基于三次B样条逆向细分的自由曲线的多分辨率表示

目前国内外关于逆向细分的研究主要集中于曲面逆向细分,对大量的特定曲线细分法的逆向细分算法研究较少,对于基于逆向细分的曲线的多分辨率构造及简化也鲜有研究.针对三次B样条细分法具有几何意义明显、规则简单等特征.本文从几何角度出发,推导并给出了基于三次B样条细分的逆向细分规则,在此基础上提出了自由曲线的一种新的多分辨率表示方法,通过在对自由曲线进行逆向细分时保留细节信息,最终可以实现自由曲线的多分辨率表示,并可应用于自由曲线的简化与精确重构中.文中给出了曲线的多分辨率表示、简化和重构的例子.该方法几何意义明显,易于编程实现.实验表明应用该逆向细分法得到的简化曲线能够更明显地反映原曲线的变化趋势.本文方法在构造分解矩阵和重构矩阵方面较以往的某些方法简单,并且在分解和重构曲线时的计算量相较于以往的方法较少.

Multiresolution representation of freedom curves based on reverse B-spline of degree three subdivision scheme

The study of reverse subdivision mainly concentrates on the surfaces, and the study of reverse sub- division 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 represen- tation 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.