Virtual Character Definition and Animation within the MPEG-4 Standard - 3D Modeling and Animation: Synthesis and Analysis Techniques for the Human Body - page 46

bone. Specifically, it is defined by means of: (1) a curve represented as a NURBS
which can be deformed; and (2) a model of influence of the curve deformation
on the skin of the model.
Each bone and each muscle influences the skin deformation. Thus, by changing
a bone position or orientation or by deforming the muscle curve, the skin vertices
belonging to the associated influence volume will be displaced accordingly. Here,
the skinned virtual character definition consists in specifying for each bone and
for each muscle an associated influence volume, i.e., the subset of the affected
skin vertices together with the related measure of affectedness through weight-
ing coefficients. The influence can be directly specified vertex-by-vertex by the
designer of the synthetic model, or computed before performing the animation.
In the first case, the list of affected vertices and the weighting coefficients are
included in the bone/muscle definition. In the second case, distinct approaches
are proposed for bones and muscles, respectively. The following sub-section
present different strategies for computing the bone and the muscle influence
volume, respectively.

Bone and muscle-based modeling and animation

The bone influence volume is defined as the support of the affectedness measure
µ

( µ ) ∪ µ ∪ µ

. Here µ is expressed as a family of functions . µ d is

[] d d ∈ 0 , l

− +

0 l

Figure 10. Bone and muscle modeling.

(a) Forearm bone influence volume. (b) The muscle influence volume.