Texture Mapping 纹理映射

Interpolation Across Triangles: Barycentric Coordinates 重心坐标

  1. A coordinate system for triangles ( $\alpha ,\beta ,\gamma$ )
    • $(x,y)=\alpha A+\beta B+\gamma C, where \alpha ,\beta ,\gamma>0 and \alpha ,\beta ,\gamma+1=0$
    • How to Calculate them? Use the triangle area:
      $$
      \alpha = \frac{A_A}{A_A+A_B+A_C}, \
      \beta = \frac{A_B}{A_A+A_B+A_C}, \
      \gamma = \frac{A_C}{A_A+A_B+A_C}
      $$
    • 重心坐标不具有投影变换不变性，所以先三维插值，再投影到二维面上去
  2. Texture Magnification: What if the texture is too small?)
    1. A pixel on a texture — a texel (纹理元素、纹素)
    2. Solution:
      • Bilinear Interpolation:
        双线性插值 Use the nearest 4 point to interpolation
        Actually use 3 interpolations, Horizontal twice and vertical once.
      • Bicubic Interpolation …
  3. Texture Magnification (hard case) (What if the texture is too large?)
    1. Antialiasing – Supersampling
      • MSAA: Yes, but costly.
      • Signal frequency too large in a pixel.
    2. So what if we don’t sample– Just need to get the average value within a range.
      • Point Query vs. Range Query
      • Mipmap, a serial of image of texture.(128x128)
        • level 0 is the texture it self.
        • level x is the $\frac{1}{4^x}$ size of the level 0
        • all of the mipmap just cost more $\frac{1}{3}$ space
    3. Computing Mipmap level D
      • Reflect pixel and its neighbor to the textrue, and choose half of them.
      • Get the map of the texture, change the pixel reflection to the square area (use the max deritative).
      • D rounded to the nearest integer level: bad
      • How to solve when D=0.8? Bilinear result between level
      • Mipmap trilinear sampling~
      • But it is overblur…
    4. Anisotropic Filtering 各向异性过滤
      RipMap, 3 times size of the former texture space
    5. EWA Filter 椭圆加权平均滤波
  4. Texture Application
    • Enviroment Map—反光
      • Enviroment Lighting
      • Use a pheir/cubic to reflect the enviroment light
    • Texture can not only present the color, but also the Relative height
      • Bump mapping 凹凸贴图 给像素增加法线扰动
        • 如何求法线 用微分求切线，两个方向切线, $n=(-dP/du,-dP/dv,1).normolization()$，注意求的是原坐标系的法线
      • Displacement mapping 位移贴图 真的移动了顶点位置，需要模型本身足够细，比纹理密度还要高(Direct X 不需要，有动态细分的功能)
    • 3D Texture 应用噪声生成三维模型的纹理（大理石）
    • Ambient Occlusion 环境光遮蔽，用纹理记录环境光的信息
    • 3D Textures and Volume Rendering 立体渲染