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<TITLE> 曲面及等值线绘图 </TITLE>
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<H1>3.2.2 曲面及等值线绘图</H1>
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如果要画一个三维的曲面，MATLAB是以<FONT COLOR=#FF0000>meshgrid</FONT>配合与<FONT COLOR=#FF0000>mesh</FONT>或<FONT COLOR=#FF0000>surf</FONT>指令来绘图。先要以<FONT COLOR=#FF0000>meshgrid</FONT>产生在x-y平面
的二维的网格数据，再以一组z轴的数据对应到这个二维的网格，即可画出三维的曲面。以下的例子可说明上
述的绘图过程。
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> x=-7.5:0.5:7.5;
y=x; % </FONT><FONT COLOR=#FF0000>先产生</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">x</FONT><FONT COLOR=#FF0000>及</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">y</FONT><FONT COLOR=#FF0000>二个阵列</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> [X,Y]=meshgrid(x,y);
% </FONT><FONT COLOR=#FF0000>再以</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">meshgrid</FONT><FONT COLOR=#FF0000>形成二维的网格数据</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> R=sqrt(X.^2+Y.^2)+eps;
% </FONT><FONT COLOR=#FF0000>加上</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">eps</FONT><FONT COLOR=#FF0000>可避免当</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">R</FONT><FONT COLOR=#FF0000>在分母时趋近零时会无法定义</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> Z=sin(R)./R;
% </FONT><FONT COLOR=#FF0000>产生</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">z</FONT><FONT COLOR=#FF0000>轴的数据</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> mesh(X,Y,Z)
% </FONT><FONT COLOR=#FF0000>将</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">z</FONT><FONT COLOR=#FF0000>轴的变化值以网格方式画出</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> surf(X,Y,Z)
% </FONT><FONT COLOR=#FF0000>将</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">z</FONT><FONT COLOR=#FF0000>轴的变化值以曲面方式画出</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> mesh(peaks)
% </FONT><FONT COLOR=#FF0000>直接将以定义的</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">peaks</FONT><FONT COLOR=#FF0000>函数以网格方式画出</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> title('Mesh
plot of peaks')<BR>
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与三维绘图有关的还有等值线图，相关指令为<FONT COLOR=#FF0000>contour</FONT>,<FONT COLOR=#FF0000>contour3</FONT>。<FONT COLOR=#FF0000>contour</FONT>是将等值线图以二维图表示，其语法有
几个方式。一是<FONT COLOR=#FF0000>contour(Z)</FONT>,<FONT COLOR=#FF0000>contour(Z,n)</FONT>，其中<FONT COLOR=#FF0000>Z</FONT>是一个二维矩阵，而 n为等值线的数目（如果不给即以自动方式
设定）。另一种语法则是将z轴的值对应到指定的x,y轴的值，语法为<FONT COLOR=#FF0000>contour(X,Y,Z)</FONT>,<FONT COLOR=#FF0000>contour(X,Y,Z,n)</FONT>，其中<FONT COLOR=#FF0000>X</FONT>,<FONT COLOR=#FF0000>Y</FONT>,
<FONT COLOR=#FF0000>Z</FONT>代表x,y,z轴的数据。<FONT COLOR=#FF0000>contour3</FONT>则是将等值线以三维图表示，其语法与<FONT COLOR=#FF0000>contour</FONT>类似，只是将对应的关键字<FONT COLOR=#FF0000>contour</FONT>
改成<FONT COLOR=#FF0000>contour3</FONT>，其余部份相同。
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<A NAME="work">以下的例子可以比较<FONT COLOR=#FF0000 FACE="Times New Roman">contour</FONT><FONT FACE="Times New Roman">,
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">contour3</FONT>图示的不同：</A>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> [X,Y,Z]=peaks;
% x,y</FONT><FONT COLOR=#FF0000>及</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">z</FONT><FONT COLOR=#FF0000>轴的数据由</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">peaks</FONT><FONT COLOR=#FF0000>函数定义</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> subplot(2,2,1)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> contour(Z,20)
% </FONT><FONT COLOR=#FF0000>画出</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">peaks</FONT><FONT COLOR=#FF0000>的</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">Z</FONT><FONT COLOR=#FF0000>轴二维等值线图，</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">20</FONT><FONT COLOR=#FF0000>为等值线的数目</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> subplot(2,2,2)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> contour(X,Y,Z,20)
% </FONT><FONT COLOR=#FF0000>画出</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">peaks</FONT><FONT COLOR=#FF0000>的二维等值线图，注意</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">x,y</FONT><FONT COLOR=#FF0000>轴与上图不同</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> subplot(2,2,3)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> contour3(Z,20)
% </FONT><FONT COLOR=#FF0000>画出</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">peaks</FONT><FONT COLOR=#FF0000>的</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">Z</FONT><FONT COLOR=#FF0000>轴二维等值线图</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> subplot(2,2,4)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> contour3(X,Y,Z,20)
% </FONT><FONT COLOR=#FF0000>画出</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">peaks</FONT><FONT COLOR=#FF0000>的三维等值线图，注意</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">x,y</FONT><FONT COLOR=#FF0000>轴与上图不同</FONT><HR>
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