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jinchao
2025-02-23 20:51:53 +08:00
parent 2bf0000c22
commit 791c17ebdf
21 changed files with 1946 additions and 1827 deletions
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docs/note/graphics/image_based_lighting/ibl_01.md
+8 -2
View File
@@ -83,7 +83,10 @@ $$\begin{split}
\end{split}$$
其中
$$
\phi_i=2\pi\xi, \theta_i=\dfrac{\pi}{2}\xi
\begin{aligned}
\phi_i&=2\pi\xi\\
\theta_i&=\dfrac{\pi}{2}\xi
\end{aligned}
$$
$\xi$表示均匀分布在[0,1]之间的随机变量
@@ -101,7 +104,10 @@ $$\begin{split}
\end{split}$$
其中
$$
\phi_i=2\pi\xi, \theta_i=\arccos(1-\xi)
\begin{aligned}
\phi_i&=2\pi\xi\\
\theta_i&=\arccos(1-\xi)
\end{aligned}
$$
````cpp :no-line-numbers
vec3 irradiance = vec3(0.0);
docs/note/graphics/image_based_lighting/ibl_02.md
+15 -5
View File
@@ -8,11 +8,17 @@ L_{os}(\vec{\omega_o})=\int_{\Omega}f_s(\vec{\omega_i}, \vec{\omega_o})L_i(\vec{
$$
同样使用蒙特卡洛进行近似积分
$$
\int_{\Omega}f_s(\vec{\omega_i}, \vec{\omega_o})L_i(\vec{\omega_i})(\vec{\omega}_i\vec{n})d\omega_i \approx \dfrac{1}{N}\sum_{k=1}^{N}\dfrac{f_s(\vec{\omega_k}, \vec{\omega_o})L_i(\vec{\omega_k})(\vec{\omega_k}\cdot\vec{n})}{\text{pdf}(\vec{\omega_k})}
\begin{aligned}
&\int_{\Omega}f_s(\vec{\omega_i}, \vec{\omega_o})L_i(\vec{\omega_i})(\vec{\omega}_i\vec{n})d\omega_i \\
\approx &\dfrac{1}{N}\sum_{k=1}^{N}\dfrac{f_s(\vec{\omega_k}, \vec{\omega_o})L_i(\vec{\omega_k})(\vec{\omega_k}\cdot\vec{n})}{\text{pdf}(\vec{\omega_k})}
\end{aligned}
$$
EPIC在此基础上提出了一种近似[计算方法](http://blog.selfshadow.com/publications/s2013-shading-course/karis/s2013_pbs_epic_notes_v2.pdf)
$$
\dfrac{1}{N}\sum_{k=1}^{N}\dfrac{f_s(\vec{\omega_k}, \vec{\omega_o})L_i(\vec{\omega_k})(\vec{\omega_k}\cdot\vec{n})}{\text{pdf}(\vec{\omega_k}, \vec{\omega_o})}\approx\left(\dfrac{1}{N}\sum_{k=1}^N L_i(\vec{\omega_k})\right)\left(\dfrac{1}{N}\sum_{k=1}^{N}\dfrac{f_s(\vec{\omega_k}, \vec{\omega_o})(\vec{\omega_k}\cdot\vec{n})}{\text{pdf}(\vec{\omega_k})}\right)
\begin{aligned}
&\dfrac{1}{N}\sum_{k=1}^{N}\dfrac{f_s(\vec{\omega_k}, \vec{\omega_o})L_i(\vec{\omega_k})(\vec{\omega_k}\cdot\vec{n})}{\text{pdf}(\vec{\omega_k}, \vec{\omega_o})}\\
\approx&\left(\dfrac{1}{N}\sum_{k=1}^N L_i(\vec{\omega_k})\right)\left(\dfrac{1}{N}\sum_{k=1}^{N}\dfrac{f_s(\vec{\omega_k}, \vec{\omega_o})(\vec{\omega_k}\cdot\vec{n})}{\text{pdf}(\vec{\omega_k})}\right)
\end{aligned}
$$
这种方法的好处是可以通过分开预计算，尽量减少实际渲染时的计算量，这个公式可以理解为“Env. lighting x BRDF”，左边的第一部分是小平面受到的所有环境光的采样值，第二部分只跟材质的BRDF属性相关。
@@ -71,7 +77,10 @@ $$\begin{split}
\end{split}$$
使用Mathmatica计算可得
$$
\text{cdf}(\theta)=\dfrac{\sin^2\theta}{\cos^2\theta(\alpha^2-1)+1}=\dfrac{1-\cos^2\theta}{\cos^2\theta(\alpha^2-1)+1}
\begin{aligned}
\text{cdf}(\theta)&=\dfrac{\sin^2\theta}{\cos^2\theta(\alpha^2-1)+1}\\
&=\dfrac{1-\cos^2\theta}{\cos^2\theta(\alpha^2-1)+1}
\end{aligned}
$$
根据前面的概率知识，可以得到微表面的法线的球坐标$\theta$和$\phi$的采样函数为
$$\begin{split}
@@ -85,7 +94,7 @@ $$
\dfrac{1}{N}\sum_{k=1}^N L_i(\vec{\omega}_k)\approx\dfrac{1}{\sum_{k=1}^{N}(\vec{n}\cdot\vec{\omega}_k)}\sum_{k=1}^{N}{L_i(\vec{\omega}_k)(\vec{n}\cdot\vec{\omega}_k)}
$$
```cpp
```cpp :no-line-numbers
// make the simplyfying assumption that V equals R equals the normal
vec3 R = N;
vec3 V = R;
@@ -96,7 +105,8 @@ float totalWeight = 0.0;
for(uint i = 0u; i < SAMPLE_COUNT; ++i)
{
// generates a sample vector that's biased towards the preferred alignment direction (importance sampling).
// generates a sample vector that's biased towards the preferred
//alignment direction (importance sampling).
vec2 Xi = Hammersley(i, SAMPLE_COUNT);
vec3 H = ImportanceSampleGGX(Xi, N, roughness);
vec3 L = normalize(2.0 * dot(V, H) * H - V);
docs/note/graphics/image_based_lighting/ibl_02.svg
+120 -123
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