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1、目 录一维插值方案2二维数据内插值(表格查找)3等高线4三维曲面5等高线26三维曲面27matlab绘制温度场(尚未深入研究)13二维曲线（非线性）拟合步骤18三维曲线（非线性）拟合步骤19三维曲线的画法20三维曲面的画法21画三维图3 只有点的数据,没有函数关系式23空间点拟合的基本原理27空间点拟合的最小二乘法28曲面生成后再进行多项式拟合37六点生成曲面38四点生成平面39用三维离散点拟合光滑曲面140用三维离散点拟合光滑曲面240一维插值方案clearyear = 1900:10:2010;product = 75.995 91.972 105.711 123.203 131.669
2、150.697 179.323 203.212 226.505 249.633 256.344 267.893 p1995 = interp1(year,product,1995)%使用一维数据内插值(该题中只能在1900和2010之间进行插值,大于2010和小于1900都%无效)命令x = 1900:1:2010y = interp1(year,product,x,spine);plot(year,product,o,x,y)插值说明:interp1(x,Y,xi,method) %用指定的算法计算插值：nearest：最近邻点插值，直接完成计算；linear：线性插值（缺省方式），直接完成
3、计算；spine：三次样条函数插值。对于该方法，命令interp1 调用函数spline、ppval、mkpp、umkpp。这些命令生成一系列用于分段多项式操作的函数。命令spline 用它们执行三次样条函数插值；pchip：分段三次Hermite 插值。对于该方法，命令interp1 调用函数pchip，用于对向量x 与y 执行分段三次内插值。该方法保留单调性与数据的外形；cubic：与pchip操作相同；v5cubic：在MATLAB 5.0 中的三次插值。对于超出x 范围的xi 的分量，使用方法nearest、linear、v5cubic的插值算法，相应地将返回NaN。对其他的方法，in
4、terp1 将对超出的分量执行外插值算法。yi = interp1(x,Y,xi,method,extrap) %对于超出x 范围的xi 中的分量将执行特殊的外插值法extrap。yi = interp1(x,Y,xi,method,extrapval) %确定超出x 范围的xi 中的分量的外插值extrapval，其值通常取NaN 或0。例1clear;x = 0:10; y = x.*sin(x);xx = 0:.25:10; yy = interp1(x,y,xx)plot(x,y,kd,xx,yy)interp2二维数据内插值(表格查找)X,Y = meshgrid(-3:.25:3)
5、;Z = peaks(X,Y);XI,YI = meshgrid(-3:.125:3);ZZ = interp2(X,Y,Z,XI,YI);surfl(X,Y,Z);hold on;surfl(XI,YI,ZZ+15)axis(-3 3 -3 3 -5 20);shading flathold off功能 三维数据插值interp3（查表）x,y,z,v = flow(20);xx,yy,zz = meshgrid(.1:.25:10, -3:.25:3, -3:.25:3);vv = interp3(x,y,z,v,xx,yy,zz);slice(xx,yy,zz,vv,6 9.5,1 2,
6、-2 .2); shading interp;colormap cool等高线clearZ=peaksfor w=1:1:100V=w/10,0,w/10contour(Z,V)%C=contour(Z,V)%Clabel(C)Hold ontitle(等高线及其标注)endend三维曲面x=0:10y=0:.1:1d,B=meshgrid(x,y)z=1./(B.*d.2+1);surf(B,d,z)x=0:0.05:10y=0:0.05:1X,Y=meshgrid(x,y)Z=( X.3+ 3.*Y.2+5*Y); %Z=( X.2+ 3.*Y.3+5*Y);%surf(X,Y,Z)%一张
7、普通的三维曲面,有时需要旋转一下才能看到下图的结果;x=0:0.05:1y=0:0.05:1X,Y=meshgrid(x,y)Z=( X.2-Y.2);% Z=( 4*X.3*Y-4*X.*Y.3);surf(X,Y,Z) %一张普通的三维曲面,有时需要旋转一下才能看到下图的结果;等高线2clearx=-2:0.1:2y=-2:0.1:2X,Y=meshgrid(x,y)Z=(X.2+Y.2).0.5for w=1:1:100V=w/3,w/pi,w/3contour(Z,V)hold onend三维曲面2clearx=-5:0.05:5y=-5:0.05:5X,Y=meshgrid(x,y)
