Barycentric coordinate g=agi+Bgi+ygk a+B+y=1, c,B,Y≥0. Si g Q= Si+Sj+Sk Si:area of the green triangle gkBarycentric coordinate 𝑔 𝑖 𝑔 𝑗 𝑔 𝑘 𝑔 𝑔 = 𝛼 𝑔 𝑖 + 𝛽 𝑔 𝑗 + 𝛾 𝑔 𝑘 𝛼 + 𝛽 + 𝛾 = 1 , 𝛼 , 𝛽 , 𝛾 ≥ 0 . 𝛼 = 𝑠𝑖 𝑠𝑖 + 𝑠𝑗 + 𝑠 𝑘 𝑠 𝑖 : area of the green triangle