计算机图形学网络课程

lang=EN-US style='font-family:"Times New Roman"'>P</span></i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>2</span></sub>为下一个象素；</p>

<p style='line-height:200%'><span lang=EN-US>&nbsp;&nbsp;&nbsp;&nbsp; 当</span><i><span
lang=EN-US style='font-family:"Times New Roman"'>d&gt;</span></i><span
lang=EN-US>0时，</span><i><span lang=EN-US style='font-family:"Times New Roman"'>M</span></i>在<i><span
lang=EN-US style='font-family:"Times New Roman"'>L</span></i><span lang=EN-US>(</span><i><span
lang=EN-US style='font-family:"Times New Roman"'>Q</span></i>点<span lang=EN-US>)上方，取</span><i><span
lang=EN-US style='font-family:"Times New Roman"'>P</span></i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>1</span></sub>为下一个象素；</p>

<p style='line-height:200%'><span lang=EN-US>&nbsp;&nbsp;&nbsp;&nbsp; 当</span><i><span
lang=EN-US style='font-family:"Times New Roman"'>d=</span></i><span lang=EN-US>0时，选</span><i><span
lang=EN-US style='font-family:"Times New Roman"'>P</span></i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>1</span></sub>或<i><span
lang=EN-US style='font-family:"Times New Roman"'>P</span></i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>2</span></sub>均可，约定取<i><span
lang=EN-US style='font-family:"Times New Roman"'>P</span></i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>1</span></sub>为下一个象素；</p>

<p style='line-height:200%'>注意到<i><span lang=EN-US style='font-family:"Times New Roman"'>d</span></i>是<i><span
lang=EN-US style='font-family:"Times New Roman"'>x</span></i><i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>p</span></sub></i><span
lang=EN-US>, </span><i><span lang=EN-US style='font-family:"Times New Roman"'>y</span></i><i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>p</span></sub></i>的线性函数，可采用增量计算，提高运算效率。</p>

<p style='line-height:200%'><span lang=EN-US>&nbsp;&nbsp;&nbsp; 若当前象素处于</span><i><span
lang=EN-US style='font-family:"Times New Roman"'>d</span></i><span lang=EN-US
style='font-family:Symbol'>&sup3;</span><span lang=EN-US>0情况，则取正右方象素</span><i><span
lang=EN-US style='font-family:"Times New Roman"'>P</span></i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>1</span></sub><span
lang=EN-US style='font-family:"Times New Roman"'>(<i>x</i></span><i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>p</span></sub></i><span
lang=EN-US>+1, y</span><i><sub><span lang=EN-US style='mso-bidi-font-size:10.0pt;
font-family:"Times New Roman"'>p</span></sub></i><span lang=EN-US>),要判下一个象素位置，应计算
</span><i><span lang=EN-US style='font-family:"Times New Roman"'>d</span></i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>1</span></sub><span
lang=EN-US>=</span><i><span lang=EN-US style='font-family:"Times New Roman"'>F</span></i><span
lang=EN-US>(</span><i><span lang=EN-US style='font-family:"Times New Roman"'>x</span></i><i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>p</span></sub></i><span
lang=EN-US>+2, </span><i><span lang=EN-US style='font-family:"Times New Roman"'>y</span></i><i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>p</span></sub></i><span
lang=EN-US>+0.5)=</span><i><span lang=EN-US style='font-family:"Times New Roman"'>a</span></i><span
lang=EN-US>(</span><i><span lang=EN-US style='font-family:"Times New Roman"'>x</span></i><i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>p</span></sub></i><span
lang=EN-US>+2)+</span><i><span lang=EN-US style='font-family:"Times New Roman"'>b</span></i><span
lang=EN-US>(</span><i><span lang=EN-US style='font-family:"Times New Roman"'>y</span></i><i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>p</span></sub></i><span
lang=EN-US>+0.5)=</span><i><span lang=EN-US style='font-family:"Times New Roman"'>d</span></i><span
lang=EN-US>+</span><i><span lang=EN-US style='font-family:"Times New Roman"'>a</span></i>，增量为<i><span
lang=EN-US style='font-family:"Times New Roman"'>a</span></i>。</p>

