OpenGL实现Bezier曲线的方法示例

Bezier曲线的形状是通过一组多边折线（特征多边形）的各顶点唯一地定义出来的。在这组顶点中：
(1)只有第一个顶点和最后一个顶点在曲线上；
(2)其余的顶点则用于定义曲线的导数、阶次和形状；
(3)第一条边和最后一条边则表示了曲线在两端点处的切线方向。

// BezierCurve.cpp : 定义控制台应用程序的入口点。
//
#include "stdafx.h"</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="4"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">#include <span class="hljs-tag"><<span class="hljs-name">gl</span>/<span class="hljs-attr">glut.h</span>></span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="5"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">#include <span class="hljs-tag"><<span class="hljs-name">gl</span>/<span class="hljs-attr">GL.h</span>></span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="6"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">#define DIMENSION 2//定义维度为2维</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="7"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">typedef GLfloat VECTOR [DIMENSION];</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="8"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">VECTOR points[4]= {{-1.0,-1.0},{0.0,2.0},{1.0,2.0},{2.0,1.0}};//四个控制点</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="9"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">GLint count =10000;//绘制10000个点</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="10"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">int ww,hh;</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="11"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">void display()</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="12"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">{</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="13"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> VECTOR c[4];//此矩阵是P和M的积，就是控制点阵和Bezier基矩阵的乘积</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="14"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> for (int i =0;i<span class="hljs-tag"><<span class="hljs-name">DIMENSION;i++)</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="15"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> {</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="16"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="17"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">c</span>[<span class="hljs-attr">3</span>][<span class="hljs-attr">i</span>] = <span class="hljs-string">(0-points[0][i])+3*points[1][i]-3*points[2][i]+points[3][i];</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="18"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">c</span>[<span class="hljs-attr">2</span>][<span class="hljs-attr">i</span>] =       <span class="hljs-string">3*points[0][i]-6*points[1][i]+3*points[2][i];</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="19"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">c</span>[<span class="hljs-attr">1</span>][<span class="hljs-attr">i</span>] =               <span class="hljs-string">(0-3*points[0][i])+3*points[1][i];</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="20"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">c</span>[<span class="hljs-attr">0</span>][<span class="hljs-attr">i</span>] =                       <span class="hljs-string">points[0][i];</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="21"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="22"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="23"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="24"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> }</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="25"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">GLfloat</span> <span class="hljs-attr">v</span>[<span class="hljs-attr">DIMENSION</span>];</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="26"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">GLfloat</span> <span class="hljs-attr">newV</span>[<span class="hljs-attr">DIMENSION</span>];</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="27"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">GLfloat</span> <span class="hljs-attr">deltat</span> = <span class="hljs-string">1.0/count;</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="28"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">GLfloat</span> <span class="hljs-attr">t</span> = <span class="hljs-string">0.0;</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="29"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="30"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="31"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glBegin</span>(<span class="hljs-attr">GL_LINE_STRIP</span>);//绘制控制曲线</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="32"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">  <span class="hljs-attr">glVertex2fv</span>(<span class="hljs-attr">points</span>[<span class="hljs-attr">0</span>]);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="33"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">  <span class="hljs-attr">glVertex2fv</span>(<span class="hljs-attr">points</span>[<span class="hljs-attr">1</span>]);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="34"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">  <span class="hljs-attr">glVertex2fv</span>(<span class="hljs-attr">points</span>[<span class="hljs-attr">2</span>]);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="35"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">  <span class="hljs-attr">glVertex2fv</span>(<span class="hljs-attr">points</span>[<span class="hljs-attr">3</span>]);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="36"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glEnd</span>();</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="37"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glFlush</span>();</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="38"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">  </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="39"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">v</span>[<span class="hljs-attr">0</span>] = <span class="hljs-string">points[0][0];v[1]</span> = <span class="hljs-string">points[0][1];</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="40"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">for</span> (<span class="hljs-attr">int</span> <span class="hljs-attr">i</span> = <span class="hljs-string">0;i</span><<span class="hljs-attr">count</span>;<span class="hljs-attr">i</span>++)//绘制最终结果</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="41"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> {</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="42"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">t</span> += <span class="hljs-string">deltat;</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="43"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">newV</span>[<span class="hljs-attr">0</span>] = <span class="hljs-string">c[0][0]</span> + <span class="hljs-attr">t</span>*(<span class="hljs-attr">c</span>[<span class="hljs-attr">1</span>][<span class="hljs-attr">0</span>] + <span class="hljs-attr">t</span>*(<span class="hljs-attr">c</span>[<span class="hljs-attr">2</span>][<span class="hljs-attr">0</span>] + <span class="hljs-attr">t</span>*<span