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面包屑導航結束 --> <!-- 頁面標題開始 --> <div id="n1l1njb9b" class="title"> <h3><a>如何在編程時運用曲線方程<small></small></a></h3> </div> <!-- 頁面標題結束 --> <hr class="featurette-divider"> <!-- 中部開始 --> <div id="n1l1njb9b" class="container"> <!-- 正文 --> <div id="n1l1njb9b" class="lead" id="print"> <p> <span style="font-family: 宋體;">一、</span> <span style="font-family: 宋體;">一般曲線和非圓曲線標準方程</span></p> <p class="MsoNormal"><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">通常非圓曲線是指橢圓、</span> <span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">雙曲線、</span> <span style="font-family:宋體;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">拋物線及一般曲線</span><span lang="EN-US">(</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">圓或者直線</span><span lang="EN-US"> ),</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">在數學上它們都有其標準方程</span><span lang="EN-US">,</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">在數控加工過程中通常采用參數方程式進行編程</span><span lang="EN-US">.</span></p> <p class="MsoNormal"><span lang="EN-US"><img src="/upload/images/201406/14034491073281.jpg" alt="" /><br /> <!--[endif]--></span></p> <p class="MsoNormal"><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">二、</span> <span style="font-family: 宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">曲線的兩種方程形式</span></p> <p class="MsoNormal"><span lang="EN-US">1 1</span><span style="font-family:宋體; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">曲線的普通方程</span><span lang="EN-US">. </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">相對于參數方程來說</span><span lang="EN-US">,</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">把直接確定曲線</span><span lang="EN-US"> C</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">上任一點的坐標</span><span lang="EN-US"> ( x , y)</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">的方程</span><span lang="EN-US"> F( x, y ) = 0</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">叫做曲線</span><span lang="EN-US">C</span><span style="font-family: 宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">的普通方程</span><span lang="EN-US">.</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">任</span></p> <p><img src="/upload/images/201406/14034491182692.jpg" alt="" /></p> <p class="MsoNormal"><span lang="EN-US"> </span><span style="font-family:宋體;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">并且對于</span><span lang="EN-US"> t</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">的每一個允許值</span><span lang="EN-US">, </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">由方程組</span><span lang="EN-US"> ( 1)</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">所確定的點</span><span lang="EN-US"> M( x, y)</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">都在這條曲線上</span><span lang="EN-US">,</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">那么方程組</span><span lang="EN-US"> ( 1)</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">叫做這條曲線的參數方程</span><span lang="EN-US">. </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">聯系</span><span lang="EN-US"> x , y</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">之間關系的變數叫做參變數</span><span lang="EN-US">, </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">簡稱參數</span><span lang="EN-US">.</span></p> <p class="MsoNormal"><span lang="EN-US">3 1</span><span style="font-family:宋體; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">求曲線的參數方程</span><span lang="EN-US">. </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">求曲線參數方程一般程序</span><span lang="EN-US">:</span></p> <p class="MsoNormal"><span lang="EN-US">( 1)</span><span style="font-family:宋體; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">設點</span><span lang="EN-US">: </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">建立適當的直角坐標系</span><span lang="EN-US">,</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">用</span><span lang="EN-US"> ( x , y)</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">表示曲線上任意一點</span><span lang="EN-US"> M </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">的坐標</span><span lang="EN-US">;</span></p> <p class="MsoNormal"><span lang="EN-US">( 2)</span><span style="font-family:宋體; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">選參</span><span lang="EN-US">: </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">選擇合適的參數</span><span lang="EN-US">;</span></p> <p class="MsoNormal"><span lang="EN-US">( 3)</span><span style="font-family:宋體; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">表示</span><span lang="EN-US">:</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">依據題設、</span> <span style="font-family: 宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">參數的幾何或物理意義</span><span lang="EN-US">,</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">建立參數與</span><span lang="EN-US">x , y</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">的關系式</span><span lang="EN-US">,</span><span style="font-family: 宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">并由此分別解出用參數表示的</span><span lang="EN-US"> x , y</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">的表達式</span><span lang="EN-US">.</span></p> <p class="MsoNormal"><span lang="EN-US">( 4)</span><span style="font-family:宋體; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">結論</span><span lang="EN-US">: </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">用參數方程的形式表示曲線的方程</span><span lang="EN-US">.</span></p> <p class="MsoNormal"><span lang="EN-US"><img src="/upload/images/201406/14034491304977.jpg" alt="" /><br /> <!--[endif]--></span></p> <p class="MsoNormal"><span lang="EN-US"><img src="/upload/images/201406/14034491422482.jpg" alt="" /><br /> <!--[endif]--></span></p> <p class="MsoNormal"><span lang="EN-US"><img src="/upload/images/201406/14034491710553.jpg" alt="" /><br /> <!--[endif]--></span></p> <p class="MsoNormal"><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">從上面實例可以看出曲線方程不管是采用普通方程還是參數方程都必須先指一個自變量</span><span lang="EN-US">, </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">然后寫出應變量的方程式</span><span lang="EN-US">,</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">再進行宏程序的編寫方便快捷</span><span lang="EN-US">.</span></p> <p class="MsoNormal" align="center" style="margin-top:4.5pt;margin-right:0cm; margin-bottom:7.5pt;margin-left:0cm;text-align:center;line-height:13.5pt; mso-pagination:widow-orphan;mso-outline-level:1"><b><span style="mso-bidi-font-size: 10.5pt;font-family:宋體;mso-bidi-font-family:宋體;color:#666666;mso-font-kerning: 0pt">本文由<span lang="EN-US"> <a ><span lang="EN-US" 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