Digital Signal Processing Reference
In-Depth Information
Fig. 2.
Overlapping clusters: the cluster
c
6
shares the vertices
x
7
,x
8
,x
12
,x
13
with
adjacent clusters
c
1
,c
2
,c
3
,c
5
,c
7
,c
9
,c
10
,and
c
11
As shown in Fig.1, the cluster
c
i
is composed of 4 vertices, and Each cluster
shares some vertices with adjacent clusters as shown in Fig. 2.
In this paper we employed distortion transportation between shape matching
based deformable objects. The difference between the goal position of deformed
cluster and undeformed cluster is transferred along the chained clusters, and the
effect of the transfer produces wave motion.
(a) shared vertex
x
13
(b) shared vertex propagates the wave (c) propagated waves
Fig. 3.
Wave energy transportaion
When an external force is applied to
x
13
in Fig. 3, the clusters which share
the vertex also deformed as shown in Fig. 3. The clusters are animated to restore
the original shape by shape matching algorithm. The shape matching applied to
each cluster produces different goal position of
x
13
such as
g
13
,
g
13
,
g
13
,and
g
10
11
13
as follows:
6
7
10
11
g
13
=(
g
13
+
g
13
+
g
13
+
g
13
)
/N
cluster
(8)
where
N
clusture
denotes the number of clusters that share the vertex.
Water Surface Boundary.
For the realistic animation of water surface, the
wave should be reflected at the boundary of the water surface. However, the
previous methods cannot easily produce the wave reflection. In our method, the
reflection can be easily produced by simply constrain the boundary vertices. Fig.
4 shows the wave reflection result when the boundary vertices are constrained
not to move. As shown in the Fig. 4 (a), the external force applied to a vertex
produces wave shown in Fig. 4 (b). The wave is reflected at the constrained
vertices as shown in Fig. 4 (c) because the goal positions of the vertices are con-
stant. Our method, therefore, easily produce wave reflection and the boundary
of the water surface can be easily specified.