class="hljs-attr">c</span>[<span class="hljs-attr">3</span>][<span class="hljs-attr">0</span>]));</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="44"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">newV</span>[<span class="hljs-attr">1</span>] = <span class="hljs-string">c[0][1]</span> + <span class="hljs-attr">t</span>*(<span class="hljs-attr">c</span>[<span class="hljs-attr">1</span>][<span class="hljs-attr">1</span>] + <span class="hljs-attr">t</span>*(<span class="hljs-attr">c</span>[<span class="hljs-attr">2</span>][<span class="hljs-attr">1</span>] + <span class="hljs-attr">t</span>*<span class="hljs-attr">c</span>[<span class="hljs-attr">3</span>][<span class="hljs-attr">1</span>]));</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="45"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glColor3f</span>(<span class="hljs-attr">0.0</span>,<span class="hljs-attr">0.0</span>,<span class="hljs-attr">1.0</span>);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="46"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glBegin</span>(<span class="hljs-attr">GL_LINES</span>);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="47"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glVertex2fv</span>(<span class="hljs-attr">v</span>);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="48"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glVertex2fv</span>(<span class="hljs-attr">newV</span>);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="49"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glEnd</span>();</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="50"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glFlush</span>();</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="51"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">v</span>[<span class="hljs-attr">0</span>] = <span class="hljs-string">newV[0];v[1]</span> = <span class="hljs-string">newV[1];</span></div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="52"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="53"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="54"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> }</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="55"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="56"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">}</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="57"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-attr">void</span> <span class="hljs-attr">init</span>()</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="58"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">{</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="59"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="60"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glClearColor</span>(<span class="hljs-attr">0.0</span> , <span class="hljs-attr">0.0</span> ,<span class="hljs-attr">0.0</span> , <span class="hljs-attr">0.0</span>);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="61"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glColor3f</span>(<span class="hljs-attr">1.0</span> ,<span class="hljs-attr">1.0</span> ,<span class="hljs-attr">1.0</span>);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="62"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="63"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glMatrixMode</span>(<span class="hljs-attr">GL_PROJECTION</span>);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="64"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glLoadIdentity</span>();</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="65"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">gluOrtho2D</span>(<span class="hljs-attr">-4.0</span> ,<span class="hljs-attr">4.0</span> ,<span class="hljs-attr">-4.0</span> ,<span class="hljs-attr">4.0</span>);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="66"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="67"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">}</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="68"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="69"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"><span class="hljs-attr">void</span> <span class="hljs-attr">main</span>(<span class="hljs-attr">int</span> <span class="hljs-attr">argc</span>,<span class="hljs-attr">char</span> **<span class="hljs-attr">argv</span>)</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="70"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">{</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="71"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glutInit</span>(&<span class="hljs-attr">argc</span>,<span class="hljs-attr">argv</span>);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="72"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glutInitDisplayMode</span>(<span class="hljs-attr">GLUT_SINGLE</span>|<span class="hljs-attr">GLUT_RGB</span>);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="73"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glutInitWindowSize</span>(<span class="hljs-attr">500</span>,<span class="hljs-attr">500</span>);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="74"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glutInitWindowPosition</span>(<span class="hljs-attr">500</span>,<span class="hljs-attr">200</span>);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="75"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glutCreateWindow</span>("<span class="hljs-attr">reshape</span>");</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="76"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> //<span class="hljs-attr">glutReshapeFunc</span>(<span class="hljs-attr">myreshape</span>);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="77"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glutDisplayFunc</span>(<span class="hljs-attr">display</span>);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="78"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">init</span>();</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="79"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> //<span class="hljs-attr">glutIdleFunc</span>(<span class="hljs-attr">myidle</span>);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="80"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> //<span class="hljs-attr">glutKeyboardFunc</span>(<span class="hljs-attr">mykeyboard</span>);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="81"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> //<span class="hljs-attr">glutSpecialFunc</span>(<span class="hljs-attr">myspecialkey</span>);</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="82"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> </div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="83"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line"> <span class="hljs-attr">glutMainLoop</span>();</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="84"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">}</div></div></li><li><div class="hljs-ln-numbers"><div class="hljs-ln-line hljs-ln-n" data-line-number="85"></div></div><div class="hljs-ln-code"><div class="hljs-ln-line">
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