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class="language-cpp" data-highlighter="prismjs" data-ext="cpp" data-title="cpp"><pre><code><span class="line"><span class="token comment">// make the simplyfying assumption that V equals R equals the normal </span></span>
<span class="line">vec3 R <span class="token operator">=</span> N<span class="token punctuation">;</span></span>
<span class="line">vec3 V <span class="token operator">=</span> R<span class="token punctuation">;</span></span>
<span class="line"></span>
<span class="line"><span class="token keyword">const</span> uint SAMPLE_COUNT <span class="token operator">=</span> <span class="token number">1024u</span><span class="token punctuation">;</span></span>
<span class="line">vec3 prefilteredColor <span class="token operator">=</span> <span class="token function">vec3_splat</span><span class="token punctuation">(</span><span class="token number">0.0</span><span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line"><span class="token keyword">float</span> totalWeight <span class="token operator">=</span> <span class="token number">0.0</span><span class="token punctuation">;</span></span>
<span class="line"></span>
<span class="line"><span class="token keyword">for</span><span class="token punctuation">(</span>uint i <span class="token operator">=</span> <span class="token number">0u</span><span class="token punctuation">;</span> i <span class="token operator">&lt;</span> SAMPLE_COUNT<span class="token punctuation">;</span> <span class="token operator">++</span>i<span class="token punctuation">)</span></span>
<span class="line"><span class="token punctuation">{</span></span>
<span class="line">    <span class="token comment">// generates a sample vector that&#39;s biased towards the preferred </span></span>
<span class="line">    <span class="token comment">//alignment direction (importance sampling).</span></span>
<span class="line">    vec2 Xi <span class="token operator">=</span> <span class="token function">Hammersley</span><span class="token punctuation">(</span>i<span class="token punctuation">,</span> SAMPLE_COUNT<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line">    vec3 H <span class="token operator">=</span> <span class="token function">ImportanceSampleGGX</span><span class="token punctuation">(</span>Xi<span class="token punctuation">,</span> N<span class="token punctuation">,</span> roughness<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line">    vec3 L  <span class="token operator">=</span> <span class="token function">normalize</span><span class="token punctuation">(</span><span class="token number">2.0</span> <span class="token operator">*</span> <span class="token function">dot</span><span class="token punctuation">(</span>V<span class="token punctuation">,</span> H<span class="token punctuation">)</span> <span class="token operator">*</span> H <span class="token operator">-</span> V<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line"></span>
<span class="line">    <span class="token keyword">float</span> NdotL <span class="token operator">=</span> <span class="token function">max</span><span class="token punctuation">(</span><span class="token function">dot</span><span class="token punctuation">(</span>N<span class="token punctuation">,</span> L<span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token number">0.0</span><span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line">    <span class="token keyword">if</span><span class="token punctuation">(</span>NdotL <span class="token operator">&gt;</span> <span class="token number">0.0</span><span class="token punctuation">)</span></span>
<span class="line">    <span class="token punctuation">{</span></span>
<span class="line">        prefilteredColor <span class="token operator">+=</span> <span class="token function">texture2D</span><span class="token punctuation">(</span>s_texSkybox<span class="token punctuation">,</span> <span class="token function">SampleSphericalMap</span><span class="token punctuation">(</span>L<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">.</span>rgb <span class="token operator">*</span> NdotL<span class="token punctuation">;</span></span>
<span class="line">        totalWeight      <span class="token operator">+=</span> NdotL<span class="token punctuation">;</span></span>
<span class="line">    <span class="token punctuation">}</span></span>
<span class="line"><span class="token punctuation">}</span></span>
<span class="line"></span>
<span class="line">prefilteredColor <span class="token operator">=</span> prefilteredColor <span class="token operator">/</span> totalWeight<span class="token punctuation">;</span></span>
