple degree reduction for DP curves has been proposed and well proven by the benefits of the Bezier degree reduction, multiple degree reduction and the relationships between Bezier and DP curves.