计算机图形学（五）Lighting and Shading

1. Lighting Conception

• Need to consider:
  • Surface orientation – normal
  • Material properties
  • Light sources
  • Location of viewer
• Light which shines from light source to the objects transmits the reflective light, transparent light and abosrptive light (not be seen)
• Reflective light includes diffuse and specular which more depends on the material of the object.

2. Lighting Model

• Local Lighting Model: all light comes from lights defined within the scene.

• three components:

  • Ambient light 环境光
  • Diffuse light 漫反射光
  • Specular light 镜面反射光

• Ambient Light 环境光

  • 虚拟的光，使空间获得均匀的照明，不考虑光源位置、观察者位置和表面法向量
  • $A=L_0+\sum_{lights}(L_A*C_A)$
    • ambient light $L_A$, material ambient value $C_A$

• Diffuse Light 漫反射光

  • $D=\sum_{lights}L_D*C_D(L\cdot N)$
    • diffuse value $L_D$; material ambient value $C_D$;
    • light vector $L$; normal vector $N$

• Specular Light 镜面反射

  • $S=\sum_{lights}L_S*C_S(V\cdot R)^K$
    • specular value $L_S$; material value $C_S$; material shininess $K$ （聚集度 0～127）
    • eye vector $V$; the reflection of a light vector $R$
  • $R=L-2(N(N\cdot L))$

• Local Illumination Model

  • $I=L_0+\sum_{light}(LAC_A)+\sum_{lights}L_D*C_D(L\cdot N)+\sum_{lights}L_SD_S(V\cdot(L-2(N(N\cdot L))))^K$
  • four vectors:
    • To Source $l$
    • To viewer $v$
    • Normal $n$
    • Perfect reflector $r$

• Blinn-Phong Lighting Model

  • the modified Blinn-Phong lighting model
    • 半角向量 $h=\frac{l+v}{|l+v|}$，将$(r\cdot v)^e$替换成$(n\cdot h)^{e’}$
    • $S=\sum_{lights}L_SC_S(n\cdot h)^{K_1}$

3. Surface orientation and Material

• two need things: normals & material

4. Light Properties

• Types of Light Sources

  • Point lights: $(x,y,z,1)^T$
  • Directional/parallel lights: $(x,y,z,0)^T$
  • Spotlights: position, direction, angle(cutoff)
  • Ambient Lights

• Light Position

  • $n$: the normal of the surface
  • $(x,y,z)$: the coordinates of a point on the surface
  • $s$: the direction of the light source at $(x,y,z)$

• Directional Sources

  • $s$ remains unchangeed across a surface

• The spot of the Light Source

  • Define:
    • the position $P$
    • direction $D$
    • cutoff $\theta $
    • dropoff $d$
  • Q is in cutoff $\theta$: $l_Q=\cos^d(\phi)=((Q-P)\cdot D)^d$, if $\phi<\theta$
  • Q is out of range cutoff $\theta$: $I_Q=0$, if$\phi>\theta$

• Light Attenuation

  • For a point light source, the attenuation factor is
    • $A_f=\frac{1}{d^2}$ (in theory)
    • $A_f=\frac{1}{a+bd+cd^2}$ (in practice)
  • For a directional light source, $A_f=1$
    • $I=L+\sum_{lights}A_f\times L_A\times C_A+\sum_{lights}A_f\times L_D\times C_D\times(L\cdot N)+\sum_{lights}A_f\times L_S\times C_S(N\cdot H)^K$

• Color for a Light Source – RGB values

  vec4 diffuse0 =vec4(1.0, 1.0, 1.0, 1.0); //white color 
  vec4 ambient0 = vec4(1.0, 1.0, 1.0, 1.0); //white color 
  vec4 specular0 = vec4(1.0, 1.0, 1.0, 1.0); //white color 
  // specify the position of a point light source
  vec4 light0_pos =vec4(1.0, 2.0, 3,0, 1.0); 
  //specify the direction of a directional light source
  vec4 light1_pos =vec4(1.0, 1.0, 1,0, 0.0);

