摘要
针对带形状参数的4次λ-Bézier曲线的近似合并问题提出了一种将2相邻4次λ-Bézier曲线合并成1条4次λ-Bézier曲线的方法.该方法通过将曲线拟合方法与广义逆矩阵理论相结合,直接得到了合并4次λ-Bézier曲线控制顶点的显示表达式,且在合并过程中分别考虑了不保端点插值和保端点插值条件的情形;给出了具体的实例与合并误差.实例结果表明:所提方法不仅可以获得较好的合并效果,而且具有易于实现、误差计算简单的特点,可以广泛地应用于CAD/CAM系统中对曲线的近似合并.
A method which can deal with approximating two adjacent quartic λ-Bézier curves by one quartic λ-Bézier curve,was presented for the approximate merging of existing curve design.After the fitting method of the curves was combined with the theory of the general inverse matrix,the explicit formula of control points of the merged quartic λ-Bézier curve was given directly.In the merging process,two cases were considered respectively.One is the case without constraints of endpoints interpolations;the other is the case with constraints of endpoints interpolations.Eventually,some merging examples were discussed and the errors of approximate merging were given.Experimental results illustrate that the proposed method has a good merging effect and is easy to implement and simple to error estimation,which can be widely applied to the approximate merging of curve in CAD/CAM systems.
出处
《华中科技大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2011年第7期45-49,共5页
Journal of Huazhong University of Science and Technology(Natural Science Edition)
基金
国家自然科学基金资助项目(60971127
11026051)
陕西省自然科学基金资助项目(2011JM1006)
陕西省教育厅基金资助项目(11JK1052)
西安理工大学科技创新研究基金资助项目(108-211004)
