Virtual Character Definition and Animation within the MPEG-4 Standard - 3D Modeling and Animation: Synthesis and Analysis Techniques for the Human Body - page 61

Figure 14. A 2D cross-section through the object.

G 2

G 2

GV

1

V

offset = ,

V

GG
offset

12

G 1 G 1

G VGG ff et =

1 1 2

with ∈ [0,1)

(9) (10)

(a) (b)

reference surfaces from different sets. As illustrated in Figure 14a, each vertex
is attached to a grid position G 1 , and the relative position of vertex V with respect
to G 1 and G 2 is given by the scalar offset (see Equation (9)). When either G 1 or
G 2 moves during the animation (shown in Figure 14b), the coordinates ( x , y , z ) of
V can be updated as given by Equation (10).
A multi-resolution model can be designed by choosing a multi-resolution refer-
ence system, each resolution level having its corresponding reference grid. The
multi-resolution reference system has a hierarchical structure (see Figure 13e),
which allows obtaining from the last resolution level reference system any lower-
resolution-level reference system by removing the appropriate reference sur-
faces.
The connectivity-wireframe obtained from a model (Figure 13b), by scanning it
according to a hierarchical reference system (Figure 13e), has a hierarchical
structure, as well. This can be proven considering that all the vertices from any
lower-resolution-level R l are preserved in the immediate higher-resolution-level
R l+1 , since the reference system of resolution level R l is a sub-set of the reference
system of resolution level R l+1 . In addition, resolution level R l+1 will insert new
vertices and, therefore, alter the connectivity between the vertices of resolution
level R l . A hierarchical connectivity-wireframe can be decomposed into single-
resolution connectivity-wireframes, and each of them can be triangulated to
obtain the corresponding mesh, as show in Figure 13d.

Hierarchical reference grid animation
The M ESH G RID model is very flexible for animation purposes, since, in addition to
the vertex-based animation typical for I NDEXED F ACE S ET or S UBDIVISION S URFACE
representations, it allows for specific animation types, such as: (1) rippling