<p style='line-height:200%'><span lang=EN-US>&nbsp;&nbsp;&nbsp; 若</span><i><span
lang=EN-US style='font-family:"Times New Roman"'>d</span></i><span lang=EN-US>&lt;0时，则取右上方象素</span><i><span
lang=EN-US style='font-family:"Times New Roman"'>P</span></i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>2</span></sub><span
lang=EN-US style='font-family:"Times New Roman"'>(<i>x</i></span><i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>p</span></sub></i><span
lang=EN-US>+1, </span><i><span lang=EN-US style='font-family:"Times New Roman"'>y</span></i><i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>p</span></sub></i><span
lang=EN-US>+1)。要判断再下一象素，则要计算</span><i><span lang=EN-US style='font-family:"Times New Roman"'>d</span></i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>2</span></sub><span
lang=EN-US>= </span><i><span lang=EN-US style='font-family:"Times New Roman"'>F</span></i><span
lang=EN-US>(</span><i><span lang=EN-US style='font-family:"Times New Roman"'>x</span></i><i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>p</span></sub></i><span
lang=EN-US>+2, </span><i><span lang=EN-US style='font-family:"Times New Roman"'>y</span></i><i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>p</span></sub></i><span
lang=EN-US>+1.5)=</span><i><span lang=EN-US style='font-family:"Times New Roman"'>a</span></i><span
lang=EN-US>(</span><i><span lang=EN-US style='font-family:"Times New Roman"'>x</span></i><i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>p</span></sub></i><span
lang=EN-US>+2)+</span><i><span lang=EN-US style='font-family:"Times New Roman"'>b</span></i><span
lang=EN-US>(</span><i><span lang=EN-US style='font-family:"Times New Roman"'>y</span></i><i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>p</span></sub></i><span
lang=EN-US>+1.5)+</span><i><span lang=EN-US style='font-family:"Times New Roman"'>c</span></i><span
lang=EN-US>=</span><i><span lang=EN-US style='font-family:"Times New Roman"'>d</span></i><span
lang=EN-US>+</span><i><span lang=EN-US style='font-family:"Times New Roman"'>a</span></i><span
lang=EN-US>+</span><i><span lang=EN-US style='font-family:"Times New Roman"'>b </span></i>，增量为<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>。画线从<span
lang=EN-US>(</span><i><span lang=EN-US style='font-family:"Times New Roman"'>x</span></i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>0</span></sub><span
lang=EN-US>, </span><i><span lang=EN-US style='font-family:"Times New Roman"'>y</span></i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>0</span></sub><span
lang=EN-US>)开始，</span><i><span lang=EN-US style='font-family:"Times New Roman"'>d</span></i>的初值
<i><span lang=EN-US style='font-family:"Times New Roman"'>d</span></i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>0</span></sub><span
lang=EN-US>=</span><i><span lang=EN-US style='font-family:"Times New Roman"'>F</span></i><span
lang=EN-US>(</span><i><span lang=EN-US style='font-family:"Times New Roman"'>x</span></i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>0</span></sub><span
lang=EN-US>+1, </span><i><span lang=EN-US style='font-family:"Times New Roman"'>y</span></i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>0</span></sub><span
lang=EN-US>+0.5)=</span><i><span lang=EN-US style='font-family:"Times New Roman"'>F</span></i><span
lang=EN-US>(</span><i><span lang=EN-US style='font-family:"Times New Roman"'>x</span></i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>0</span></sub><span
lang=EN-US>, </span><i><span lang=EN-US style='font-family:"Times New Roman"'>y</span></i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>0</span></sub><span
lang=EN-US>)+</span><i><span lang=EN-US style='font-family:"Times New Roman"'>a</span></i><span
lang=EN-US>+0.5</span><i><span lang=EN-US style='font-family:"Times New Roman"'>b</span>，</i>因<i><span
lang=EN-US style='font-family:"Times New Roman"'>&nbsp; F</span></i><span
lang=EN-US>(</span><i><span lang=EN-US style='font-family:"Times New Roman"'>x</span></i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>0</span></sub><span
lang=EN-US>, </span><i><span lang=EN-US style='font-family:"Times New Roman"'>y</span></i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>0</span></sub><span
lang=EN-US>)=0，所以</span><i><span lang=EN-US style='font-family:"Times New Roman"'>d</span></i><sub><span
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'>0</span></sub><span
lang=EN-US>=</span><i><span lang=EN-US style='font-family:"Times New Roman"'>a</span></i><span
lang=EN-US>+0.5</span><i><span lang=EN-US style='font-family:"Times New Roman"'>b</span></i>。</p>

<p style='line-height:200%'><span lang=EN-US>&nbsp;&nbsp;&nbsp; 由于我们使用的只是</span><i><span
lang=EN-US style='font-family:"Times New Roman"'>d</span></i>的符号，而且<i><span
lang=EN-US style='font-family:"Times New Roman"'>d</span></i>的增量都是整数，只是初始值包含小数。因此，我们可以用<span
lang=EN-US>2</span><i><span lang=EN-US style='font-family:"Times New Roman"'>d</span></i>代替<i><span
lang=EN-US style='font-family:"Times New Roman"'>d</span></i>来摆脱小数，写出仅包含整数运算的算法程序。</p>

<p style='line-height:200%'><span lang=EN-US style='color:navy'><!--[if gte vml 1]><v:shape
 id="_x0000_i1051" type="#_x0000_t75" alt="" style='width:10.5pt;height:10.5pt'>
 <v:imagedata src="./第二章%20光栅图形学.files/image004.gif" o:href="http://learn.bitsde.com/hep/jisuanjituxing/material/CG_Gif_pub_031.gif"/>
</v:shape><![endif]--><![if !vml]><img border=0 width=14 height=14
src="./第二章%20光栅图形学.files/image004.gif" v:shapes="_x0000_i1051"><![endif]></span><span
style='font-size:10.0pt;color:navy'>中点画线算法程序：</span></p>

