keywords:ambient diffuse specular、Phong Shading、Phong reflection model

公式概述

ADS光照模型又称为“冯氏反射模型”(Phong reflection model),为什么叫冯氏:

裴祥风(Bùi Tường Phong音译, 1942年—1975年),美国电脑CG研究学者,于越南出生。他于1973年在尤他大学取得哲学博士学位,并发明了Phong反射模型及Phong著色法,并广为CG界采用。1975死于白血病。

ADS光照模型公式缩写:

LightIntensity = Ambient + Diffuse + Specular;

参数说明:

  • Ambient 环境光
  • Diffuse 漫反射
  • Specular 全反射光 / 镜面光

三个参数渲染效果示例:

三个参数拆解如下:

Ambient = La * Ka;
Diffuse = Ld * Kd * max( dot(s, n), 0.0 );
Specular = Ls * Ks * pow( max( dot(r, v), 0.0 ), f );

参数说明:

  • La 环境光强度(Ambient light intensity)
  • Ka 材质环境光反射率 / 材质环境光反射系数(Ambient reflectivity)
  • Ld 漫射光强度 / 散射光强度(Diffuse light intensity)
  • Kd 材质漫反射率 / 材质漫反射系数(Diffuse reflectivity)
  • s 顶点 / 曲面点 到光源方向的单位向量(Direction from the surface point to the light source)
  • n 顶点 / 曲面点 的法线单位向量(Normal vector at the surface point)
  • Ls 镜面光强度 / 全反射光强度(Specular light intensity)
  • Ks 材质镜面反射率 / 材质镜面反射系数(Specular reflectivity)
  • r 完全反射向量( the vector of perfect reflection)
  • v 顶点 / 曲面点 到摄像机方向的向量( the vector towards the viewer)
  • f 镜面高光(specular highlights),值范围在1到200之间,值越小,镜面亮点越大

光源出射强度 / 出射光强度(Intensity of the outgoing light ) I 的完整计算公式如下: $$ I = La \cdot Ka+Ld \cdot Kd \cdot \left(\vec{s} \cdot \vec{n}\right)+Ls \cdot Ks \cdot \left(\vec{r} \cdot \vec{v}\right)^f $$

渲染实例

OpenGL API 版本为4.1。

假设不考虑环境光和镜面光,只考虑漫射光,渲染效果:

shader 代码:
diffuse.vert

#version 410

layout (location = 0) in vec3 VertexPosition;
layout (location = 1) in vec3 VertexNormal;

out vec3 LightIntensity;

uniform vec4 LightPosition; // Light position in eye coords.
uniform vec3 Kd;            // Diffuse reflectivity
uniform vec3 Ld;            // Diffuse light intensity

uniform mat4 ModelViewMatrix;
uniform mat3 NormalMatrix;
uniform mat4 ProjectionMatrix;
uniform mat4 MVP;

void main()
{
    vec3 tnorm = normalize( NormalMatrix * VertexNormal);
    vec4 eyeCoords = ModelViewMatrix * vec4(VertexPosition,1.0);
    vec3 s = normalize(vec3(LightPosition - eyeCoords));

    LightIntensity = Ld * Kd * max( dot( s, tnorm ), 0.0 );

    gl_Position = MVP * vec4(VertexPosition,1.0);
}

diffuse.frag

#version 410

in vec3 LightIntensity;

layout( location = 0 ) out vec4 FragColor;

void main() {
    FragColor = vec4(LightIntensity, 1.0);
}

同时计算环境光、漫反射、镜面反射的渲染效果:

shader 代码:
phong.vert

#version 410

layout (location = 0) in vec3 VertexPosition;
layout (location = 1) in vec3 VertexNormal;

out vec3 LightIntensity;

struct LightInfo {
  vec4 Position; // Light position in eye coords.
  vec3 La;       // Ambient light intensity
  vec3 Ld;       // Diffuse light intensity
  vec3 Ls;       // Specular light intensity
};
uniform LightInfo Light;

struct MaterialInfo {
  vec3 Ka;            // Ambient reflectivity
  vec3 Kd;            // Diffuse reflectivity
  vec3 Ks;            // Specular reflectivity
  float Shininess;    // Specular shininess factor
};
uniform MaterialInfo Material;

uniform mat4 ModelViewMatrix;
uniform mat3 NormalMatrix;
uniform mat4 ProjectionMatrix;
uniform mat4 MVP;

void main()
{
    vec3 tnorm = normalize( NormalMatrix * VertexNormal);
    vec4 eyeCoords = ModelViewMatrix * vec4(VertexPosition,1.0);
    vec3 s = normalize(vec3(Light.Position - eyeCoords));
    vec3 v = normalize(-eyeCoords.xyz);
    vec3 r = reflect( -s, tnorm );
    float sDotN = max( dot(s,tnorm), 0.0 );
    vec3 ambient = Light.La * Material.Ka;
    vec3 diffuse = Light.Ld * Material.Kd * sDotN;
    vec3 spec = vec3(0.0);
    if( sDotN > 0.0 )
       spec = Light.Ls * Material.Ks *
              pow( max( dot(r,v), 0.0 ), Material.Shininess );

    LightIntensity = ambient + diffuse + spec;
    gl_Position = MVP * vec4(VertexPosition,1.0);
}

phong.frag

#version 410

in vec3 LightIntensity;

layout( location = 0 ) out vec4 FragColor;

void main() {
    FragColor = vec4(LightIntensity, 1.0);
}

demo完整代码:
https://github.com/dawnarc/ShadingDemo


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