Geometric Degree Reduction of Wang-Ball Curves

There are substantial methods of degree reduction in the literature. Existing methods share some common limitations, such as lack of geometric continuity, complex computations, and one-degree reduction at a time. In this paper, an approximate geometric multidegree reduction algorithm of Wang-Ball curves is proposed. G0-, G1-, and G2-continuity conditions are applied in the degree reduction process to preserve the boundary control points. The general equation for high-order (G2 and above) multidegree reduction algorithms is nonlinear, and the solutions of these nonlinear systems are quite expensive. In this paper, C1-continuity conditions are imposed besides the G2-continuity conditions. While some existing methods only achieve the multidegree reduction by repeating the one-degree reduction method recursively, our proposed method achieves multidegree reduction at once. The distance between the original curve and the degree-reduced curve is measured with the L2-norm. Numerical example and figures are presented to state the adequacy of the algorithm. The proposed method not only outperforms the existing method of degree reduction of Wang-Ball curves but also guarantees geometric continuity conditions at the boundary points, which is very important in CAD and geometric modeling.