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 />
g(x) =<br />
3∑<br />
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 />
◮ Linearity: λ i is linear.<br />
◮ Bernstein-Bezier basis for polynomials, degree d:<br />
p(x) =<br />
∑<br />
i+j+k=d<br />
n!<br />
i!j!k! λi 1(x)λ j 2 (x)λk 3(x)c ijk .