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<TITLE> 曲面及等值線繪圖 </TITLE>
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<H1>3.2.2 曲面及等值線繪圖</H1>
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如果要畫一個(gè)三維的曲面，MATLAB是以<FONT COLOR=#FF0000>meshgrid</FONT>配合與<FONT COLOR=#FF0000>mesh</FONT>或<FONT COLOR=#FF0000>surf</FONT>指令來繪圖。先要以<FONT COLOR=#FF0000>meshgrid</FONT>產(chǎn)生在x-y平面
的二維的網(wǎng)格數(shù)據(jù)，再以一組z軸的數(shù)據(jù)對(duì)應(yīng)到這個(gè)二維的網(wǎng)格，即可畫出三維的曲面。以下的例子可說明上
述的繪圖過程。
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> x=-7.5:0.5:7.5;
y=x; % </FONT><FONT COLOR=#FF0000>先產(chǎn)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>二個(gè)陣列</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>形成二維的網(wǎng)格數(shù)據(jù)</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>可避免當(dāng)</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">R</FONT><FONT COLOR=#FF0000>在分母時(shí)趨近零時(shí)會(huì)無法定義</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> Z=sin(R)./R;
% </FONT><FONT COLOR=#FF0000>產(chǎn)生</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">z</FONT><FONT COLOR=#FF0000>軸的數(shù)據(jù)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> mesh(X,Y,Z)
% </FONT><FONT COLOR=#FF0000>將</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">z</FONT><FONT COLOR=#FF0000>軸的變化值以網(wǎng)格方式畫出</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> surf(X,Y,Z)
% </FONT><FONT COLOR=#FF0000>將</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">z</FONT><FONT COLOR=#FF0000>軸的變化值以曲面方式畫出</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> mesh(peaks)
% </FONT><FONT COLOR=#FF0000>直接將以定義的</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">peaks</FONT><FONT COLOR=#FF0000>函數(shù)以網(wǎng)格方式畫出</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> title('Mesh
plot of peaks')<BR>
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與三維繪圖有關(guān)的還有等值線圖，相關(guān)指令為<FONT COLOR=#FF0000>contour</FONT>,<FONT COLOR=#FF0000>contour3</FONT>。<FONT COLOR=#FF0000>contour</FONT>是將等值線圖以二維圖表示，其語(yǔ)法有
幾個(gè)方式。一是<FONT COLOR=#FF0000>contour(Z)</FONT>,<FONT COLOR=#FF0000>contour(Z,n)</FONT>，其中<FONT COLOR=#FF0000>Z</FONT>是一個(gè)二維矩陣，而 n為等值線的數(shù)目（如果不給即以自動(dòng)方式
設(shè)定）。另一種語(yǔ)法則是將z軸的值對(duì)應(yīng)到指定的x,y軸的值，語(yǔ)法為<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軸的數(shù)據(jù)。<FONT COLOR=#FF0000>contour3</FONT>則是將等值線以三維圖表示，其語(yǔ)法與<FONT COLOR=#FF0000>contour</FONT>類似，只是將對(duì)應(yīng)的關(guān)鍵字<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">以下的例子可以比較<FONT COLOR=#FF0000 FACE="Times New Roman">contour</FONT><FONT FACE="Times New Roman">,
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">contour3</FONT>圖示的不同：</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>軸的數(shù)據(jù)由</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">peaks</FONT><FONT COLOR=#FF0000>函數(shù)定義</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>畫出</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>軸二維等值線圖，</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">20</FONT><FONT COLOR=#FF0000>為等值線的數(shù)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>畫出</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">peaks</FONT><FONT COLOR=#FF0000>的二維等值線圖，注意</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">x,y</FONT><FONT COLOR=#FF0000>軸與上圖不同</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>畫出</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>軸二維等值線圖</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>畫出</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">peaks</FONT><FONT COLOR=#FF0000>的三維等值線圖，注意</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">x,y</FONT><FONT COLOR=#FF0000>軸與上圖不同</FONT><HR>
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