<span class="line"></span></code></pre></div><h2 id="_3-3-brdf部分" tabindex="-1"><a class="header-anchor" href="#_3-3-brdf部分"><span>3.3 BRDF部分</span></a></h2><p>观察公式的第二个拆分项</p>`,3),m("mjx-container",{class:"MathJax",jax:"CHTML",display:"true",style:{position:"relative"}},[m("mjx-math",{display:"true",style:{"margin-left":"0","margin-right":"0"},class:"MJX-TEX","aria-hidden":"true"},[m("mjx-mstyle",null,[m("mjx-mfrac",null,[m("mjx-frac",{type:"d"},[m("mjx-num",null,[m("mjx-nstrut",{type:"d"}),m("mjx-mn",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c31"})])]),m("mjx-dbox",null,[m("mjx-dtable",null,[m("mjx-line",{type:"d"}),m("mjx-row",null,[m("mjx-den",null,[m("mjx-dstrut",{type:"d"}),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D441 TEX-I"})])])])])])])])]),m("mjx-munderover",{space:"2"},[m("mjx-over",{style:{"padding-bottom":"0.2em","padding-left":"0.408em"}},[m("mjx-TeXAtom",{size:"s",texclass:"ORD"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D441 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id="_3-4-1-brdf贴图的生成" tabindex="-1"><a class="header-anchor" href="#_3-4-1-brdf贴图的生成"><span>3.4.1 BRDF贴图的生成</span></a></h3><div class="language-cpp" data-highlighter="prismjs" data-ext="cpp" data-title="cpp"><pre><code><span class="line">vec2 <span class="token function">IntegrateBRDF</span><span class="token punctuation">(</span><span class="token keyword">float</span> NdotV<span class="token punctuation">,</span> <span class="token keyword">float</span> roughness<span class="token punctuation">)</span></span>
<span class="line"><span class="token punctuation">{</span></span>
<span class="line">    vec3 V<span class="token punctuation">;</span></span>
<span class="line">    V<span class="token punctuation">.</span>x <span class="token operator">=</span> <span class="token function">sqrt</span><span class="token punctuation">(</span><span class="token number">1.0</span> <span class="token operator">-</span> NdotV<span class="token operator">*</span>NdotV<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line">    V<span class="token punctuation">.</span>y <span class="token operator">=</span> <span class="token number">0.0</span><span class="token punctuation">;</span></span>
<span class="line">    V<span class="token punctuation">.</span>z <span class="token operator">=</span> NdotV<span class="token punctuation">;</span></span>
<span class="line"></span>
<span class="line">    <span class="token keyword">float</span> A <span class="token operator">=</span> <span class="token number">0.0</span><span class="token punctuation">;</span></span>
<span class="line">    <span class="token keyword">float</span> B <span class="token operator">=</span> <span class="token number">0.0</span><span class="token punctuation">;</span> </span>
<span class="line"></span>
<span class="line">    vec3 N <span class="token operator">=</span> <span class="token function">vec3</span><span class="token punctuation">(</span><span class="token number">0.0</span><span class="token punctuation">,</span> <span class="token number">0.0</span><span class="token punctuation">,</span> <span class="token number">1.0</span><span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line">    </span>
<span class="line">    <span class="token keyword">const</span> uint SAMPLE_COUNT <span class="token operator">=</span> <span class="token number">1024u</span><span class="token punctuation">;</span></span>
<span class="line">    <span class="token keyword">for</span><span class="token punctuation">(</span>uint i <span class="token operator">=</span> <span class="token number">0u</span><span class="token punctuation">;</span> i <span class="token operator">&lt;</span> SAMPLE_COUNT<span class="token punctuation">;</span> <span class="token operator">++</span>i<span class="token punctuation">)</span></span>
<span class="line">    <span class="token punctuation">{</span></span>
<span class="line">        <span class="token comment">// generates a sample vector that&#39;s biased towards the</span></span>
<span class="line">        <span class="token comment">// preferred alignment direction (importance sampling).</span></span>
