摘要
首先介绍了用三次NURBS表示圆弧和整圆的方法,然后提出了用三次NURBS表示椭圆的方法及其生成算法,并用解析法解出了用三次NURBS表示椭圆的条件.讨论了用三次NURBS表示椭圆和用三次NURBS表示圆之间的区别和联系,指出圆的三次NURBS表示实质上是椭圆的三次NURBS表示的一种特殊情况:当椭圆的长半轴、短半轴相等(a0=b0)时,椭圆的三次NURBS表示转化为圆的三次NURBS表示,这与圆和椭圆的代数方程的关系是一致的.
This paper introduces a method of cubic NURBS representation of circular arcs and circle at first. Then, it presents a method of ellipse representation by cubic NURBS and the creation algorithm .At the same time it gets a condition for the representation of ellipse. The differentiate and the connection between the representation of ellipse and circle by cubic NURBS was also discussed in it. This paper indicates that actually the representation of circle by cubic NURBS is a special situation for the representation of ellipse by cubic NURBS: the representation of ellipse by cubic NURBS translate into the representation of circle by cubic NURBS while the long axis is equal to the short axis and this is in according with the relation of algebra equation between circle and ellipse.
出处
《湘潭大学自然科学学报》
CAS
CSCD
2004年第3期120-122,127,共4页
Natural Science Journal of Xiangtan University
关键词
椭圆表示
NURBS曲线
算法
解析法
Ellipse representation
,NURBS curve
algorithm
method of analyse
