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<h1 class="post-title p-name">纹理映射</h1>
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<h4 id="重心坐标"><a href="#重心坐标" 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>重心坐标</h4>
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<h6 id="重心坐标定义"><a href="#重心坐标定义" 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>重心坐标定义</h6>
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<p><img src="/../../images/barycentric_coordinates.png" alt=""></p>
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<p>对于一个三角形的三点坐标A,B,C,平面内的一点（x,y）可以写成三点的线性组合式</p>
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<p>$$(x,y)=\alpha A + \beta B + \gamma C = \alpha + \beta + \gamma = 1$$</p>
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<p>此时三个顶点的权重（$\alpha , \beta , \gamma$）为（x,y）的重心坐标</p>
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<p>注意：如果三个坐标值都为非负，则这个重心位于三角形内部</p>
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<h6 id="三角形的几何角度下求解"><a href="#三角形的几何角度下求解" 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>三角形的几何角度下求解</h6>
|
||
<p><img src="../../images/geometric_barycentric.png" alt=""></p>
|
||
<p>将点与三个顶点相连，三个三角形的面积分别为$A_A,A_B,A_C$对应的重心坐标的计算式,</p>
|
||
<p>$$\alpha = \frac{A_A}{A_A+A_B+A_C}$$</p>
|
||
<p>$$\beta = \frac{A_B}{A_A+A_B+A_C}$$</p>
|
||
<p>$$\gamma = \frac{A_C}{A_A+A_B+A_C}$$</p>
|
||
<p>在已知四点坐标的情况下则可通过行列式的几何意义求解（任意两个二维向量组合成矩阵的行列式的绝对值为这两条向量所围成平行四边形的面积）</p>
|
||
<p>设任意一点为P(x,y)则</p>
|
||
<p>$$A_B = \lvert AP,AC \rvert $$
|
||
$$A_C = \lvert AB,AP \rvert $$
|
||
$$A_A = \lvert BC,BP \rvert $$</p>
|
||
<p>可得出
|
||
$$\gamma = \frac{(y_a - y_b) + (x_b - x_a)y + x_a y_b - x_b y_a }{(y_a - y_b)x_c + (x_b - x_a)y_c + x_a y_b - x_b y_a}$$</p>
|
||
<p>$$\beta = \frac{(y_a - y_c)x + (x_c - x_a)y + x_a y_c - x_c y_a}{(y_a - y_c)x_b + (x_c - x_a)y_b + x_a y_c - x_c y_a}$$</p>
|
||
<p>$$\alpha = 1 - \beta - \gamma$$</p>
|
||
<h6 id="三角形的坐标系角度下求解"><a href="#三角形的坐标系角度下求解" 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>三角形的坐标系角度下求解</h6>
|
||
<p>对于重心坐标系存在另一种等价视角：</p>
|
||
<p>以A点为原点，AB,AC分别为新的坐标系的单位向量构建坐标系，如图</p>
|
||
<p><img src="../../images/barycentric_in_coordinates.jpg" alt=""></p>
|
||
<p>给定的任意点P的坐标可表示为$P(\beta , \gamma)$ ,可推出P点坐标满足以下关系</p>
|
||
<p>$$p = a + \beta(b - a) + \gamma(c - a)$$</p>
|
||
<p>化简后得</p>
|
||
<p>$$p = (1 - \beta - \gamma )a + \beta b + \gamma c $$</p>
|
||
<p>表现为一个线性方程组如下</p>
|
||
<p>$$
|
||
\begin{bmatrix}
|
||
x_b - x_a & x_c - x_a
|
||
\\
|
||
y_b - y_a & y_c - y_a
|
||
\end{bmatrix}
|
||
\begin{bmatrix}
|
||
\beta
|
||
\\
|
||
\gamma
|
||
\end{bmatrix}=
|
||
\begin{bmatrix}
|
||
x_p - x_a
|
||
\\
|
||
y_p - y_a
|
||
\end{bmatrix}
|
||
$$</p>
|
||
<h6 id="重心坐标的用处"><a href="#重心坐标的用处" 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>重心坐标的用处</h6>
|
||
<p>对顶点处的值进行线性插值，如下图</p>
|
||
<p><img src="../../images/barycentric_coor_interpo.png" alt=""></p>
|
||
<p>$$V = \alpha V_A + \beta V_B + \gamma V_C$$</p>
|
||
<p>$V_A,V_B,V_C$ 可以对应为：</p>
|
||
<ol>
|
||
<li>位置</li>
|
||
<li>纹理坐标</li>
|
||
<li>颜色</li>
|
||
<li>法线</li>
|
||
<li>深度</li>
|
||
<li>材质属性</li>
|
||
</ol>
|
||
<h6 id="插值部分代码实现"><a href="#插值部分代码实现" 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>插值部分代码实现</h6>
|
||
<div class="highlight"><div class="chroma">
|
||
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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="c1">//三维向量插值
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1"></span><span class="k">static</span> <span class="n">Eigen</span><span class="o">::</span><span class="n">Vector3f</span> <span class="n">interpolate</span><span class="p">(</span><span class="kt">float</span> <span class="n">alpha</span><span class="p">,</span> <span class="kt">float</span> <span class="n">beta</span><span class="p">,</span> <span class="kt">float</span> <span class="n">gamma</span><span class="p">,</span> <span class="k">const</span> <span class="n">Eigen</span><span class="o">::</span><span class="n">Vector3f</span><span class="o">&</span> <span class="n">vert1</span><span class="p">,</span> <span class="k">const</span> <span class="n">Eigen</span><span class="o">::</span><span class="n">Vector3f</span><span class="o">&</span> <span class="n">vert2</span><span class="p">,</span> <span class="k">const</span> <span class="n">Eigen</span><span class="o">::</span><span class="n">Vector3f</span><span class="o">&</span> <span class="n">vert3</span><span class="p">,</span> <span class="kt">float</span> <span class="n">weight</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="p">(</span><span class="n">alpha</span> <span class="o">*</span> <span class="n">vert1</span> <span class="o">+</span> <span class="n">beta</span> <span class="o">*</span> <span class="n">vert2</span> <span class="o">+</span> <span class="n">gamma</span> <span class="o">*</span> <span class="n">vert3</span><span class="p">)</span> <span class="o">/</span> <span class="n">weight</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></span><span class="line"><span class="cl"><span class="c1">// 二维向量插值
