Barycentric coordinates and transfinite interpolation

On arbitrary curves
p ( x, θ)
2
p 3
( x, θ)
p 1
( x, θ)
x
θ
where
g(x) =
∫ 2π
0
n(x,θ)
∑
j=1
φ(x) =
Hormann: φ(x) > 0.
/
(−1) j−1
‖p j (x, θ) − x‖ f (p j(x, θ)) dθ φ(x),
∫ 2π
0
n(x,θ)
∑
j=1
(−1) j−1
‖p j (x, θ) − x‖ dθ.