Graphics Reference
In-Depth Information
B
C
A
D
Fig. 11.15. A concave polygon.
If we use barycentric coordinates to define a point P 0 as
P 0 = r A + s B + t C + u D
where r + s + t + u =1.
When t =0, P 0 can exist anywhere inside triangle ∆ ABD . Thus, if any
vertex creates a concavity, it will be ignored by barycentric coordinates.
11.6 Areas
Barycentric coordinates are also known as areal coordinates due to their area
dividing properties. For example, in Figure 11.16 the areas of the three internal
triangles are in proportion to the barycentric coordinates of the point P
To prove this, let P have barycentric coordinates
P = r A + s B + t C
where
r + s + t =1
and
0
r, s, t
1
C
r
ABC
s
ABC
P
t
ABC
A
B
Fig. 11.16. The areas of the internal triangles are directly proportional to the barycen-
tric coordinates of P .
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