Virtual Character Definition and Animation within the MPEG-4 Standard - 3D Modeling and Animation: Synthesis and Analysis Techniques for the Human Body - page 43

Figure 8. Mesh deformation principle. (continued)

ϕ

(d) Deformation by superposition
of

(c) applied to the

subset

j

ϕ ϕ and .

.

Ω

j

i

j

( C = { S , V ( S ), µ }

A family of controllers is said to be associated with a

i i i i i

mesh M (Ω ) (Figure 9) if and only if the following relationships are fulfilled:

{ }

Ω = Ω ∩ V ( S ) ψ Ω

(1) ∀ i ∈ 0 1 ..., n and (2) there exists a mapping from

i i i i

to S i , such that any vertex

v ∈ Ω

is linked to a set of the elements of S i . Applying

i

Figure 9. Deformation controllers associated with the mesh.