Barycentric coordinates and transfinite interpolation
Barycentric coordinates and transfinite interpolation
Barycentric coordinates and transfinite interpolation
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Properties<br />
◮ Lagrange property: λ i (v j ) = δ ij .<br />
◮ Interpolation: if<br />
n∑<br />
g(x) = λ i (x)f (v i ),<br />
i=1<br />
then g(v i ) = f (v i ).<br />
◮ Linear precision: if f is linear then g = f .<br />
◮ λ i lies between the two functions:<br />
1<br />
1<br />
0<br />
0<br />
0<br />
0<br />
0<br />
0<br />
◮ Generalized Bernstein-Bezier:<br />
p(x) = ∑ ( ) d<br />
λ i 1<br />
i 1<br />
(x) · · · λ in n (x)c i .<br />
|i|=d<br />
0<br />
0<br />
0<br />
0