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中文摘要：
为进一步完善广义Ball基理论,增强广义Ball曲线的造型能力,研究了一类新的广义Ball基及其相应曲线.通过加入多个带约束条件的参数,由初始函数在满足正性、规范性、对称性、端点性质和线性无关性的基础上进行递归的方法构造出基函数,并通过一般的控制顶点加权基函数的方法定义了相应广义Ball曲线.曲线具有凸包性、端点性质、几何不变性与仿射不变性、升阶公式,以及C0、C1和C2拼接条件和递归求值算法.这类基统一表示了以往所有的二项展开型广义Ball基和Bernstein基,并添加了多组新基,为广义Ball曲线提供了更丰富的造型.
英文摘要：
In order to improve the generalized Ball basis theory and enhance the shaping ability of generalized Ball curves,a new family of generalized Ball basis and its corresponding curves were studied.By adding some constrained parameters,and inducing from initial functions which satisfied positivity,normalization,symmetry,endpoint property and linear independence,this work constructed the basis,and defined the corresponding generalized Ball curve by usual way of control points weighed basis functions.The curve had convex hull property,endpoint property,geometric invariability and affine invariability,and its degree elevation formula,C0,C1,C2 joining conditions and recursive evaluation algorithm were given.This family of basis unifies the representations of the existing generalized Ball and Bernstein basis with forms like terms of binomial expansion,adds many new terms of basis,and applies more shapes for generalized Ball curves.
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