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2025-02-23 20:53:24 +08:00
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docs/note/graphics/illumination_model/classic/Blinn-Phong_Vectors.svg
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# 光照模型(Illumination Model)
## 1. Phong模型
### 1.1 基本定义
![](./Phong_Vectors.svg)
* $\vec{\mathrm{N}}$表示表面的单位法线矢量
* $\vec{\mathrm{L}}$是指向光源的单位矢量
* $\vec{\mathrm{R}}$是反射光线的单位矢量
* $\vec{\mathrm{V}}$是指向相机的单位矢量
### 1.2 算法
[https://en.wikipedia.org/wiki/Phong_reflection_model](https://en.wikipedia.org/wiki/Phong_reflection_model)
![](./Phong_components_version_4.png)
$$
I_\mathrm{phong}=I_\mathrm{ambient}+\sum({I_\mathrm{diffuse}+I_\mathrm{specular}})
$$
### 1.2.1 **环境光（Ambient Reflection）**
$$
I_\mathrm{ambient}=L_aK_a
$$
其中$L_a$是环境光亮度，$I_a$是环境光反射系数$0\le K_a\le 1$
### 1.2.2 **漫反射（Diffuse Reflection）**
![](./Diffuse_Reflection.svg)
根据Lambert规则，材质的漫反射是均匀发射到周围的，和观察角度无关，只和光源的入射角度有关
$$
I_\mathrm{diffuse}=(\vec{L}\cdot\vec{N})L_dK_d
$$
其中$L_d$是光源的光亮度，$K_d$是漫反射系数$0\le K_d\le 1$
### 1.2.3 **高光反射(Specular Reflection)**
![](./Specular_Reflection.svg)
$$
I_\mathrm{specular}=(\vec{\mathrm{R}}\cdot\vec{\mathrm{V}})^nL_sK_s
$$
其中$L_s$是光源亮度，$K_s$是高光反射系数$0\le K_s\le 1$，$n$高光强度
### 1.2.3 **反射射线**
在计算高光反射时，需要计算反射射线$\vec{\mathrm{R}}$
$$
\vec{\mathrm{R}}=2(\vec{\mathrm{L}}\cdot\vec{\mathrm{N}})\vec{\mathrm{N}}-\vec{\mathrm{L}}
$$
docs/note/graphics/illumination_model/classic/illumination_model_02.md
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# 光照模型（二）
## 2. Blinn-Phong模型
### 2.1 基本定义
![](./Blinn-Phong_Vectors.svg)
和Phong模型很类似，只不过增加了半角向量$\vec{\mathrm{H}}$，也就是指向光源的向量$\vec{\mathrm{L}}$和指向相机的向量$\vec{\mathrm{V}}$的中间向量
$$
\vec{\mathrm{V}}=\frac{\vec{\mathrm{L}}+\vec{\mathrm{V}}}{\|\vec{\mathrm{L}}+\vec{\mathrm{V}}\|}
$$
### 2.2 算法
[https://en.wikipedia.org/wiki/Blinn%E2%80%93Phong_shading_model](https://en.wikipedia.org/wiki/Blinn%E2%80%93Phong_shading_model)
$$
I_\mathrm{BlinnPhong}=I_\mathrm{ambient}+\sum({I_\mathrm{diffuse}+I_\mathrm{specular}})
$$
其中环境光和漫反射和Phong相同
$$
I_\mathrm{diffuse}=(\vec{L}\cdot\vec{N})L_dK_d \\
I_\mathrm{specular}=(\vec{\mathrm{R}}\cdot\vec{\mathrm{V}})^\alpha L_sK_s
$$
高光部分使用$\vec{\mathrm{N}}\cdot\vec{\mathrm{H}}$代替$\vec{\mathrm{R}}\cdot\vec{\mathrm{V}}$
$$
I_\mathrm{specular}=(\vec{\mathrm{N}}\cdot\vec{\mathrm{H}})^nL_sK_s
$$