Barycentric Coordinates for Arbitrary Polygons in the Plane

BARYCENTRIC COORDINATES FOR ARBITRARY POLYGONS 9
Figure 5: Colour interpolation with generalized barycentric coordinates for the polygons
from Figure 4.
function F (v)
for i = 1 to n do
s i := v i − v
for i = 1 to n do
r i := ‖s i ‖
A i := det(s i , s i+1 )/2
D i := 〈s i , s i+1 〉
if r i = 0 then
// v = v i
return f i
if A i = 0 and D i < 0 then // v ∈ e i
r i+1 = ‖s i+1 ‖
return (r i+1 f i + r i f i+1 )/(r i + r i+1 )
f := 0
W := 0
for i = 1 to n do
w := 0
if A i−1 ≠ 0 then
w := w + (r i−1 − D i−1 /r i )/A i−1
if A i ≠ 0 then
w := w + (r i+1 − D i /r i )/A i
f := f + wf i
W := W + w
return f/W
Figure 6: Pseudo-code for evaluating the interpolation function.
Technical Report IfI-05-05