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<h1 class="post-title p-name">采样与光栅化</h1>
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<h4 id="屏幕空间"><a href="#屏幕空间" class="anchor-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon anchor-icon"><path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"/></svg></a>屏幕空间</h4>
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<p>屏幕空间可以被看做是由一组像素点构成，每个像素点可以被视为中心为$(x+0.5,y+0.5)$的一个正方形，</p>
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<p><img src="../../images/pixel_and_screen_space.png" alt=""></p>
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<hr>
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<h4 id="模型的面"><a href="#模型的面" class="anchor-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon anchor-icon"><path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"/></svg></a>模型的面</h4>
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<p>大多数模型的面(mesh)以三角形为主（也有一些不同的面）
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选择三角形的原因：</p>
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<ol>
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<li>大多数多边形最终都可以被分割为三角形</li>
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<li>边界清晰，便于判定某个点是否位于面内(与采样有关)</li>
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<li>对于三角形的每个顶点值有清晰的插值方式(质心插值)</li>
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</ol>
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<hr>
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<h4 id="采样的功能光栅化"><a href="#采样的功能光栅化" class="anchor-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon anchor-icon"><path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"/></svg></a>采样的功能（光栅化）</h4>
|
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<p>遍历整个屏幕上所有的像素点，如果某个像素点的中心位于三角形内，则对这个像素点进行采样</p>
|
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<p>伪代码</p>
|
||
<div class="highlight"><div class="chroma">
|
||
<div class="table-container"><table class="lntable"><tr><td class="lntd">
|
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<pre tabindex="0" class="chroma"><code><span class="lnt">1
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</span><span class="lnt">2
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</span><span class="lnt">3
|
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</span></code></pre></td>
|
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<td class="lntd">
|
||
<pre tabindex="0" class="chroma"><code class="language-c++" data-lang="c++"><span class="line"><span class="cl"><span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">x</span> <span class="o">=</span> <span class="mi">0</span> <span class="p">;</span> <span class="n">x</span> <span class="o"><</span> <span class="n">xmax</span><span class="p">;</span> <span class="o">++</span><span class="n">x</span><span class="p">)</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">y</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span> <span class="n">y</span><span class="o"><</span> <span class="n">xmax</span> <span class="p">;</span> <span class="o">++</span><span class="n">y</span><span class="p">)</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="n">image</span><span class="p">[</span><span class="n">x</span><span class="p">][</span><span class="n">y</span><span class="p">]</span> <span class="o">=</span> <span class="n">inside</span><span class="p">(</span><span class="n">tri</span><span class="p">,</span><span class="n">x</span><span class="o">+</span><span class="mf">0.5</span><span class="p">,</span><span class="n">y</span><span class="o">+</span><span class="mf">0.5</span><span class="p">);</span>
|
||
</span></span></code></pre></td></tr></table></div>
|
||
</div>
|
||
</div><p>可视化过程如图</p>
|
||
<p><img src="../../images/sample_progress.png" alt=""></p>
|
||
<hr>
|
||
<h4 id="判断像素点在三角形内部"><a href="#判断像素点在三角形内部" class="anchor-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon anchor-icon"><path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"/></svg></a>判断像素点在三角形内部</h4>
|
||
<p>inside的判断主要由叉乘(cross product)来实现</p>
|
||
<p>计算三角形各边的向量和目标测试点与三角形三个顶点的向量，将各边向量分别与测试点与顶点的向量进行叉乘，得出三个值，如果三个值得符号相同，则目标测试点位于三角形内，相反则测试点在三角形外</p>
|
||
<p>代码实现</p>
|
||
<div class="highlight"><div class="chroma">
|
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<td class="lntd">
|
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<pre tabindex="0" class="chroma"><code class="language-C++" data-lang="C++"><span class="line"><span class="cl"><span class="c1">//判断测试点是否在三角形内
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1"></span><span class="k">static</span> <span class="kt">bool</span> <span class="nf">insideTriangle</span><span class="p">(</span><span class="kt">int</span> <span class="n">x</span><span class="p">,</span> <span class="kt">int</span> <span class="n">y</span><span class="p">,</span> <span class="k">const</span> <span class="n">Vector3f</span><span class="o">*</span> <span class="n">_v</span><span class="p">)</span>
|
||