5. Moving Light Sources

• 移动物体或光源，受视图-模型矩阵影响

6. Shading 着色、明暗绘制

• Shading
  • 计算每个图形对象的颜色
  • 使用每个顶点的属性计算对象上每个像素的颜色
  • 意味着颜色可以通过光照模型来设置和计算
  • OpenGL可以使用均匀着色（flat shading）和平滑着色（smooth shading, Gouraud）两种着色
• Constant (Flat) Shading
  • 多边形上每个点的颜色值都相同，对每个多边形只需要进行一次明暗计算
  • 效果不好，因为人视觉系统有侧抑制（laeral inhibition）的性质，Mach带效应（March band）。
• Gouraud (Smooth) Shading
  • 每个顶点都分配一个法向量（可能是多边形的法向量，也可能是相邻面的法向量的平均值）
  • 插值计算
    • $n_c(\alpha)=(1-\alpha)n_A+\alpha n_B$，$\alpha=\frac{distance\ of\ AC}{distance\ of\ AB}$
    • $n(\alpha,\beta)=(1-\beta)n_C+\beta n_D$
    • 基于片元的着色（per-fragment shading）
  • $I_{P2}=I_{P1}+\Delta I_{RQ}\times\Delta t$
• Other Shading Models
  • Phong Shading
    • interpolate the normals across a polygon，对多边形上的法向量进行插值
    • 计算每个像素颜色使用独立的局部光照模型
    • $n_{P2}=n_{P1}+\Delta n_{RQ}\times\Delta t$

7. Computing Light in OpenGL

• Light: $(LR,LG,LB)$，material: $(MR,MG,MB)$
• The color of a material mainly depends on the diffuse reflectance.
• The diffuse reflection alone provides most information about the curvature and the depth of an object
• The ambient reflectance of a material is often the same as the diffuse reflectance.
• The highlights produced in specular reflections are the blurred images of the light sources.

8. Front and Back Faces

• Emissive Term
  • If we want to simulate a lamp, light source in OpenGL is defined as an emissive component
• Transparency
  • RGBA

9. Implementing Light Model

• State-based shading functions have been deprecated ($glNormal$, $glMaterial$, $glLight$)

• Method I

  • Vertex Shader

  void main() {
  // Transform vertex position into eye coordinates 
    vec3 pos = (ModelView * vPosition).xyz;
  
      vec3 L = normalize( LightPosition.xyz - pos ); 
    vec3 E = normalize( -pos );
      vec3 H = normalize( L + E );
  
  // Transform vertex normal into eye coordinates
      vec3 N = normalize( ModelView*vec4(vNormal, 0.0) ).xyz;
  
  // Compute terms in the illumination equation 
    vec4 ambient = AmbientProduct;
  
      float Kd = max( dot(L, N), 0.0 );
      vec4 diffuse = Kd*DiffuseProduct;
      float Ks = pow( max(dot(N, H), 0.0), Shininess );
      vec4 specular = Ks * SpecularProduct;
      if( dot(L, N) < 0.0 ) specular = vec4(0.0, 0.0, 0.0, 1.0); 
    gl_Position =     Projection * ModelView * vPosition;
  
      color = ambient + diffuse + specular;
      color.a = 1.0; 
  }

  • Fragment Shader

  // fragment shader
  in vec4 color;
  
  void main() {
      gl_FragColor = color; 
  }

• Method II

  • Vertex Shader

  // vertex shader
  in vec4 vPosition; 
  in vec3 vNormal;
  
  // output values that will be interpolatated per-fragment 
  out vec3 fN;
  out vec3 fE;
  out vec3 fL;
  
  uniform mat4 ModelView; 
  uniform mat4 Projection; 
  uniform vec4 LightPosition;
  
  void main() {
      fN = vNormal;
      fE = vPosition.xyz;
      fL = LightPosition.xyz;
  
      if( LightPosition.w != 0.0 ) {
          fL = LightPosition.xyz - vPosition.xyz;
      }
  
      gl_Position = Projection*ModelView*vPosition; 
  }

  • Fragment Shader

  // fragment shader
  // per-fragment interpolated values from the vertex shader 
  in vec3 fN;
  in vec3 fL;
  in vec3 fE;
  
  uniform vec4 AmbientProduct, DiffuseProduct, SpecularProduct; 
  uniform float Shininess;
  
  void main() {
  // Normalize the input lighting vectors vec3 N = normalize(fN);
      vec3 E = normalize(fE);
      vec3 L = normalize(fL);
      vec3 H = normalize( L + E ); 
    vec4 ambient = AmbientProduct;
  
    float Kd = max(dot(L, N), 0.0); 
    vec4 diffuse = Kd*DiffuseProduct;
  
      float Ks = pow(max(dot(N, H), 0.0), Shininess); 
    vec4 specular = Ks*SpecularProduct;
  
  // discard the specular highlight if the light's behind the vertex 
    if( dot(L, N) < 0.0 )
          specular = vec4(0.0, 0.0, 0.0, 1.0);
  
    gl_FragColor = ambient + diffuse + specular;
      gl_FragColor.a = 1.0; 
  }

10. Other Techniques

• Anisotropic Shading 各向异性的光照
  • CD、光盘的照亮
• Bump Mapping
• Global Illumination
  • Ray Tracing: great specular, approx diffuse
  • Radiosity: great diffuse, ignore specular