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1"></span><span class="k">static</span> <span class="n">Eigen</span><span class="o">::</span><span class="n">Vector2f</span> <span class="n">interpolate</span><span class="p">(</span><span class="kt">float</span> <span class="n">alpha</span><span class="p">,</span> <span class="kt">float</span> <span class="n">beta</span><span class="p">,</span> <span class="kt">float</span> <span class="n">gamma</span><span class="p">,</span> <span class="k">const</span> <span class="n">Eigen</span><span class="o">::</span><span class="n">Vector2f</span><span class="o">&</span> <span class="n">vert1</span><span class="p">,</span> <span class="k">const</span> <span class="n">Eigen</span><span class="o">::</span><span class="n">Vector2f</span><span class="o">&</span> <span class="n">vert2</span><span class="p">,</span> <span class="k">const</span> <span class="n">Eigen</span><span class="o">::</span><span class="n">Vector2f</span><span class="o">&</span> <span class="n">vert3</span><span class="p">,</span> <span class="kt">float</span> <span class="n">weight</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">auto</span> <span class="n">u</span> <span class="o">=</span> <span class="p">(</span><span class="n">alpha</span> <span class="o">*</span> <span class="n">vert1</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">beta</span> <span class="o">*</span> <span class="n">vert2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">gamma</span> <span class="o">*</span> <span class="n">vert3</span><span class="p">[</span><span class="mi">0</span><span class="p">]);</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="k">auto</span> <span class="n">v</span> <span class="o">=</span> <span class="p">(</span><span class="n">alpha</span> <span class="o">*</span> <span class="n">vert1</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">beta</span> <span class="o">*</span> <span class="n">vert2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">gamma</span> <span class="o">*</span> <span class="n">vert3</span><span class="p">[</span><span class="mi">1</span><span class="p">]);</span>
|
||
</span></span><span class="line"><span class="cl">
|
||
</span></span><span class="line"><span class="cl"> <span class="n">u</span> <span class="o">/=</span> <span class="n">weight</span><span class="p">;</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="n">v</span> <span class="o">/=</span> <span class="n">weight</span><span class="p">;</span>
|
||
</span></span><span class="line"><span class="cl">
|
||
</span></span><span class="line"><span class="cl"> <span class="k">return</span> <span class="n">Eigen</span><span class="o">::</span><span class="n">Vector2f</span><span class="p">(</span><span class="n">u</span><span class="p">,</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">//计算重心
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1"></span><span class="k">static</span> <span class="n">std</span><span class="o">::</span><span class="n">tuple</span><span class="o"><</span><span class="kt">float</span><span class="p">,</span> <span class="kt">float</span><span class="p">,</span> <span class="kt">float</span><span class="o">></span> <span class="n">computeBarycentric2D</span><span class="p">(</span><span class="kt">float</span> <span class="n">x</span><span class="p">,</span> <span class="kt">float</span> <span class="n">y</span><span class="p">,</span> <span class="k">const</span> <span class="n">Vector4f</span><span class="o">*</span> <span class="n">v</span><span class="p">){</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="kt">float</span> <span class="n">c1</span> <span class="o">=</span> <span class="p">(</span><span class="n">x</span><span class="o">*</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">2</span><span class="p">].</span><span class="n">y</span><span class="p">())</span> <span class="o">+</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 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">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">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">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">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">y</span><span class="p">())</span> <span class="o">/</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="o">*</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">2</span><span class="p">].</span><span class="n">y</span><span class="p">())</span> <span class="o">+</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 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">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">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">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">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">y</span><span class="p">());</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="kt">float</span> <span class="n">c2</span> <span class="o">=</span> <span class="p">(</span><span class="n">x</span><span class="o">*</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">0</span><span class="p">].</span><span class="n">y</span><span class="p">())</span> <span class="o">+</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="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">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">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">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">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">y</span><span class="p">())</span> <span class="o">/</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="o">*</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">0</span><span class="p">].</span><span class="n">y</span><span class="p">())</span> <span class="o">+</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="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">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">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">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">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">y</span><span class="p">());</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="kt">float</span> <span class="n">c3</span> <span class="o">=</span> <span class="p">(</span><span class="n">x</span><span class="o">*</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">1</span><span class="p">].