Barycentric coordinates and transfinite interpolation
Barycentric coordinates and transfinite interpolation
Barycentric coordinates and transfinite interpolation
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In R n we interpolate the data f <strong>and</strong> ∂f<br />
∂n<br />
on ∂Ω by the function<br />
p(x) = g 0 (x) + ψ(x)g 1 (x), x ∈ Ω,<br />
where<br />
<strong>and</strong><br />
m(y) =<br />
∫<br />
/<br />
f (p(x, v))<br />
g 0 (x) =<br />
S ‖p(x, v) − x‖ dv φ(x),<br />
/<br />
ψ(x) = 1 φ(x),<br />
∫<br />
g 1 (x) =<br />
S<br />
/<br />
m(p(x, v))<br />
‖p(x, v) − x‖ dv φ(x),<br />
∫<br />
φ(x) =<br />
1<br />
‖p(x, v) − x‖ dv.<br />
S<br />
( ∂f<br />
∂n (y) − ∂g 0<br />
∂n (y) ) / ∂ψ<br />
∂n (y),<br />
y ∈ ∂Ω.