| 权因子、参数变换与有理二次Bezier曲线参数化 |
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| 引用本文： | 施法中.权因子、参数变换与有理二次Bezier曲线参数化[J].航空学报,1994,15(9):1151-1154. |
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| 作者姓名： | 施法中 |
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| 作者单位： | 北京航空航天大学７０３教研室 |
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| 基金项目： | 国家自然科学基金资助课题 |
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| 摘 要： | 正则参数变换不改变参数曲线的形状,但改变了从曲线定义域内的点到曲线上点的映射关系,因而改变了曲线参数化。在形状不变因子不变情况下,如果改变有理二次Ｂｅｚｉｅｒ曲线的权因子,称之为权因子变换,能得到与正则参数变换同样的效果。同时,给出了在有理二次Ｂｅｚｉｅｒ曲线上点与权因子间的关系,并导出了与权因子变换对参数化有同样影响的参数变换公式。
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| 关 键 词： | 有理函数 数学变换 参数化法 |
WEIGHTS,PARAMETRIC TRANSFORMATION AND PARAMETRIZATION OF RATIONAL QUADRATIC BEZIER CURVES |
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| Shi Fazhong.WEIGHTS,PARAMETRIC TRANSFORMATION AND PARAMETRIZATION OF RATIONAL QUADRATIC BEZIER CURVES[J].Acta Aeronautica et Astronautica Sinica,1994,15(9):1151-1154. |
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| Authors: | Shi Fazhong |
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| Institution: | Faculty 703,Beijing University of Aeronautics and Astronautics, Beijing,100083 |
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| Abstract: | A regular parametric transformation does not change the shape of a parametric curve,but the mapping of the points in the domain of definition of the curve onto the points on the curve is changed and therefore the curve parametrization is changed.With the shape invariable factor unchanged, if the weights for a rational quadratic Bezier curve are changed,which is called a weight transformation,the same effect can be obtained as that of a regular parametric transformation.The relationship between the parameter of a point on a rational quadratic Bezier curve and its weights is given,and the parametric transformation formula is derived which has the same influence on parametrization as the weight transformation. |
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| Keywords: | rational functions transformation parametrization |
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