计算机图形学网络课程

style='font-size:14.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman";color:blue'>图形变换</span><span
lang=EN-US style='font-size:14.0pt;mso-bidi-font-size:10.0pt;color:blue'><o:p></o:p></span></p>

<p align=center style='text-align:center'><b><span lang=EN-US style='font-size:
18.0pt;color:green'>6.1</span><span lang=EN-US style='color:green'> </span></b><b><span
style='font-size:18.0pt;font-family:仿宋_GB2312;color:green'>数学基础</span></b></p>

<p><span lang=EN-US style='mso-ascii-font-family:楷体_GB2312;mso-fareast-font-family:
楷体_GB2312'>&nbsp;&nbsp;</span><span lang=EN-US style='font-family:楷体_GB2312'> 本节简要回顾图形变换中需要大量用到的矢量和矩阵的有关内容。</span></p>

<p><b><span lang=EN-US style='font-size:10.0pt;font-family:幼圆;color:gray'><a
href="http://learn.bitsde.com/hep/jisuanjituxing/Chapter6/CG_Txt_6_005.htm"><span
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lang=EN-US style='font-family:幼圆;color:gray'><a
href="http://learn.bitsde.com/hep/jisuanjituxing/Chapter6/CG_Txt_6_005.htm"><span
style='color:gray'>矢量运算</span></a><o:p></o:p></span></b></p>

<p style='line-height:200%'>矢量是一有向线段，具有方向和大小两个参数。设有两个矢量<span lang=EN-US>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span><i><span lang=EN-US style='font-family:"Times New Roman"'>V</span></i><sub><span
lang=EN-US>1</span></sub>（<i><span lang=EN-US style='font-family:"Times New Roman"'>x</span></i><sub><span
lang=EN-US>1</span></sub>，<i><span lang=EN-US style='font-family:"Times New Roman"'>y</span></i><sub><span
lang=EN-US>1</span></sub>，<i><span lang=EN-US style='font-family:"Times New Roman"'>z</span></i><sub><span
lang=EN-US>1</span></sub>），<i><span lang=EN-US style='font-family:"Times New Roman"'>V</span></i><sub><span
lang=EN-US>2</span></sub>（<i><span lang=EN-US style='font-family:"Times New Roman"'>x</span></i><sub><span
lang=EN-US>2</span></sub>，<i><span lang=EN-US style='font-family:"Times New Roman"'>y</span></i><sub><span
lang=EN-US>2</span></sub>，<i><span lang=EN-US style='font-family:"Times New Roman"'>z</span></i><sub><span
lang=EN-US>2</span></sub>）。</p>

<p><span lang=EN-US>&nbsp; 1) 矢量的长度 </span></p>

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<p><span lang=EN-US>&nbsp; 2) 数乘矢量 </span></p>

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<p><span lang=EN-US>&nbsp; 3) 两个矢量之和 </span></p>

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<p><span lang=EN-US>&nbsp; 4) 两个矢量的点积 </span></p>

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<p style='margin-left:36.0pt'>点积满足交换律和分配律</p>

<p style='margin-left:36.0pt'><span lang=EN-US><!--[if gte vml 1]><v:shape
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src="./第六章%20附录——图形变换.files/image007.gif" v:shapes="_x0000_i1031"><![endif]>&nbsp;</span></p>

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<p><span lang=EN-US>&nbsp; 5) 两个矢量的叉积</span></p>

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<p style='margin-right:36.0pt;margin-left:36.0pt'>叉积满足反交换律和分配律</p>

<p style='margin-right:36.0pt;margin-left:36.0pt'><span lang=EN-US><!--[if gte vml 1]><v:shape
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<p><span lang=EN-US><![if !supportEmptyParas]>&nbsp;<![endif]><o:p></o:p></span></p>

<p><b><span lang=EN-US style='font-size:10.0pt;font-family:幼圆;color:gray'><a
href="http://learn.bitsde.com/hep/jisuanjituxing/Chapter6/CG_Txt_6_006.htm"><span
style='text-decoration:none;text-underline:none'><!--[if gte vml 1]><v:shape
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 <v:imagedata src="./第六章%20附录——图形变换.files/image001.gif" o:href="http://learn.bitsde.com/hep/jisuanjituxing/material/CG_Gif_pub_021.gif"/>
</v:shape><![endif]--><![if !vml]><img border=0 width=28 height=50
src="./第六章%20附录——图形变换.files/image001.gif" v:shapes="_x0000_i1038"><![endif]></span></a></span></b><b><span
lang=EN-US style='font-family:幼圆;color:gray'><a
href="http://learn.bitsde.com/hep/jisuanjituxing/Chapter6/CG_Txt_6_006.htm"><span
style='color:gray'>矩阵运算</span></a><o:p></o:p></span></b></p>

<p style='margin-right:36.0pt;margin-left:36.0pt'>设有一个<i><span lang=EN-US
style='font-family:"Times New Roman"'>m</span></i>行<i><span lang=EN-US
style='font-family:"Times New Roman"'>n</span></i>列矩阵<i><span lang=EN-US
style='font-family:"Times New Roman"'>A</span></i></p>

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<p style='margin-right:36.0pt;margin-left:36.0pt;line-height:200%'><span
lang=EN-US><!--[if gte vml 1]><v:shape id="_x0000_i1040" type="#_x0000_t75"
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<p><span lang=EN-US>&nbsp; 1) 矩阵的加法运算 </span></p>

<p style='margin-left:36.0pt;line-height:200%'>设两个矩阵<i><span lang=EN-US
style='font-family:"Times New Roman"'>A</span></i>和<i><span lang=EN-US
style='font-family:"Times New Roman"'>B</span></i>都是<i><span lang=EN-US
style='font-family:"Times New Roman"'>m</span></i><span lang=EN-US>x</span><i><span
lang=EN-US style='font-family:"Times New Roman"'>n</span></i>的，把他们对应位置的元素相加而得到的矩阵叫做<i><span
lang=EN-US style='font-family:"Times New Roman"'>A</span></i>、<i><span
lang=EN-US style='font-family:"Times New Roman"'>B</span></i>的<span
style='color:maroon'>和</span>，记为<i><span lang=EN-US style='font-family:"Times New Roman";
color:maroon'>A</span></i><span style='color:maroon'>＋</span><i><span
lang=EN-US style='font-family:"Times New Roman";color:maroon'>B</span></i></p>

<p align=center style='margin-left:36.0pt;text-align:center'><span lang=EN-US><!--[if gte vml 1]><v:shape
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<p style='margin-left:36.0pt'>只有在两个矩阵的行数和列数都相同时才能加法。</p>

<p><span lang=EN-US>&nbsp; 2) 数乘矩阵 </span></p>

<p style='margin-left:36.0pt'>用数<span lang=EN-US>k乘矩阵A的每一个元素而得的矩阵叫做</span><i><span
lang=EN-US style='font-family:"Times New Roman"'>k</span></i>与<i><span
lang=EN-US style='font-family:"Times New Roman"'>A</span></i>之<span
style='color:maroon'>积</span>，记为<i><span lang=EN-US style='font-family:"Times New Roman";
color:maroon'>kA</span></i></p>

<p align=center style='margin-left:36.0pt;text-align:center'><span lang=EN-US><!--[if gte vml 1]><v:shape
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<p><span lang=EN-US>&nbsp; 3) 矩阵的乘法运算 </span></p>

<p style='margin-left:36.0pt'>只有当前一矩阵的<span style='color:maroon'>列数</span>等于后一矩阵的<span
style='color:maroon'>行数</span>时两个矩阵才能相乘。</p>

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