c080200.htm

计算机图形学的课件,让你学习不在无所适从.想学的就看看吧,回有用的.

    <p align="left"><font size="4"><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA" lang="EN-US">2. 
    第i个曲线段求导数：</span></font></p>
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    <img src="C80208.gif" v:shapes="_x0000_i1025" width="197" height="85"></span></span></p>
    <p align="left"><font size="4"><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA" lang="EN-US">第i个曲线段与第i+1个曲线段一定是光滑的。</span></font></p>
    <p align="center"><img border="0" src="C080208.gif" width="234" height="151"><span lang="EN-US" style="font-size:10.5pt;mso-bidi-font-size:
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    <p align="left"><font size="4"><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><!--[if gte mso 9]><xml>
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</xml><![endif]--><b><font color="#FFFF00">三次</font><a name="#B_Spline曲线的性质"><font color="#FFFF00">B_Spline曲线的性质</font></a></b>
    </span></font></p>
    <p align="left"><font size="4" color="#000000"><span lang="EN-US"><b><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">1. 
    一般地，曲线不通过任何控制点，但若没多重点，则可以使曲线通过某个控制点。</span></b></span></font></p>
    <p align="left"><font size="4" color="#000000"><span lang="EN-US"><b><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">2. 
    曲线在控制点确定的凸包内，且比Bezier曲线更逼近由控制点决定地折线。</span></b></span></font></p>
    <p align="left"><font size="4" color="#000000"><span lang="EN-US"><b><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">3. 
    可以局部修改，修改P<sub>i</sub>控制点，只影响与P<sub>i</sub>相关地四个曲线段P<sub>i-3</sub>(t),P<sub>i-2</sub>(t),P<sub>i-1</sub>(t),P<sub>i</sub>(t)。</span></b></span></font></p>
    <p align="left"><font size="4" color="#000000"><span lang="EN-US"><b><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">4. 
    每增加一个控制点，则增加一个曲线段。</span></b></span></font></p>
    <p align="left"><b><font color="#FFFF00" size="4"><a name="#三次周期性B_Spline曲线分段方法"> 三次周期性<font face="Times New Roman">B_Spline</font>曲线</a>分段方法</font></b></p>
    <p align="left"><b><font size="4" color="#000000">设有n+1个控制点P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>0</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>1</sub></span></b></font><b><font size="4" color="#000000">...P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>n</sub></span></b></font></p>
    <p align="left"><font size="4" color="#000000"><b><span lang="EN-US"><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>三次周期性分段可以是：</sub></span></span></b></font></p>
    <p align="left"><font size="4" color="#000000"><b><span lang="EN-US"><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>第0</sub><sub>段的四个控制点：</sub></span></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>0</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>1</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>2</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>3</sub></span></b></font></p>
    <p align="left"><font size="4" color="#000000"><b><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA" lang="EN-US"><sub>第1</sub><sub>段的四个控制点：</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>1</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>2</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>3</sub></span></b></font><b><font size="4" color="#000000">P<span lang="EN-US"><sub><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">4</span></sub></span></font></b></p>
    <p align="left"><font size="4" color="#000000"><b><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA" lang="EN-US"><sub>第2</sub><sub>段的四个控制点：</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>2</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>3</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>4</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>5</sub></span></b></font></p>
    <p align="left"><font size="4" color="#000000"><b><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA" lang="EN-US"><sub>第i</sub><sub>段的四个控制点：</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>i</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>i+1</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>i+2</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>i+3</sub></span></b></font></p>
    <p align="left"><font size="4" color="#000000"><b><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA" lang="EN-US"><sub>第i+1</sub><sub>段的四个控制点：</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>i+1</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>i+2</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>i+3</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>i+4</sub></span></b></font></p>
    <p align="left"><font size="4" color="#000000"><b><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA" lang="EN-US"><sub>第n-3</sub><sub>段的四个控制点：</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>n-3</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>n-2</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>n-1</sub></span></b></font><b><font size="4" color="#000000">P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>n</sub></span></b></font></p>
