摘要
给定四点 pi(xi,yi) (i=1,2 ,3,4 )以逆时针方向构成一简单四边形并在两端点 p1和 p4处给定两直线L1和L2 .张三元等人提出和研究了一种通过上述四点并与L1和L2 相切的代数曲线插值并建立了一些新的结果 .作者进一步研究了这些代数曲线并给出了三次曲线C(λ)具有通过四点pi(xi,yi) (i=1,2 ,3,4 )的连续凸曲线分支的充分且必要条件 ,也研究了当四边形不在控制区域上的其它情形 .
Given four points p i(x i,y i)(i=1,2,3,4 ) which can construct a simple quadrilateral with counterclockwise direction and given two lines L 1 and L 2 passing the endpoints p 1 and p 4 respectively.Recently Zhang et al . [2] proposed and researched a kind of cubic algebraic curve interpolation which passes the above four points p i(x i,y i)(i=1,2,3,4 ) and the lines L 1 and L 2 are the tangent lines at p 1 and p 4 respectiveley. They established some new results. In this paper we further investigate these cubic algebraic curves and give the necessary and sufficient conditions on which the curve C(λ) has a continuous and convex branch passing points p i(i=1,2,3,4) . We also investigate other case when the quadrilateral is not completely on a control area.
出处
《计算机学报》
EI
CSCD
北大核心
2003年第9期1201-1205,共5页
Chinese Journal of Computers
基金
浙江省自然科学基金 ( 1990 46)资助
