三次樣條差值擬合車門曲線

1、數(shù)學實驗三次樣條數(shù)學實驗三次樣條插值實驗1:某汽車制造商用三次樣條插值設計車門的曲線，其中一段的數(shù)據(jù)如下:x012345678910V0.00.791.532.192.713.033.272.893.063.193.29V0.80.2用三次樣條插值求Sio(x)，用軟件繪制S1o(x)的圖像，即車門的曲線1、計算S1o(x):程序：/splineaaaa.cpp:定義控制臺應用程序的入口點。/*三次樣條差值*/*第一步，利用差商，代替導數(shù)，求差商；/*第二步，利用追趕法求解三對角方程組，得到Mi;/*第三步，將求得值帶入三次樣條函數(shù)，求得S(x)#include<stdlib.h>

2、#include<stdio.h>#include<math.h>#defineN10doublexN+1,fxN+1,hN,HN,fN,aN+1,bN+1,cN+1,MN+1,betaN+1,yN+1,sN;/定義變量數(shù)組；doubletiaojian1,tiaojian2;/邊界條件；/求插商；voidchashang()inti;|for(i=0;i<=N-1;i+)hi=xi+1-xi;Ifor(i=0;i<=N-1;i+)fi=(fxi+1-fxi)/(xi+1-xi);for(i=1;i<=N-1;i+)ai=hi-1/(hi-1+hi);

3、bi=hi/(hi-1+hi);ci=3*(ai*fi-1+bi*fi);匚for(i=1;i<=N-1;i+)(Hi=pow(hi,2);/求hi的平方；)/利用追趕法解三對角方程組前期初始值；aN=1；/aN相當于卬N;b0=1;/入0;c0=6.*(f0-tiaojian1)/h0;/相當于d0;cN=6.*(tiaojian2-fN-1)/hN-1;/相當于dN;)/追趕法計算彎矩向量Mi;voidZhuigan()(inti;|beta0=b0/2.;y0=c0/2.;|for(i=1;i<=N-1;i+)betai=bi/(2.-ai*betai-1);/計算pi;fo

4、r(i=1;i<=Ni+)yi=(ci-ai*yi-1)/(2.-ai*betai-1);/順序求解計算yi;MN=yN;|for(i=N-1;i>=0;i-)/逆序求解計算MiMi=yi-betai*Mi+1;)/輸出三次樣條差值函數(shù)S1(x)S10(x)voidPrints()(inti;for(i=0;i<Ni+)printf("s%d=%lf*(%lf-x)人3+%lf*(x-%l伊3+%lf*(%lf-x)+%lf*(x-%lf)n",i+1,Mi/(6.*hi),xi+1,Mi+1/(6.*hi),xi,fxi/hi-Mi*Hi/6.,xi+1

5、,fxi+1/hi-Mi+1*Hi/6.,xi);)/主函數(shù)調用；voidmain()(inti;x0=0;fx0=0.0;x1=1;fx1=0.79;x2=2;fx2=1.53;x3=3;fx3=2.19;x4=4;fx4=2.71;x5=5;fx5=3.03;x6=6;fx6=3.27;x7=7;fx7=2.89;x8=8;fx8=3.06;x9=9;fx9=3.19;x10=10;fx10=3.29;tiaojianl=0.8;tiaojian2=0.2;chashang();printf("追趕法計算所得Mi:n");Zhuigan();for(i=0;i<=

6、Ni+)printf("%fn",Mi);printf("三次插值多項式si=n");Prints();結果：追趕法計算所得Mi:-0.6038191.1476380.6032690.6392880.3795800.362392-0.149149-0.1857950.2623290.0364770.281761三次插值多項式si=s1=-0.100636.*(1.000000-x1).人3+0.191273.*x1.人3+0.790000.*x1;s2=0.191273.*(2.000000-x2).人3+0.100545.*(x2-1.000000).