</span></span><span class="line"><span class="cl"><span class="p">{</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="c1">// TODO : Implement this function to check if the point (x, y) is inside
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1"></span> <span class="c1">// the triangle represented by _v[0], _v[1], _v[2]
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1"></span>
|
||
</span></span><span class="line"><span class="cl"> <span class="c1">//测试点的坐标为(x, y)
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1"></span> <span class="c1">//三角形三点的坐标分别为_v[0], _v[1], _v[2]
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1"></span>
|
||
</span></span><span class="line"><span class="cl"> <span class="c1">//叉乘公式为(x1, y1)X(x2, y2) = x1*y2 - y1*x2
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1"></span>
|
||
</span></span><span class="line"><span class="cl"> <span class="c1">//准备三角形各边的的向量
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1"></span> <span class="n">Eigen</span><span class="o">::</span><span class="n">Vector2f</span> <span class="n">side1</span><span class="p">;</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="n">side1</span> <span class="o"><-</span> <span class="n">_v</span><span class="p">[</span><span class="mi">1</span><span class="p">].</span><span class="n">x</span><span class="p">()</span> <span class="o">-</span> <span class="n">_v</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="n">x</span><span class="p">(),</span> <span class="n">_v</span><span class="p">[</span><span class="mi">1</span><span class="p">].</span><span class="n">y</span><span class="p">()</span> <span class="o">-</span> <span class="n">_v</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="n">y</span><span class="p">();</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="n">Eigen</span><span class="o">::</span><span class="n">Vector2f</span> <span class="n">side2</span><span class="p">;</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="n">side2</span> <span class="o"><-</span> <span class="n">_v</span><span class="p">[</span><span class="mi">2</span><span class="p">].</span><span class="n">x</span><span class="p">()</span> <span class="o">-</span> <span class="n">_v</span><span class="p">[</span><span class="mi">1</span><span class="p">].</span><span class="n">x</span><span class="p">(),</span> <span class="n">_v</span><span class="p">[</span><span class="mi">2</span><span class="p">].</span><span class="n">y</span><span class="p">()</span> <span class="o">-</span> <span class="n">_v</span><span class="p">[</span><span class="mi">1</span><span class="p">].</span><span class="n">y</span><span class="p">();</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="n">Eigen</span><span class="o">::</span><span class="n">Vector2f</span> <span class="n">side3</span><span class="p">;</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="n">side3</span> <span class="o"><-</span> <span class="n">_v</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="n">x</span><span class="p">()</span> <span class="o">-</span> <span class="n">_v</span><span class="p">[</span><span class="mi">2</span><span class="p">].</span><span class="n">x</span><span class="p">(),</span> <span class="n">_v</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="n">y</span><span class="p">()</span> <span class="o">-</span> <span class="n">_v</span><span class="p">[</span><span class="mi">2</span><span class="p">].</span><span class="n">y</span><span class="p">();</span>
|
||
</span></span><span class="line"><span class="cl">
|
||
</span></span><span class="line"><span class="cl"> <span class="c1">//计算测量点和三角形各点连线的向量
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1"></span> <span class="n">Eigen</span><span class="o">::</span><span class="n">Vector2f</span> <span class="n">v1</span><span class="p">;</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="n">v1</span> <span class="o"><-</span> <span class="n">x</span> <span class="o">-</span> <span class="n">_v</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="n">x</span><span class="p">(),</span> <span class="n">y</span> <span class="o">-</span> <span class="n">_v</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="n">y</span><span class="p">();</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="n">Eigen</span><span class="o">::</span><span class="n">Vector2f</span> <span class="n">v2</span><span class="p">;</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="n">v2</span> <span class="o"><-</span> <span class="n">x</span> <span class="o">-</span> <span class="n">_v</span><span class="p">[</span><span class="mi">1</span><span class="p">].</span><span class="n">x</span><span class="p">(),</span> <span class="n">y</span> <span class="o">-</span> <span class="n">_v</span><span class="p">[</span><span class="mi">1</span><span class="p">].</span><span class="n">y</span><span class="p">();</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="n">Eigen</span><span class="o">::</span><span class="n">Vector2f</span> <span class="n">v3</span><span class="p">;</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="n">v3</span> <span class="o"><-</span> <span class="n">x</span> <span class="o">-</span> <span class="n">_v</span><span class="p">[</span><span class="mi">2</span><span class="p">].</span><span class="n">x</span><span class="p">(),</span> <span class="n">y</span> <span class="o">-</span> <span class="n">_v</span><span class="p">[</span><span class="mi">2</span><span class="p">].</span><span class="n">y</span><span class="p">();</span>
