Barycentric coordinates and transfinite interpolation
Barycentric coordinates and transfinite interpolation
Barycentric coordinates and transfinite interpolation
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Mean value <strong>coordinates</strong><br />
v i+1<br />
v i<br />
x<br />
α i<br />
α i−1<br />
v i−1<br />
For a convex polygon, n vertices, let λ i (x) = w i (x)/ ∑ n<br />
j=1 w j(x),<br />
where<br />
w i (x) =<br />
(<br />
1<br />
tan<br />
‖v i − x‖<br />
(<br />
αi−1 (x)<br />
2<br />
)<br />
+ tan<br />
Then λ 1 , . . . , λ n are barycentric <strong>coordinates</strong>.<br />
(<br />
αi (x)<br />
2<br />
))<br />
.