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基于周期性延伸的三次B樣條閉曲線插值
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Cubic B-spline Closed Curve Based on Periodic Extension
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    摘要:

    針對閉曲線具有可周期性延伸的特點，提出了一種基于求解雙列帶陣線性方程組的三次B樣條完全閉曲線插算法。通過節(jié)點向量和控制點在曲線閉合點兩端的周期性延伸，使插值曲線在閉合點實現(xiàn)了理論上的完全封閉。針對曲線插值線性方程組中系數(shù)矩陣具有不完全帶陣的特點，提出了一種雙列帶陣線性方程組求解算法。應用實例表明，算法性能穩(wěn)定、效率高、可插值任意形狀的復雜閉曲線，適于處理大數(shù)據(jù)量閉曲線插值運算。

    Abstract:

    According to the periodic extension fact for closed curve, a method of cubic B-spline interpolation for closed curve was proposed. By extending knots and control points, the interpolated curve closed entirely at closing point. Considering the character of incomplete bond matrix for coefficient matrix of interpolation system of equations, an algorithm for solving linear banded system of equations with two columns of non-zero elements was introduced to improve the computational efficiency. Examples of application show that the proposed technology has the stable performance and high efficiency, can be used to interpolate complex closed curve with whatever shape, and it is especially useful for problems with large number of data points.

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李學藝,王釗,連小珉,曾慶良.基于周期性延伸的三次B樣條閉曲線插值[J].農(nóng)業(yè)機械學報,2009,40(12):250-254. Cubic B-spline Closed Curve Based on Periodic Extension[J]. Transactions of the Chinese Society for Agricultural Machinery,2009,40(12):250-254.

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