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class="language-cpp" data-highlighter="prismjs" data-ext="cpp" data-title="cpp"><pre><code><span class="line">vec3 irradiance <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 punctuation">;</span> </span>
<span class="line"></span>
<span class="line"><span class="token comment">// tangent space calculation from origin point(x&#39;=up, y&#39;=N, z&#39;=left)(left-hand)</span></span>
<span class="line">vec3 up <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">1.0</span><span class="token punctuation">,</span> <span class="token number">0.0</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token comment">//x&#39;</span></span>
<span class="line">vec3 left <span class="token operator">=</span> <span class="token function">cross</span><span class="token punctuation">(</span>up<span class="token punctuation">,</span> N<span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token comment">//z&#39;</span></span>
<span class="line">up <span class="token operator">=</span> <span class="token function">cross</span><span class="token punctuation">(</span>N<span class="token punctuation">,</span> left<span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token comment">//x&#39;</span></span>
<span class="line"></span>
<span class="line"><span class="token keyword">float</span> sampleDelta <span class="token operator">=</span> <span class="token number">0.025</span><span class="token punctuation">;</span></span>
<span class="line"><span class="token keyword">float</span> nrSamples <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">for</span><span class="token punctuation">(</span><span class="token keyword">float</span> phi <span class="token operator">=</span> <span class="token number">0.0</span><span class="token punctuation">;</span> phi <span class="token operator">&lt;</span> <span class="token number">2.0</span> <span class="token operator">*</span> PI<span class="token punctuation">;</span> phi <span class="token operator">+=</span> sampleDelta<span class="token punctuation">)</span></span>
<span class="line"><span class="token punctuation">{</span></span>
<span class="line"> <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">float</span> theta <span class="token operator">=</span> <span class="token number">0.0</span><span class="token punctuation">;</span> theta <span class="token operator">&lt;</span> <span class="token number">0.5</span> <span class="token operator">*</span> PI<span class="token punctuation">;</span> theta <span class="token operator">+=</span> sampleDelta<span class="token punctuation">)</span></span>
<span class="line"> <span class="token punctuation">{</span></span>
<span class="line"> <span class="token keyword">float</span> cosTheta <span class="token operator">=</span> <span class="token function">cos</span><span class="token punctuation">(</span>theta<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line"> <span class="token keyword">float</span> sinTheta <span class="token operator">=</span> <span class="token function">sin</span><span class="token punctuation">(</span>theta<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line"> </span>
<span class="line"> <span class="token comment">// spherical to cartesian (in tangent space)</span></span>
<span class="line"> vec3 tangentSample <span class="token operator">=</span> <span class="token function">vec3</span><span class="token punctuation">(</span><span class="token function">cos</span><span class="token punctuation">(</span>phi<span class="token punctuation">)</span> <span class="token operator">*</span> sinTheta<span class="token punctuation">,</span> cosTheta<span class="token punctuation">,</span> <span class="token function">sin</span><span class="token punctuation">(</span>phi<span class="token punctuation">)</span> <span class="token operator">*</span> sinTheta<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line"> <span class="token comment">// tangent space to world</span></span>
<span class="line"> vec3 sampleVec <span class="token operator">=</span> tangentSample<span class="token punctuation">.</span>x <span class="token operator">*</span> up <span class="token operator">+</span> tangentSample<span class="token punctuation">.</span>y <span class="token operator">*</span> N <span class="token operator">+</span> tangentSample<span class="token punctuation">.</span>z <span class="token operator">*</span> left<span class="token punctuation">;</span> </span>
<span class="line"></span>
<span class="line"> irradiance <span class="token operator">+=</span> <span class="token function">texture</span><span class="token punctuation">(</span>environmentMap<span class="token punctuation">,</span> sampleVec<span class="token punctuation">)</span><span class="token punctuation">.</span>rgb <span class="token operator">*</span> cosTheta <span class="token operator">*</span> sinTheta<span class="token punctuation">;</span></span>
