数学建模实验报告之曲线插值

PAGEPAGE3东南大学《数学实验》报告学号09008226姓名毕斌成绩实验内容：曲线插值一实验目的常见插值函数的求解及应用二预备知识(1)熟悉一般的曲线插值的方法(2)熟悉“\”、polyfit、polyval、interp1、spline、cscvn等Matlab命令三实验内容与要求(1)已知某平原地区的一条公路经过如下坐标所表示的点，请用样条插值绘出这条公路（不考虑公路的宽度）。X(m)03050708090120148170180Y(m)80644742486680120121138X(m)202212230248268271280290300312Y(m)160182200208212210200196188186X(m)320340360372382390416430478440Y(m)200184188200202240246280296308X(m)420380360340320314280240200Y(m)334328334346356360392390400完整代码：functioninterpolation%路线x轴上单调递增到最大值road_x1=[0,30,50,70,80,90,120,148,170,180,202,212,230,248,268,271,280,290,300,312,320,340,360,372,382,390,416,430,478];road_y1=[80,64,47,42,48,66,80,120,121,138,160,182,200,208,212,210,200,196,188,186,200,184,188,200,202,240,246,280,296];%插值0到478x1=0:478;y1=interp1(road_x1,road_y1,x1,'spline');length1=0;%计算这段路程长度fori=0:477y_i=abs(interp1(road_x1,road_y1,i+1)-interp1(road_x1,road_y1,i));length1=length1+sqrt(1+(y_i)^2);end%做图并保持到下一个，一起绘制图形plot(road_x1,road_y1,'.',x1,y1);holdon;%x轴上单调递减，第二段road_x2=[478,440,420,380,360,340,320,314,280,240,200];road_y2=[296,308,334,328,334,346,356,360,392,390,400];%插值200到478x2=200:478;y2=interp1(road_x2,road_y2,x2,'spline');%计算该段路程长度length2=0;forj=200:477y_j=abs(interp1(road_x2,road_y2,j+1)-interp1(road_x2,road_y2,j));length2=length2+sqrt(1+(y_j)^2);end%绘图plot(road_x2,road_y2,'.',x2,y2);%plot(road_x2,road_y2