7、人3+0.598727.*(2.000000-x2)+1.429455.*(x2-1.000000);s3=0.100545.*(3.000000-x3).人3+0.106548.*(x3-2.000000).人3+1.429455.*(3.000000-x3)+2.083452.*(x3-2.000000);s4=0.106548.*(4.000000-x4).人3+0.063263.*(x4-3.000000).人3+2.083452.*(4.000000-x4)+2.646737.*(x4-3.000000);s5=0.063263.*(5.000000-x5).人3+0.060399.

8、*(x5-4.000000).人3+2.646737.*(5.000000-x5)+2.969601.*(x5-4.000000);s6=0.060399.*(6.000000-x6).人3+-0.024858.*(x6-5.000000).人3+2.969601.*(6.000000-x6)+3.294858.*(x6-5.000000);s7=-0.024858.*(7.000000-x7).人3+-0.030966.*(x7-6.000000).人3+3.294858.*(7.000000-x7)+2.920966.*(x7-6.000000);s8=-0.030966.*(8.0000

9、00-x8).人3+0.043722.*(x8-7.000000).人3+2.920966.*(8.000000-x8)+3.016278.*(x8-7.000000);s9=0.043722.*(9.000000-x9).人3+0.006080.*(x9-8.000000).人3+3.016278.*(9.000000-x9)+3.183920.*(x9-8.000000);s10=0.006080.*(10.000000-x10).人3+0.046960.*(x10-9.000000).人3+3.183920.*(10.000000-x10)+3.243040.*(x10-9.000000

10、);2、繪制車門曲線S10(x):matlab程序：clcclearsymsxsymss;symssj;x11=0:1:10;s11=0.0;0.79;1.53;2.19;2.71;3.03;3.27;2.89;3.06;3.19;3.29;pp=csape(x11,s11,'complete',0.8,0.2);sj=ppval(pp,x11);x1=0.0001:0.01:1;x2=1:0.01:2;x3=2:0.01:3;x4=3:0.01:4;x5=4:0.01:5;x6=5:0.01:6;x7=6:0.01:7;x8=7:0.01:8;x9=8:0.01:9;x10=

11、9:0.01:10;s1=-0.100636.*(1.000000-x1).人3+0.191273.*x1.人3+0.790000.*x1;s2=0.191273.*(2.000000-x2).人3+0.100545.*(x2-1.000000).人3+0.598727.*(2.000000-x2)+1.429455.*(x2-1.000000);s3=0.100545.*(3.000000-x3).人3+0.106548.*(x3-2.000000).人3+1.429455.*(3.000000-x3)+2.083452.*(x3-2.000000);s4=0.106548.*(4.0000

12、00-x4).人3+0.063263.*(x4-3.000000).人3+2.083452.*(4.000000-x4)+2.646737.*(x4-3.000000);s5=0.063263.*(5.000000-x5).人3+0.060399.*(x5-4.000000).人3+2.646737.*(5.000000-x5)+2.969601.*(x5-4.000000);s6=0.060399.*(6.000000-x6).人3+-0.024858.*(x6-5.000000).人3+2.969601.*(6.000000-x6)+3.294858.*(x6-5.000000);s7=-

13、0.024858.*(7.000000-x7).人3+-0.030966.*(x7-6.000000).人3+3.294858.*(7.000000-x7)+2.920966.*(x7-6.000000);s8=-0.030966.*(8.000000-x8).人3+0.043722.*(x8-7.000000).人3+2.920966.*(8.000000-x8)+3.016278.*(x8-7.000000);s9=0.043722.*(9.000000-x9).人3+0.006080.*(x9-8.000000).人3+3.016278.*(9.000000-x9)+3.183920.*(x9-8.000000);s10=0.006080.*(10.000000-x10).人3+0.046960.*(x10-9.000000).人3+3.183920.*(10.000000-x10)+3.243040.*(x10-9.000000);x=x1,x2,x3,x4,x5,x6,x7,x8,x9,x10;S=s1,s2,s3,s4,s5,s6,s7,s8,s9,s10;QX=plot(x,S,'r')set(QX,'LineWidth',1.85);holdonplot(x11,s11,