插值曲线的构造和光滑问题

THE PROBLEM OF CONSTRUCTION AND SMOOTHNESS OF INTERPOLATION CURVES

通过对Ｂ－Ｂ曲线和Ｌａｇｒａｎｇｅ曲线相互关系的研究，给出端点信息为ｄｉｄｔｉＧ（ｊ）（ｊ＝０，１，ｉ＝１，２，…，ｒ＜［ｄ／２］），而内点信息为Ｐｉ＝Ｇ（ｔｉ）（０＜ｔｉ＜ｔｉ＋１＜１，ｉ＝０，１，…，ｄ－２ｒ＋２）的ｄ次多项式曲线Ｈ（ｔ）的一种构造方法，从而解决了“既插值给定的内点信息，又在连接点处ｒ一阶光滑”

The relationship between Lagrange curves and B B curves is studied.A method of formulating a curve of polynomials with d degree is presented in which the end information is d i d t iG(j)(j=0,1,i=1,2,…,r<) and the inner information is P i=G(t i)(0<t i<t i+1 <1,i=0,1,…,d-2r+2) ,so that the important problem of interpolating given inner information with r stepped smoothness at the connecting points is solved.