Last Lecture

• Shading 1
  • Blinn-Phong reflectance model
    • Diffuse
    • Specular
    • Ambient
  • At a specific shading point

Today

• Shading 2
  • Blinn-Phong reflectance model
    • Specular and ambient terms
  • Shading frequencies
  • Graphics pipeline
  • Texture mapping
  • Barycentric coordinates

Blinn-Phong reflectance model

Recap: Lambertian (Diffuse) Term

Specular Term (Blinn-Phong)

• intensity depends on view direction
  • Bright near mirror reflection direction
• $\mathbf{v}$ close to mirror direction $\Leftrightarrow$ half vector near normal

  • Measure “near” by dot product of unit vectors

    $$ \mathbf{h} = bisector(\mathbf{v}, \mathbf{l}) = \frac{\mathbf{v}+\mathbf{l}}{\lVert\mathbf{v}+\mathbf{l}\rVert} $$

    $$ \begin{aligned}L_{s}&= k_s(I/r^2)\max(0, cos\alpha)^p\\&=k_s(I/r^2)\max(0, \mathbf{n}\cdot\mathbf{h})^p\end{aligned} $$

  • $L_s$ → specularly reflected light; $k_s$ → specular coefficient

  • 用半程向量是因为好计算，如果用反射向量则为Phone模型，计算量更大

• Cosine Power Plots
  • Increasing $p$ narrows the reflection lobe → $p$越大，高光越「小」
  • 在Blinn-Phong模型中一般取值100-200

Ambient Term

• Shading that does not depend on anything

  • Add constant color to account for disregarded illumination and fill in black shadows

  • This is approximate / fake! → 不讲究入射角度，不讲究观测角度，也不讲究法线角度 → 常数

    $$ L_a = k_aI_a $$

  • $L_a$ → reflected ambient light; $k_a$ → ambient coefficient

Blinn-Phone Reflection Model

• Ambient + Diffuse + Specular = Blinn-Phong Reflection
• $\begin{aligned}L&=L_a+L_d+L_s\\&= k_aI_a+k_d(I/r^2)\max(0, \mathbf{n}\cdot\mathbf{l})+k_s(I/r^2)\max(0, \mathbf{n}\cdot\mathbf{h})^p\end{aligned}$

Shading Frequencies

Shade each triangle (flat shading)

• Flat shading
  • Triangle face is flat - one normal vector
  • Not good for smooth surfaces

Shade each vertex (Gouraud shading)

• Gouraud shading
  • Interpolate colors form vertices across triangle
  • Each vertex has a normal vector (how?)