山区地貌问题：在某山区测得一些地点的高程如下表。（平面区域为：1200<=x<=4000,1200<=y<=3600)。试作出该山区的地貌图和等高线图，并对几种插值方法进行比较。3600320028002400200016001200Y/x1480 1500 1550 1510 1430 1300 1200 9801500 1550 1600 1550 1600 1600 1600 15501500 1200 1100 1550 1600 1550 1380 10701500 1200 1100 1350 1450 1200 1150 10101390 1500 1500 1400900 1100 10609501320 1450 1420 1400 13007009008501130 1250 1280 1230 10409005007001200 1600 2000 2400 2800 3200 3600 4000解：x0=1200:400:4000;y0=1200:400:3600;z0=[1130,1250,1280,1230,1040,900,500,700; 1320,1450,1420,1400,1300,700,900,850; 1390,1500,1500,1400,900,1100,1060,950; 1500,1200,1100,1350,1450,1200,1150,1010; 1500,1200,1100,1550,1600,1550,1380,1070; 1500,1550,1600,1550,1600,1600,1600,1550; 1480,1500,1550,1510,1430,1300,1200,980];meshc(x0,y0,z0)xlabel('x');ylabel('y');zlabel('z')title('原始图')1原始图160014001200z1000800600400400030004000300020002000y10001000x原始图160014001200z1000800600400400030004000300020002000y10001000x（1）分段线性插值输入命令：[xi2,yi2]=meshgrid(1200:10:4000,1200:10:3600);zi2=interp2(x0,y0,z0,xi2,yi2,'linear');meshc(xi2,yi2,zi2)2 xlabel('x');ylabel('y');zlabel('z')title('插值后')（2）三次样条插值输入命令： [xi,yi]=meshgrid(1200:10:4000,1200:10:3600);zi=interp2(x0,y0,z0,xi,yi,'spline');meshc(xi,yi,zi),title('三次样条插值表面图') xlabel('x');ylabel('y');zlabel('z')3（3）双三次插值输入命令：[xi,yi]=meshgrid(1200:10:4000,1200:10:3600);zi=interp2(x0,y0,z0,xi,yi,'cubic');meshc(xi,yi,zi),title('双三次插值后的表面图')xlabel('x 轴');ylabel('y 轴');zlabel('z 轴')（4）画等高线图：4n=9;pcolor(x0,y0,z0)shading interpzmax=max(max(z0));zmin=min(min(z0));caxis([zmin,zmax])colorbarhold onC=contour(x0,y0,z0,n,'k:');clabel(C)title('未拟合图形')hold off未 拟 合 图 形35001.49e+0031.49e+0031.051.38e+0031.27e+1.16e+1.38e+0031.27e+01.16e+16001.051.49e+0031.49e+0031500140030001.49e+0031.49e+003130012001.0525001.16e+0031.16e+00311001.051.27e+0031.27e+003 1.38e+0031.38e+003100020001.49e+0031.49e+0039409409001.38e+0031.27e+0031.16e+0031.38e+0031.27e+0031.16e+00394094080072072070015001.27e+0031.27e+0036001.16e+003830720830610 720610150020002500300035004000500pcolor(xi,yi,zi)shading interpzmax1=max(max(zi));zmin1=min(min(zi));caxis([zmin1,zmax1])colorbarhold onC=contour(xi,yi,zi,n,'k:');clabel(C)title('拟合图形')5hold off1.42e+0031.42e+0031.01.01.11.11.3e1.3e1.53e+0031.53e+0031.53e+0031.53e+0031.3e+0031.3e+0031.42e+0031.42e+0031.07e+0031.07e+0031.18e+0031.18e+0031.53e+0031.53e+0039549541.18e+0031.3e+0031.3e+0031.18e+0031.07e+0031.18e+0031.07e+003838838 607723607723相应的图形中都画出了地貌图和等高线，在以上的三种插值方法中，最为精确的要属双三次插值方法，可能在间隔取值较小时，它与三次样条插值所绘出的图形差异不大，不很明显。6
