基于三次B 样条逆向细分的自由曲线的多分辨率表示

Abstract

The study of reverse subdivision mainly concentrates on the surfaces, and the study of reverse subdivision for the particular curve subdivision is relatively rare. Studies about the multiresolution representation and simplification of freedom curves based on reverse subdivision are also rare. According to the facts that the geometric meaning and the rules of B-spline of degree three are obvious and simple, we present the reverse B-spline of degree three subdivision rules, and on the basis of that we introduce a new method of multiresolution representation of freedom curves. By establishing the error vectors when decomposing the freedom curves and combining the B-spline of degree three subdivision rules, we can achieve decomposition and exact reconstruction of freedom curves. We offer examples of multiresolution representation, decomposition and reconstruction of freedom curves using our method. The presented method is easy to be programmed, and more obvious in geometrical meaning than some existing methods. The experiments suggest that the decomposed curves which are generated by our reverse rules can match the shape of the primary curves. The structure of decomposition and reconstruction filters is very brief, and the amount of computations of decomposition and reconstruction of the curves using our method is less than that using some previous methods.