<p style='margin-top:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:
0cm'><span lang=EN-US style='font-size:10.0pt;color:purple'>void Midpoint Line
(int x0,int y0,int x1, int y1,int color)</span></p>

<p style='margin-top:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:
0cm'><span lang=EN-US style='font-size:10.0pt;color:purple'>{ int a, b, d1, d2,
d, x, y；</span></p>

<p style='margin-top:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:
0cm'><span lang=EN-US style='font-size:10.0pt;color:purple'>&nbsp; a=y0-y1；
b=x1-x0；d=2*a+b；</span></p>

<p style='margin-top:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:
0cm'><span lang=EN-US style='font-size:10.0pt;color:purple'>&nbsp; d1=2*a；d2=2*
(a+b)；</span></p>

<p style='margin-top:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:
0cm'><span lang=EN-US style='font-size:10.0pt;color:purple'>&nbsp; x=x0；y=y0；</span></p>

<p style='margin-top:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:
0cm'><span lang=EN-US style='font-size:10.0pt;color:purple'>&nbsp; drawpixel(x,
y, color);</span></p>

<p style='margin-top:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:
0cm'><span lang=EN-US style='font-size:10.0pt;color:purple'>&nbsp; while
(x&lt;x1)</span></p>

<p style='margin-top:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:
0cm'><span lang=EN-US style='font-size:10.0pt;color:purple'>&nbsp; { if
(d&lt;0)&nbsp;&nbsp; {x++；y++； d+=d2; }</span></p>

<p style='margin-top:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:
0cm'><span lang=EN-US style='font-size:10.0pt;color:purple'>&nbsp;&nbsp;&nbsp;
else&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; {x++； d+=d1;}</span></p>

<p style='margin-top:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:
0cm'><span lang=EN-US style='font-size:10.0pt;color:purple'>&nbsp;&nbsp;&nbsp;
drawpixel (x, y, color);</span></p>

<p style='margin-top:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:
0cm'><span lang=EN-US style='font-size:10.0pt;color:purple'>&nbsp; } /* while
*/</span></p>

<p style='margin-top:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:
0cm'><span lang=EN-US style='font-size:10.0pt;color:purple'>} /* mid PointLine
*/</span></p>

<p><span lang=EN-US style='font-size:10.0pt;color:#006666'><!--[if gte vml 1]><v:shape
 id="_x0000_i1052" type="#_x0000_t75" alt="" style='width:10.5pt;height:10.5pt'>
 <v:imagedata src="./第二章%20光栅图形学.files/image005.gif" o:href="http://learn.bitsde.com/hep/jisuanjituxing/material/CG_Gif_pub_032.gif"/>
</v:shape><![endif]--><![if !vml]><img border=0 width=14 height=14
src="./第二章%20光栅图形学.files/image005.gif" v:shapes="_x0000_i1052"><![endif]></span><span
style='color:#006666'>举例：用中点画线方法扫描转换连接两点<span lang=EN-US>P0（0,0）和P1（5,2）的直线段。</span></span></p>

<p><span lang=EN-US style='font-size:10.0pt'>a=y0-y1=-2; b=x1-x0=5; d0=2*a+b=1;d1=2*a=-4;d2=2*(a+b)=6
,</span></p>

<p><!--[if gte vml 1]><v:shape id="_x0000_s1027" type="#_x0000_t75" alt=""
 style='position:absolute;margin-left:165.5pt;margin-top:0;width:205.5pt;
 height:126pt;z-index:2;mso-wrap-distance-left:0;mso-wrap-distance-right:0;
 mso-position-horizontal:right;mso-position-vertical-relative:line'
 o:allowoverlap="f">
 <v:imagedata src="./第二章%20光栅图形学.files/image010.png" o:title="CG_Gif_2_003"/>
 <w:wrap type="square"/>
</v:shape><![endif]--><![if !vml]><img width=274 height=168
src="./第二章%20光栅图形学.files/image011.gif" align=right v:shapes="_x0000_s1027"><![endif]><span
lang=EN-US style='font-size:10.0pt'>x y&nbsp;&nbsp; d </span></p>

<p><span lang=EN-US style='font-size:10.0pt'>0 0&nbsp;&nbsp; 1 </span></p>

<p><span lang=EN-US style='font-size:10.0pt'>1 0&nbsp;&nbsp; -3</span></p>

<p><span lang=EN-US style='font-size:10.0pt'>2 1&nbsp;&nbsp; 3 </span></p>

<p><span lang=EN-US style='font-size:10.0pt'>3 1&nbsp;&nbsp;
-1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></p>

<p><span lang=EN-US style='font-size:10.0pt'>4 2&nbsp;&nbsp;&nbsp;
5&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&n