<span class="line"> nrSamples<span class="token operator">++</span><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">irradiance <span class="token operator">=</span> PI <span class="token operator">*</span> irradiance <span class="token operator">*</span> <span class="token keyword">float</span><span class="token punctuation">(</span>nrSamples<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line"></span></code></pre></div><h4 id="_2-2-2-蒙特卡洛估算" tabindex="-1"><a class="header-anchor" href="#_2-2-2-蒙特卡洛估算"><span>2.2.2 蒙特卡洛估算</span></a></h4><p>使用蒙特卡洛采样估算积分</p>`,4),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-msubsup",null,[m("mjx-mo",{class:"mjx-lop"},[m("mjx-c",{class:"mjx-c222B TEX-S2"})]),m("mjx-script",{style:{"vertical-align":"-0.896em","margin-left":"-0.388em"}},[m("mjx-TeXAtom",{size:"s",texclass:"ORD",style:{"margin-left":"0.647em"}},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D44F TEX-I"})])]),m("mjx-spacer",{style:{"margin-top":"1.665em"}}),m("mjx-TeXAtom",{size:"s",texclass:"ORD"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D44E TEX-I"})])])])]),m("mjx-mi",{class:"mjx-i",space:"2"},[m("mjx-c",{class:"mjx-c1D453 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function">vec3</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">vec3 up <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">1.0</span><span class="token punctuation">,</span> <span class="token number">0.0</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token comment">//x&#39;</span></span>
<span class="line">vec3 left <span class="token operator">=</span> <span class="token function">cross</span><span class="token punctuation">(</span>up<span class="token punctuation">,</span> N<span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token comment">//z&#39;</span></span>
<span class="line">up <span class="token operator">=</span> <span class="token function">cross</span><span class="token punctuation">(</span>N<span class="token punctuation">,</span> left<span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token comment">//x&#39;</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">0</span><span class="token punctuation">;</span> i<span class="token operator">&lt;</span>sampleCounts<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span></span>
<span class="line"><span class="token punctuation">{</span></span>
<span class="line"> <span class="token comment">//http://holger.dammertz.org/stuff/notes_HammersleyOnHemisphere.html</span></span>
<span class="line"> vec2 uv <span class="token operator">=</span> <span class="token function">Hammersley</span><span class="token punctuation">(</span>i<span class="token punctuation">,</span> totalCounts<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line"></span>
<span class="line"> <span class="token comment">// tangent space sample point</span></span>
<span class="line"> <span class="token keyword">float</span> phi <span class="token operator">=</span> uv<span class="token punctuation">.</span>y <span class="token operator">*</span> <span class="token number">2.0</span> <span class="token operator">*</span> PI<span class="token punctuation">;</span></span>
<span class="line"> <span class="token keyword">float</span> cosTheta <span class="token operator">=</span> <span class="token number">1.0</span> <span class="token operator">-</span> uv<span class="token punctuation">.</span>x<span class="token punctuation">;</span></span>
<span class="line"> <span class="token keyword">float</span> sinTheta <span class="token operator">=</span> <span class="token function">sqrt</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token operator">-</span>cosTheta<span class="token operator">*</span>cosTheta<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line"> vec3 tangentSample <span class="token operator">=</span> <span class="token function">vec3</span><span class="token punctuation">(</span><span class="token function">cos</span><span class="token punctuation">(</span>phi<span class="token punctuation">)</span> <span class="token operator">*</span> sinTheta<span class="token punctuation">,</span> cosTheta<span class="token punctuation">,</span> <span class="token function">sin</span><span class="token punctuation">(</span>phi<span class="token punctuation">)</span> <span class="token operator">*</span> sinTheta<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
<span class="line"></span>
<span class="line"> <span class="token comment">// tangent space to world</span></span>
<span class="line"> vec3 sampleVec <span class="token operator">=</span> tangentSample<span class="token punctuation">.</span>x <span class="token operator">*</span> up <span class="token operator">+</span> tangentSample<span class="token punctuation">.</span>y <span class="token operator">*</span> N <span class="token operator">+</span> tangentSample<span class="token punctuation">.</span>z <span class="token operator">*</span> left<span class="token punctuation">;</span> </span>
<span class="line"></span>
<span class="line"> irradiance <span class="token operator">+=</span> <span class="token function">texture2D</span><span class="token punctuation">(</span>s_texSkybox<span class="token punctuation">,</span> sampleVec<span class="token punctuation">)</span><span class="token punctuation">.</span>rgb <span class="token operator">*</span> cosTheta<span class="token punctuation">;</span></span>
<span class="line"><span class="token punctuation">}</span></span>
<span class="line"></span>
<span class="line">irradiance <span class="token operator">=</span> <span class="token number">2</span><span class="token operator">*</span>irradiance <span class="token operator">/</span> <span class="token keyword">float</span><span class="token punctuation">(</span>sampleCounts<span class="token punctuation">)</span><span class="token punctuation">;</span></span>
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