|
||
</span></span><span class="line"><span class="cl">
|
||
</span></span><span class="line"><span class="cl"> <span class="c1">//三角形各边的的向量叉乘测量点和三角形各点连线的向量
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1"></span> <span class="kt">float</span> <span class="n">z1</span> <span class="o">=</span> <span class="n">side1</span><span class="p">.</span><span class="n">x</span><span class="p">()</span> <span class="o">*</span> <span class="n">v1</span><span class="p">.</span><span class="n">y</span><span class="p">()</span> <span class="o">-</span> <span class="n">side1</span><span class="p">.</span><span class="n">y</span><span class="p">()</span> <span class="o">*</span> <span class="n">v1</span><span class="p">.</span><span class="n">x</span><span class="p">();</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="kt">float</span> <span class="n">z2</span> <span class="o">=</span> <span class="n">side2</span><span class="p">.</span><span class="n">x</span><span class="p">()</span> <span class="o">*</span> <span class="n">v2</span><span class="p">.</span><span class="n">y</span><span class="p">()</span> <span class="o">-</span> <span class="n">side2</span><span class="p">.</span><span class="n">y</span><span class="p">()</span> <span class="o">*</span> <span class="n">v2</span><span class="p">.</span><span class="n">x</span><span class="p">();</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="kt">float</span> <span class="n">z3</span> <span class="o">=</span> <span class="n">side3</span><span class="p">.</span><span class="n">x</span><span class="p">()</span> <span class="o">*</span> <span class="n">v3</span><span class="p">.</span><span class="n">y</span><span class="p">()</span> <span class="o">-</span> <span class="n">side3</span><span class="p">.</span><span class="n">y</span><span class="p">()</span> <span class="o">*</span> <span class="n">v3</span><span class="p">.</span><span class="n">x</span><span class="p">();</span>
|
||
</span></span><span class="line"><span class="cl">
|
||
</span></span><span class="line"><span class="cl"> <span class="c1">//判断叉乘结果是否有相同的符号
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1"></span> <span class="k">if</span> <span class="p">((</span><span class="n">z1</span> <span class="o">></span> <span class="mi">0</span> <span class="o">&&</span> <span class="n">z2</span> <span class="o">></span> <span class="mi">0</span> <span class="o">&&</span> <span class="n">z3</span> <span class="o">></span> <span class="mi">0</span><span class="p">)</span> <span class="o">||</span> <span class="p">(</span><span class="n">z1</span> <span class="o"><</span> <span class="mi">0</span> <span class="o">&&</span> <span class="n">z2</span> <span class="o"><</span> <span class="mi">0</span> <span class="o">&&</span> <span class="n">z3</span> <span class="o"><</span> <span class="mi">0</span><span class="p">))</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="p">{</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="k">return</span> <span class="nb">true</span><span class="p">;</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="p">}</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="k">else</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="p">{</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="k">return</span> <span class="nb">false</span><span class="p">;</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="p">}</span>
|
||
</span></span><span class="line"><span class="cl"><span class="p">}</span>
|
||
</span></span></code></pre></td></tr></table></div>
|
||
</div>
|
||
</div><h4 id="加速算法"><a href="#加速算法" class="anchor-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon anchor-icon"><path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"/></svg></a>加速算法</h4>
|
||
<h5 id="bounding-box"><a href="#bounding-box" class="anchor-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon anchor-icon"><path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"/></svg></a>Bounding box</h5>
|
||
<p>每一次判断屏幕上的像素点是否在三角形内都检测所有在屏幕上像素点会带来额外的性能开销和渲染时间</p>
|
||
<p>使用包围盒将三角形包围后，只判断包围盒内的像素点是否在三角形内能够减少这种情况的出现</p>
|
||
<p><img src="../../images/BoundingBox.png" alt=""></p>
|
||
<p>代码实例</p>
|
||
<div class="highlight"><div class="chroma">
|
||
<div class="table-container"><table class="lntable"><tr><td class="lntd">
|
||
<pre tabindex="0" class="chroma"><code><span class="lnt">1
|
||
</span><span class="lnt">2
|
||
</span><span class="lnt">3
|
||
</span><span class="lnt">4
|
||
</span><span class="lnt">5
|
||
</span><span class="lnt">6
|
||
</span></code></pre></td>
|
||
<td class="lntd">
|
||
