在计算几何领域中,对于拟合、插值、重构,Box样条函数已显示出其重要的应用优势,是一类应用广泛的插值函数.但是在拟合算法中,大量的工作量是计算Box样条基函数,因此,减少Box样条函数的计算量,可以提高Box样条的拟合速度.研究目的在于构造出具体的Box样条函数的分段多项式形式,提高拟合算法的计算效率.首先,应用积分方法以及Box样条的对称性和轮换性分析Box的显示表达式.然后,通过对七方向Box样条在三维空间中进行Ⅲ-型剖分,在剖分上构造出三维空间中分段多项式形式的Box样条的支撑函数,并且给出了具体的推导过程.最后实现了分段多项式形式的Box样条函数.另外,由此支撑函数构造了拟插值算子和重构算法.通过此算法的数值实验,在拟合算法效率上得到了预期的结果.%In the field of computation geometry,for fitting,approximation,reconstruction,Box spline has showed its important application advantages and it is a kind of widely used interpolation function.But in the fitting algorithm,a large amount of workload is to calculate the Box spline.Therefore,the method of improving the fitting speed of Box spline is to reduce the calculation of it.The purpose of the research is to construct the polynomial form of the Box spline function,and improve the efficiency of the algorithm.By 3-partition in the three-dimensional space,the integration method and the symmetry and rotation of Box spline are used firstly to analyze its explicit form.And then the Box spline in polynomial form is constructed in the type-3 partition.Finally,the piecewise polynomial form of Box spline function is realized.Besides,the specific procedure is given.In addition,by using the support function,quasi-interpolation operators and reconstruction algorithm are constructed.Through the numerical experiments,the expected results are obtained in the efficiency of titting algorithm.
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