与特征多边形第二边相切的平面参数三次曲线

A PLANE PARAMETRIC CUBIC CURVE THAT CONTACTS THE SECOND EDGE OF THE CHARACTERISTIC POLYGON

一、引言 参数三次曲线段及参数三次样条曲线是目前CAGD(计算机辅助几何设计)和CAM(计算机辅助制造)中用得较多且行之有效的曲线。之所以如此。

The Bezier curves commonly used in CAGD(Computer Aided Geometric Design)contact their characteristic polygons at no more than two points-Starting andterminal points of the polygons-and are rather far from their characteristic polygons.Timmer curves intersect their polygons at the midpoint of the second edge of thepolygons. The Intersecting points become tangent when tbe line between the startingand terminal points is parallel to the second edge of the relating polygons. But theynever contact the polygons when the condition does not hold and, often, unexpectedinflection points arise. In the article, we solve the problem by adding a parameterin the common plane parametric cubic curve and construct a new kind of planecurve. The curve is close to its characteristic polygon and tangent to the secondedge of the polygon. And, further more, the position of the tangent point and theshape of the curve can be modulated easily by adjusting the added parameter tomeet any special need. The tendency of the contact poiut variation with the changeof the added parameter is discussed.