    <p align="left"><font size="4"><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><b><!--[if gte mso 9]><xml>
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</xml><![endif]--><font color="#000000">共有n-2个曲线段。曲线段之间有三个公共点。</font></b></span></font></p>
    <p align="left"><font size="4"><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><b><font color="#FFFF00">三次</font><a name="#B_Spline曲线的特殊情况"><font color="#FFFF00">B_Spline曲线的特殊情况</font></a></b></span></font><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><font size="4"><!--[if gte mso 9]><xml>
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        <td width="59%"><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><font size="4"><b>1.三个控制点共线,曲线在直线上</b></font></span></td>
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          <p align="center"><img border="0" src="C080209.gif" width="173" height="64"></td>
      </tr>
      <tr>
        <td width="59%"><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><font size="4"><b><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">2</span></b></font></span><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><font size="4"><b>.四个控制点共线,曲线上有一条直线段</b></font></span></td>
        <td width="41%">
          <p align="center"><img border="0" src="C080210.gif" width="173" height="64"></td>
      </tr>
      <tr>
        <td width="59%"><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><font size="4"><b>3.两个控制点重点,曲线更逼近</b></font></span></td>
        <td width="41%">
          <p align="center"><img border="0" src="C080211.gif" width="144" height="109"></td>
      </tr>
      <tr>
        <td width="59%"><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><font size="4"><b>4. 
          三个控制点共点（三重点），曲线上有尖角</b></font></span></td>
        <td width="41%">
          <p align="center"><img border="0" src="C080212.gif" width="129" height="87"></td>
      </tr>
    </table>
    <p align="left"><font size="4"><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><span style="mso-text-raise:-7.0pt"><!--[if gte mso 9]><xml>
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 </o:OLEObject>
</xml><![endif]--></span><!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1025"
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</xml><![endif]-->思考：对用n+1个控制点拟合的B_Spline曲线，如何使曲线通过</span></font><font size="4" color="#000000"><b>P<span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>0</sub></span></b></font><b><font size="4" color="#000000"><span lang="EN-US"><sub><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">,</span></sub></span>P</font></b><font size="4" color="#000000"><b><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><sub>n</sub></span></b></font><font size="4"><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA" lang="EN-US">控制点？</span></font></p>
    <p align="left"><font size="4"><span lang="EN-US" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">&nbsp;
    </span><b><span style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA" lang="EN-US"><font color="#FFFF00"><a name="#双三次B_Spline曲面">双三次B_Spline曲面</a></font></span></b></font></p>
    <p align="center"><span lang="EN-US" style="font-size:10.5pt;mso-bidi-font-size:
12.0pt;font-family:&quot;Times New Roman&quot;;mso-fareast-font-family:宋体;mso-font-kerning:
1.0pt;mso-ansi-language:EN-US;mso-fareast-language:ZH-CN;mso-bidi-language:
AR-SA"><span style="mso-text-raise:-15.0pt"><!--[if gte vml 1]><v:shapetype
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  <v:f eqn="sum @0 1 0"/>
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  <v:f eqn="prod @2 1 2"/>
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  <v:f eqn="sum @0 0 1"/>
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  <v:f eqn="sum @8 21600 0"/>
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  <v:f eqn="sum @10 21600 0"/>
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    <img src="C80209.gif" v:shapes="_x0000_i1025" width="317" height="48"></span></span></p>
    <p align="left"><font size="4"><span style="mso-text-raise: -15.0pt; mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA" lang="EN-US"><span style="mso-text-raise: -15.0pt; mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">两个曲面片之间有12个公共点。每增加四个控制点，则增加一个曲面</span>片。</span></font></p>
    <p align="center"><span lang="EN-US" style="font-size:10.5pt;mso-bidi-font-size:
12.0pt;font-family:&quot;Times New Roman&quot;;mso-fareast-font-family:宋体;mso-font-kerning:
1.0pt;mso-ansi-language:EN-US;mso-fareast-language:ZH-CN;mso-bidi-language:
AR-SA"><img border="0" src="Image555.gif" width="313" height="348"></span></p>
  </div>
    </td>
</tr>
</table>
</div>
<p>　</p>
<p>　</p>
<p>　</p>
<p class="MsoNormal">　</p>
<p class="MsoNormal">　</p>

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