8、Z=1./(X+1).2+(Y+1).2+1)-1.5./(X-1).2+(Y-1).2+1)mesh(X,Y,Z)clear;A=1.486,3.059,0.1;2.121,4.041,0.1;2.570,3.959,0.1;3.439,4.396,0.1;4.505,3.012,0.1;3.402,1.604,0.1;2.570,2.065,0.1;2.150,1.970,0.1;1.794,3.059,0.2;2.121,3.615,0.2;2.570,3.473,0.2;3.421,4.160,0.2;4.271,3.036,0.2;3.411,1.876,0.2;2.561,2.56
9、2,0.2;2.179,2.420,0.2;2.757,3.024,0.3;3.439,3.970,0.3;4.084,3.036,0.3;3.402,2.077,0.3;2.879,3.036,0.4;3.421,3.793,0.4;3.953,3.036,0.4;3.402,2.219,0.4;3.000,3.047,0.5;3.430,3.639,0.5;3.822,3.012,0.5;3.411,2.385,0.5;3.103,3.012,0.6;3.430,3.462,0.6;3.710,3.036,0.6;3.402,2.562,0.6;3.224,3.047,0.7;3.411,
10、3.260,0.7;3.542,3.024,0.7;3.393,2.763,0.7;x=A(:,1);y=A(:,2);z=A(:,3);scatter(x,y,5,z)%散点图figureX,Y,Z=griddata(x,y,z,linspace(1.486,4.271),linspace(1.604,4.276),v4);%插值pcolor(X,Y,Z);shading interp%伪彩色图figure,contourf(X,Y,Z) %等高线图clear;A=1.486,3.059,1858;2.121,4.041, 1858;2.570,3.959, 1858;3.439,4.396
11、, 1858;4.505,3.012, 1858;3.402,1.604, 1858;2.570,2.065, 1858;2.150,1.970, 1858;1.794,3.059,2350;2.121,3.615, 2350;2.570,3.473, 2350;3.421,4.160, 2350;4.271,3.036, 2350;3.411,1.876, 2350;2.561,2.562, 2350;2.179,2.420, 2350;2.757,3.024, 2600;3.439,3.970, 2600;4.084,3.036, 2600;3.402,2.077, 2600;2.879,
12、3.036, 2849;3.421,3.793, 2849;3.953,3.036, 2849;3.402,2.219, 2849;3.000,3.047, 3010;3.430,3.639, 3010;3.822,3.012, 3010;3.411,2.385, 3010;3.103,3.012, 3345;3.430,3.462, 3345;3.710,3.036, 3345;3.402,2.562, 3345;3.224,3.047, 3629;3.411,3.260, 3629;3.542,3.024, 3629;3.393,2.763, 3629;x=A(:,1);y=A(:,2);
13、z=A(:,3);scatter(x,y,5,z)%散点图,5是点的大小figure %打开显示图的界面X,Y,Z=griddata(x,y,z,linspace(1.486,4.271),linspace(1.604,4.276),v4);%插值pcolor(X,Y,Z);shading interp%伪彩色图figure;contourf(X,Y,Z) %等高线图figure;mesh(X,Y,Z)A=1.109,1.059,1718;2.021,0.841, 1758;2.870,0.359, 1858;4.039,0.196, 1838;4.505,3.012, 3345;3.402,
14、1.604, 3347;2.570,2.065, 3629;2.150,1.970, 3330;1.794,3.059,2250;2.121,3.615, 3027;2.570,3.473, 2935;3.421,4.160, 1930;4.271,3.036, 2050;3.411,1.876, 3144;2.561,2.562, 3739;2.179,2.420, 1950;2.757,3.024, 3530;3.439,3.970, 2720;4.084,3.036, 2610;3.402,2.077, 3500;2.879,3.036, 3249;3.421,3.793, 2149;3.953,3.036, 2849;3.402,2.219, 2849;3.000,3.047, 3010;3.430,3.639, 3010;3.822,3.012, 2310;3.411,2.385, 3410;3.103,3.012, 3345;3.430,3.462, 3845;3.710,3.036, 2645;3.402,2.562, 2745;3.224,3.047, 3229;3.411,3.260, 3329;3.542,3.024, 3429;3.393,2.763, 3529;x=A(:,1);y=A(:,2);z=A(:,3);sc
