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首页> 外文期刊>Journal of Computational and Applied Mathematics >Approximating uniform rational B-spline curves by polynomial B-spline curves
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Approximating uniform rational B-spline curves by polynomial B-spline curves

机译：用多项式B样条曲线逼近一致的有理B样条曲线

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摘要

Approximation of rational B-spline curves by B-spline curves is an important issue in computer aided geometric design. This paper presents a method to approximate a uniform rational B-spline with B-spline curve sequence as follows. We first elevate the degree of the original rational B-spline curve and take the control points of the degree-elevated curve as new control points of the B-spline approximation curve. Next we take an extended knot vector of the original curve as a new knot vector of the approximation curve. This generates a B-spline approximation curve with the same degree as the degree-elevated curve. Based on the discrete B-spline and multiple products of B-spline functions, we finally prove that the derivatives of any given degree of the uniform B-spline approximation curve sequence converge uniformly to the corresponding derivatives of the original rational B-spline curve. This approximation method is very simple and guarantees the convergence of the approximation.
机译：B样条曲线对有理B样条曲线的逼近是计算机辅助几何设计中的重要问题。本文提出了一种用B样条曲线序列近似均匀B样条的方法。我们首先将原始有理B样条曲线的度数升高，并将该度数升高的曲线的控制点作为B样条近似曲线的新控制点。接下来，我们将原始曲线的扩展结向量作为近似曲线的新结向量。这将生成与度高曲线相同度的B样条近似曲线。基于离散的B样条和B样条函数的乘积，我们最终证明，任意给定程度的均匀B样条近似曲线序列的导数均会收敛到原始有理B样条曲线的相应导数。这种逼近方法非常简单，可以保证逼近的收敛性。

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