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Facial Animation and Expression 169

this expression). The prototypes for anger, P anger , and fear, P fear , each have a distinct
configuration for the lips (furious lips form a snarl, terrified lips form a grimace).
Each dimension of the affect space is bounded by the minimum and maximum allowable
values of (min, max) = (−1250, 1250). The placement of the prototype postures is given
in figure 10.5. The current net affective assessment from the emotion system defines the
[A, V, S] = (a,v, s)pointinaffectspace.Thespecific(a,v, s)valuesareusedtoweightthe
relative motor contributions of the basis postures. Using a weighted interpolation scheme,
the net emotive expression, P net , is computed. The contributions are computed as follows:

(10.1)
P net = C arousal + C valence + C stance
where
P net is the emotive expression computed by weighted interpolation
C arousal is the weighted motor contribution due to the arousal state
C valence is the weighted motor contribution due to the valence state
C stance is the weighted motor contribution due to stance state
These contributions are specified by the equations:

C arousal = αP high + (1 − α)P low
C valence = β P positive + (1 − β)P negative
C stance = F(a,v, s, n) + (1 − δ)(γ P open + (1 − γ)P closed )

where the fractional interpolation coefficients are:
α, 0 ≤ α ≤ 1 for arousal
β, 0 ≤ β ≤ 1 for valence
γ, 0 ≤ γ ≤ 1 for stance
δ, 0 ≤ δ ≤ 1 for the specialized prototype postures

such that δ and F(A, V, S, N) are defined as follows:
δ = f anger (A, V, S, N) + f fear (A, V, S, N) + f disgust (A, V, S, N)
F(A, V, S, N) = f anger (A, V, S, N) · P anger +
f fear (A, V, S, N) · P fear +
f disgust (A, V, S, N) · P disgust
The weighting function f i (A, V, S, N) limits the influence of each specialized proto-
type posture to remain local to their region of affect space. Recall, there are three spe-
cialized postures, P i , for the expressions of anger, fear, and disgust. Each is located at
corre-
(A P i , V P i , S P i ) where A P i corresponds to the arousal coordinate for posture P i , V P i
corresponds to the stance coordinate. Given the
sponds to the valence coordinate, and S P i
current net affective state (a,v, s) as computed by the emotion system, one can compute