线性p-Bézier曲线的几何形状  

Geometric Shape of Linear p-Bézier Curve

作　　者：沈莞蔷[1] 汪国昭[2,3] 徐红林[1] 

机构地区：[1]江南大学理学院,无锡214122 [2]浙江大学数学系计算机图象图形研究所,杭州310027 [3]浙江大学CAD&LCG国家重点实验室,杭州310027

出　　处：《计算机辅助设计与图形学学报》2014年第8期1211-1218,共8页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金重点项目(60933008);国家自然科学基金(11326243,61272300,11371174);江苏省自然科学基金(BK20130117)

摘　　要：为了丰富非多项式空间的拟Bézier系统的几何性质,针对线性三角多项式空间的p-Bézier曲线进行研究.首先通过几何变换与参数变换将椭圆的参数方程化为p-Bézier形式;然后通过对比,指出除去退化情况外线性p-Bézier曲线必为椭圆弧;再给出该椭圆的中心,焦点,长、短轴顶点这些几何元素与其控制顶点间的关系式;最后给出了线性p-Bézier曲线为圆弧的充要条件.实例结果表明,文中的几何元素可以通过控制顶点的线性插值得到.To develop the geometric properties of the Bézier-like systems for non-polynomial spaces,researches are done for p-Bézier curves of the linear trigonometric polynomial space.Firstly,a parameter equation of an ellipse is changed into the p-Bézier form from geometric transformations and parameter transformations.Secondly,according to comparison,a conclusion that every linear p-Bézier curve except degenerated cases is an elliptic arc is drawn.Thirdly,the relations between the geometric elements of the ellipse,such as the center,foci,vertices of major and minor axes,and the control points are given.Lastly,a sufficient and necessary condition under which a linear p-Bézier curve is an arc is given.Moreover,example analysis shows that these geometric elements can be represented as linear interpolation forms of control points.

关 键 词：p-Bézier曲线 椭圆弧 几何元素 线性插值 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]