Barycentric coordinates and transfinite interpolation
Barycentric coordinates and transfinite interpolation
Barycentric coordinates and transfinite interpolation
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Transfinite <strong>interpolation</strong>, Warren et al 2004<br />
c ( t i+1 )<br />
c ( t i)<br />
For convex curve c : [a, b] → R 2 sample points v i = c(t i ) <strong>and</strong> take<br />
limit of Wachspress interpolants as max i (t i+1 − t i ) → 0. Gives a<br />
‘<strong>transfinite</strong> interpolant’<br />
∫ /<br />
b<br />
∫ b<br />
g(x) = w(x, t)f (c(t)) dt w(x, t) dt,<br />
a<br />
where w(x, t) = (c ′ (t) × c ′′ (t))/((c(t) − x) × c ′ (t)) 2 .<br />
a