| Bézier 曲线的多项式重新参数化检测 |
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| 作者姓名： | 沈莞蔷 王宏凯 |
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| 作者单位： | (江南大学理学院，江苏 无锡 214122) |
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| 基金项目： | 国家自然科学基金项目(61772013)；中央高校基本科研业务费专项基金项目(JUSRP21816) |
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| 摘 要： | 研究了一种用于精确检测一条Bézier 曲线的次数是否可以通过多项式重新参数化
降低的算法。该算法对任意一条Bézier 曲线，将重新参数化前后的基函数的关系用方程组的形
式表达，但不需要解方程，而是通过系数表示的金字塔算法直接计算，可以精确求出用于重新
参数化的多项式和降低次数后的Bézier 曲线的控制顶点，并且该重新参数化的多项式在相差一
个线性变换的前提下是唯一的。通过实例应用，该算法运算速度较之前的算法快。
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| 关 键 词： | Bé zier曲线 多项式 重新参数化 基函数 金字塔算法 |
Polynomial reparameterization detection of Bézier curves |
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| Authors: | SHEN Wan-qiang WANG Hong-kai |
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| Affiliation: | (School of Science, Jiangnan University, Wuxi Jiangsu 214122, China) |
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| Abstract: | An algorithm is presented to determine whether the degree of Bézier curve can be reduced
by polynomial reparameterization. In the algorithm, for any Bézier curve, the relation between the
basis functions before and after reparameterization is expressed as a system of equations. Instead of
solving the equations, the polynomial for reparameterization and the control points of the lower
degree Bézier curve can be calculated directly by a pyramid algorithm of coefficient
reparameterization. In addition, the polynomial for reparameterization is unique to within a scale
factor and a constant. Compared with the previous algorithm by examples, this algorithm possesses
shorter computational time. |
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| Keywords: | Bézier curve polynomial reparameterization basis function pyramid algorithm |
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