<pre tabindex="0" class="chroma"><code class="language-c++" data-lang="c++"><span class="line"><span class="cl"> <span class="k">auto</span> <span class="n">v</span> <span class="o">=</span> <span class="n">t</span><span class="p">.</span><span class="n">toVector4</span><span class="p">();</span><span class="c1">//包含三角形三个顶点的结构体
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1">//利用三角形的三个顶点，计算三角形的包围盒
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1"></span> <span class="kt">float</span> <span class="n">min_x</span> <span class="o">=</span> <span class="n">std</span><span class="o">::</span><span class="n">min</span><span class="p">(</span><span class="n">v</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="n">x</span><span class="p">(),</span> <span class="n">std</span><span class="o">::</span><span class="n">min</span><span class="p">(</span><span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">].</span><span class="n">x</span><span class="p">(),</span> <span class="n">v</span><span class="p">[</span><span class="mi">2</span><span class="p">].</span><span class="n">x</span><span class="p">()));</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="kt">float</span> <span class="n">max_x</span> <span class="o">=</span> <span class="n">std</span><span class="o">::</span><span class="n">max</span><span class="p">(</span><span class="n">v</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="n">x</span><span class="p">(),</span> <span class="n">std</span><span class="o">::</span><span class="n">max</span><span class="p">(</span><span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">].</span><span class="n">x</span><span class="p">(),</span> <span class="n">v</span><span class="p">[</span><span class="mi">2</span><span class="p">].</span><span class="n">x</span><span class="p">()));</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="kt">float</span> <span class="n">min_y</span> <span class="o">=</span> <span class="n">std</span><span class="o">::</span><span class="n">min</span><span class="p">(</span><span class="n">v</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="n">y</span><span class="p">(),</span> <span class="n">std</span><span class="o">::</span><span class="n">min</span><span class="p">(</span><span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">].</span><span class="n">y</span><span class="p">(),</span> <span class="n">v</span><span class="p">[</span><span class="mi">2</span><span class="p">].</span><span class="n">y</span><span class="p">()));</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="kt">float</span> <span class="n">max_y</span> <span class="o">=</span> <span class="n">std</span><span class="o">::</span><span class="n">max</span><span class="p">(</span><span class="n">v</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="n">y</span><span class="p">(),</span> <span class="n">std</span><span class="o">::</span><span class="n">max</span><span class="p">(</span><span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">].</span><span class="n">y</span><span class="p">(),</span> <span class="n">v</span><span class="p">[</span><span class="mi">2</span><span class="p">].</span><span class="n">y</span><span class="p">()));</span>
|
||
</span></span></code></pre></td></tr></table></div>
|
||
</div>
|
||
</div><h5 id="incremental-triangle-traversal"><a href="#incremental-triangle-traversal" class="anchor-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon anchor-icon"><path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"/></svg></a>incremental triangle Traversal</h5>
|
||
<p>对于每一行像素点，只遍历三角形最左到最右的像素点，只适用于较窄的且经过旋转的三角形</p>
|
||
<p><img src="../../images/IncrementalTriangleTraversal.png" alt=""></p>
|
||
|
||
</div>
|
||
|
||
|
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|
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</article>
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<div class="updated-badge-container">
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<span title="Updated @ 2023-06-18 21:19:01 CST" style="cursor:help">
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<svg xmlns="http://www.w3.org/2000/svg" width="130" height="20" class="updated-badge"><linearGradient id="b" x2="0" y2="100%"><stop offset="0" stop-color="#bbb" stop-opacity=".1"/><stop offset="1" stop-opacity=".1"/></linearGradient><clipPath id="a"><rect width="130" height="20" rx="3" fill="#fff"/></clipPath><g clip-path="url(#a)"><path class="updated-badge-left" d="M0 0h55v20H0z"/><path class="updated-badge-right" d="M55 0h75v20H55z"/><path fill="url(#b)" d="M0 0h130v20H0z"/></g><g fill="#fff" text-anchor="middle" font-size="110"><text x="285" y="150" fill="#010101" fill-opacity=".3" textLength="450" transform="scale(.1)">updated</text><text x="285" y="140" textLength="450" transform="scale(.1)">updated</text><text x="915" y="150" fill="#010101" fill-opacity=".3" textLength="650" transform="scale(.1)">2023-06-18</text><text x="915" y="140" textLength="650" transform="scale(.1)">2023-06-18</text></g></svg>
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