Game Engine Architecture

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and ()P 2 j, respectively. Furthermore, the barycentric coordinate (⅓, ⅓, ⅓) lies
at the centroid of the triangle and gives us an equal blend between the three
poses. This is exactly what we’d expect.

11.6.3.4. Generalized Two-Dimensional LERP Blending

The barycentric coordinate technique can be extended to an arbitrary number
of animation clips positioned at arbitrary locations within the two-dimension-
al blend space. We won’t describe it in its entirety here, but the basic idea is
to use a technique known as Delaunay triangulation (htt p://en.wikipedia.org/
wiki/Delaunay_triangulation) to fi nd a set of triangles given the positions of
the various animation clips bi. Once the triangles have been determined, we
can fi nd the triangle that encloses the desired point b and then perform a
three-clip LERP blend as described above. This is shown in Figure 11.37.

b 0

by

b

b 1

b 2

α

β

γ

bx

Figure 11.36. Various barycentric coordinates within a triangle.

b 0 Clip A

Clip B

b 1

Clip C

Clip D Clip E Clip F

Clip G

Clip H Clip I

Clip J

b 2

b 3

b 4 b^5

b 6

b 7

b 8

b 9

by

bx

Figure 11.37. Delaunay triangulation between an arbitrary number of animation clips
positioned at arbitrary locations in two-dimensional blend space.

11.6. Animation Blending