Digital Signal Processing Reference
In-Depth Information
4 Hierarchical Shape Matching for Realistic Animation
In order to avoid the problems of the multi-cluster approach, we propose a hier-
archical shape matching. When the goal locations are computed, the hierarchical
approach not only performs the local cluster-based shape matching but also em-
ploys the global shape matching for preserving the initial shape of the tree.
4.1 Global Shape Matching
The multi-cluster approach cannot maintain the original shape of the tree since
the shape matching forces only considers the shape of each local cluster. In this
method, each vertex is forced to move back to the original location of the vertex.
The whole shape of the tree can then be easily restored by global shape matching
with the adjusted velocity as follows:
global
i
original
i
local
i
v
=
v
+
k
d
(
p
− p
i
)
(8)
global
i
local
where
v
i
is the
velocity computed in the cluster-based local shape matching.
p
i
is the location of
the particle determined by the local shape matching while
p
is the velocity of
i
after the global shape matching, and
v
original
i
denotes the
original location of the vertex.
k
d
denotes the damping or controlling parameter
for the speed of the global restoration.
Fig. 2.
Hierarchical shape matching concept
Fig. 2 shows the concept of the hierarchical shape matching with the local
and global shape matchings. Each cluster in a tree model changes its shape
when an external force is applied. The local shape matching restores the original
shape of each cluster with the waves and oscillations generated. The global shape
matching makes the tree more plausible by removing the unrealistic waves and
oscillations on the tree.
