dFdy give derivatives of vertex position and texture coordinate. Computer Graphics Course @Waseda University 38 𝐩: vertex position 𝐮: texture coordinate screen pixels 𝜕𝐩 𝜕𝑥 = dFdx 𝐩 , 𝜕𝐩 𝜕𝑦 = dFdy 𝐩 , 𝜕𝐮 𝜕𝑥 = dFdx 𝐮 , 𝜕𝐮 𝜕𝑦 = dFdy 𝐮 , 𝜕𝐩 𝜕𝑥 = 𝜕𝑢 𝜕𝑥 ⋅ 𝜕𝐩 𝜕𝑢 + 𝜕𝑣 𝜕𝑥 ⋅ 𝜕𝐩 𝜕𝑣 𝜕𝐩 𝜕𝑦 = 𝜕𝑢 𝜕𝑦 ⋅ 𝜕𝐩 𝜕𝑢 + 𝜕𝑣 𝜕𝑦 ⋅ 𝜕𝐩 𝜕𝑣 chain rule of partial derivative (known values, unknown values) It’s simple linear system!