</span><span class="n">y</span><span class="p">())</span> <span class="o">+</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="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">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">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">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">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">y</span><span class="p">())</span> <span class="o">/</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 class="o">*</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">1</span><span class="p">].</span><span class="n">y</span><span class="p">())</span> <span class="o">+</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="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">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">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">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">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">y</span><span class="p">());</span>
|
||
</span></span><span class="line"><span class="cl"> <span class="k">return</span> <span class="p">{</span><span class="n">c1</span><span class="p">,</span><span class="n">c2</span><span class="p">,</span><span class="n">c3</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></span><span class="line"><span class="cl"><span class="c1">//光栅化时，判断深度之后进行插值计算得出对应的数值
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1"></span>
|
||
</span></span><span class="line"><span class="cl"><span class="c1">// auto interpolated_color（颜色）
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1"></span><span class="k">auto</span> <span class="n">interpolated_color</span><span class="o">=</span><span class="n">interpolate</span><span class="p">(</span><span class="n">alpha</span><span class="p">,</span><span class="n">beta</span><span class="p">,</span><span class="n">gamma</span><span class="p">,</span><span class="n">t</span><span class="p">.</span><span class="n">color</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="n">t</span><span class="p">.</span><span class="n">color</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span><span class="n">t</span><span class="p">.</span><span class="n">color</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span><span class="mi">1</span><span class="p">);</span>
|
||
</span></span><span class="line"><span class="cl"><span class="c1">// auto interpolated_normal（法线）
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1"></span><span class="k">auto</span> <span class="n">interpolated_normal</span> <span class="o">=</span> <span class="n">interpolate</span><span class="p">(</span><span class="n">alpha</span><span class="p">,</span><span class="n">beta</span><span class="p">,</span><span class="n">gamma</span><span class="p">,</span><span class="n">t</span><span class="p">.</span><span class="n">normal</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="n">t</span><span class="p">.</span><span class="n">normal</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span><span class="n">t</span><span class="p">.</span><span class="n">normal</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span><span class="mi">1</span><span class="p">).</span><span class="n">normalized</span><span class="p">();</span>
|
||
</span></span><span class="line"><span class="cl"><span class="c1">// auto interpolated_texcoords（纹理坐标）
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1"></span><span class="k">auto</span> <span class="n">interpolated_texcoords</span> <span class="o">=</span> <span class="n">interpolate</span><span class="p">(</span><span class="n">alpha</span><span class="p">,</span><span class="n">beta</span><span class="p">,</span><span class="n">gamma</span><span class="p">,</span><span class="n">t</span><span class="p">.</span><span class="n">tex_coords</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="n">t</span><span class="p">.</span><span class="n">tex_coords</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span><span class="n">t</span><span class="p">.</span><span class="n">tex_coords</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span><span class="mi">1</span><span class="p">);</span>
|
||
</span></span><span class="line"><span class="cl"><span class="c1">// auto interpolated_shadingcoords（着色坐标）
|
||
</span></span></span><span class="line"><span class="cl"><span class="c1"></span><span class="k">auto</span> <span class="n">interpolated_shadingcoords</span> <span class="o">=</span> <span class="n">interpolate</span><span class="p">(</span><span class="n">alpha</span><span class="p">,</span><span class="n">beta</span><span class="p">,</span><span class="n">gamma</span><span class="p">,</span><span class="n">view_pos</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="n">view_pos</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span><span class="n">view_pos</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span><span class="mi">1</span><span class="p">);</span>
|
||
</span></span></code></pre></td></tr></table></div>
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<ul class="post-copyright">
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<li class="copyright-item author"><span class="copyright-item-text">作者</span>：<a href="http://www.inksoul.top" class="p-author h-card" target="_blank" rel="noopener">InkSoul</a></li>
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