Game Engine Architecture

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LERP

Clip A

Clip B

Output Pose

β

Figure 11.47. A binary LERP blend, represented by a binary expression tree.

11.10.3.1. Binary LERP Blend

As we saw in Section 11.6.1, a binary linear interpolation (LERP) blend takes
two input poses and blends them together into a single output pose. A blend
weight β controls the percentage of the second input pose that should appear
at the output, while (1 – β) specifi es the percentage of the fi rst input pose. This
can be represented by the binary expression tree shown in Figure 11.47.

11.10.3.2. Generalized One-Dimensional LERP Blend

In Section 11.6.3.1, we learned that it can be convenient to defi ne a generalized
one-dimensional LERP blend by placing an arbitrary number of clips along a
linear scale. A blend factor b specifi es the desired blend along this scale. Such
a blend can be pictured as an n-input operator, as shown in Figure 11.48.
Given a specifi c value for b, such a linear blend can always be transformed
into a binary LERP blend. We simply use the two clips immediately adjacent
to b as the inputs to the binary blend and calculate the blend weight β as speci-
fi ed in Equation (11.12). This is illustrated in Figure 11.48.

For this specific value of

b, this tree converts to...

β = 0

β = 1

β

b

bA

bB

bC

bD

LERP Output Pose

b

Clip A

Clip B

Clip C

Clip D

LERP

Clip B

Clip C

Output Pose

β

Figure 11.48. A multi-input expression tree can be used to represent a generalized 1D blend.
Such a tree can always be transformed into a binary expression tree for any specifi c value of
the blend factor b.

11.10. The Animation Pipeline