<span class="line">        vec2 Xi <span class="token operator">=</span> <span class="token function">Hammersley</span><span class="token punctuation">(</span>i<span class="token punctuation">,</span> SAMPLE_COUNT<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line">        vec3 H <span class="token operator">=</span> <span class="token function">ImportanceSampleGGX</span><span class="token punctuation">(</span>Xi<span class="token punctuation">,</span> N<span class="token punctuation">,</span> roughness<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line">        vec3 L <span class="token operator">=</span> <span class="token function">normalize</span><span class="token punctuation">(</span><span class="token number">2.0</span> <span class="token operator">*</span> <span class="token function">dot</span><span class="token punctuation">(</span>V<span class="token punctuation">,</span> H<span class="token punctuation">)</span> <span class="token operator">*</span> H <span class="token operator">-</span> V<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line"></span>
<span class="line">        <span class="token keyword">float</span> NdotL <span class="token operator">=</span> <span class="token function">max</span><span class="token punctuation">(</span>L<span class="token punctuation">.</span>z<span class="token punctuation">,</span> <span class="token number">0.0</span><span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line">        <span class="token keyword">float</span> NdotH <span class="token operator">=</span> <span class="token function">max</span><span class="token punctuation">(</span>H<span class="token punctuation">.</span>z<span class="token punctuation">,</span> <span class="token number">0.0</span><span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line">        <span class="token keyword">float</span> VdotH <span class="token operator">=</span> <span class="token function">max</span><span class="token punctuation">(</span><span class="token function">dot</span><span class="token punctuation">(</span>V<span class="token punctuation">,</span> H<span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token number">0.0</span><span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line"></span>
<span class="line">        <span class="token keyword">if</span><span class="token punctuation">(</span>NdotL <span class="token operator">&gt;</span> <span class="token number">0.0</span><span class="token punctuation">)</span></span>
<span class="line">        <span class="token punctuation">{</span></span>
<span class="line">            <span class="token keyword">float</span> G <span class="token operator">=</span> <span class="token function">GeometrySmith</span><span class="token punctuation">(</span>N<span class="token punctuation">,</span> V<span class="token punctuation">,</span> L<span class="token punctuation">,</span> roughness<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line">            <span class="token keyword">float</span> G_Vis <span class="token operator">=</span> <span class="token punctuation">(</span>G <span class="token operator">*</span> VdotH<span class="token punctuation">)</span> <span class="token operator">/</span> <span class="token punctuation">(</span>NdotH <span class="token operator">*</span> NdotV<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line">            <span class="token keyword">float</span> Fc <span class="token operator">=</span> <span class="token function">pow</span><span class="token punctuation">(</span><span class="token number">1.0</span> <span class="token operator">-</span> VdotH<span class="token punctuation">,</span> <span class="token number">5.0</span><span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line"></span>
<span class="line">            A <span class="token operator">+=</span> <span class="token punctuation">(</span><span class="token number">1.0</span> <span class="token operator">-</span> Fc<span class="token punctuation">)</span> <span class="token operator">*</span> G_Vis<span class="token punctuation">;</span></span>
<span class="line">            B <span class="token operator">+=</span> Fc <span class="token operator">*</span> G_Vis<span class="token punctuation">;</span></span>
<span class="line">        <span class="token punctuation">}</span></span>
<span class="line">    <span class="token punctuation">}</span></span>
<span class="line">    A <span class="token operator">/=</span> <span class="token keyword">float</span><span class="token punctuation">(</span>SAMPLE_COUNT<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line">    B <span class="token operator">/=</span> <span class="token keyword">float</span><span class="token punctuation">(</span>SAMPLE_COUNT<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line">    <span class="token keyword">return</span> <span class="token function">vec2</span><span class="token punctuation">(</span>A<span class="token punctuation">,</span> B<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line"><span class="token punctuation">}</span></span>
<span class="line"></span>
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