山区地貌问题

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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。

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')

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原始图160014001200z10008006004004000300030002000y100010002000x4000

原始图160014001200z10008006004004000300030002000y100010002000x4000

（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)

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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')

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