三次Bézier曲线曲面的拟合实例  

The Fitting of the Cubic Bézier Curve and Surface

作　　者：杨艳 郑玉婷 YANG Yan;ZHENG Yu - ting(Department of Mathematics, Lvliang University, Lishi Shanxi 033001, China)

机构地区：[1]吕梁学院数学系,山西离石033001

出　　处：《吕梁学院学报》2018年第2期5-8,共4页Journal of Lyuiang University

基　　金：吕梁学院教学改革创新项目(JYYB201704);吕梁学院大学生创新创业训练计划项目(CXCYZD201724)

摘　　要：Bézier曲线曲面在计算机设计中起到重要作用,在已知实物的条件下,用计算机表达实物,同样可以用Bézier曲线曲面完成.首先介绍了Bézier曲线曲面的定义,几何连续的定义;然后通过三次Bézier曲线表示圆,得到旋转体曲面的控制顶点;最后以一花瓶为例,演示了用计算机表示其曲面的过程:从正视图上得到花瓶曲线,交互式得到用来拼接该曲线的两条Bézier曲线的控制顶点,使其达到几何一阶光滑,最后通过整理控制顶点,得到花瓶曲面的表达.The Bézier curve and surface play an important role in computer design. The known objects can be presented by a computer,which can also be done with the Bézier curve and surface. First,the definition of Bézier curve and surface is introduced,and the definition of geometric continuity as well. Then the cubic Bézier curve is used to indicate circles and the control vertex of the rotating body surface is obtained. Finally,a vase is taken as an example to demonstrate the process of using a computer to present the curved surface： the flower vase curve is obtained from the front view; the interactive method is used to obtain the control points of the two Bézier curves which are spliced to form the vase curse and achieve the geometric first order smoothing. Finally,the expression of the vase surface is obtained by combining the control points.

关 键 词：BÉZIER曲线 曲线拟合 曲线拼接 交互式控制顶点 

分 类 号：O242.1[理学—计算数学]