Digital Signal Processing Reference
In-Depth Information
4.2
Improved Animation Based on Physical Properties
The shape matching method does not take into account the physical properties
such as mass. Therefore, in some cases, unrealistic animation is generated where
thick branches and thin branches are similarly bended by external forces. How-
ever, the thick branches should be less accelerated than thin ones. In order to
express such behaviors, we assigned larger masses to the vertices in the thicker
branches. If we model every branch with the same number of vertices, the ver-
tices in a cluster with bigger volume can be regarded a sample of the larger area.
Therefore, such vertices should be assigned larger masses. Therefore, the mass
of each vertex can be computed by considering the volume of the cluster where
the vertex is located.
V
c
, the volume of the cluster of which shape is truncated
cone can be easily computed as follows:
V
c
=
3
∗
t
+
r
t
r
b
+
r
b
)
(
r
∗ l
(9)
where
r
t
and
r
b
are the radii of the circles at the top and the bottom respectively,
and
l
is the length of the truncated cone. The volume-based mass assignment
generates plausible branch animation. Let us assume the volume of the cluster
is decreasing in accordance with the height. In that case, the cluster at top-most
location will be lighter than others. When an external force is applied to the
clusters, the top-most cluster will be accelerated more than any other clusters.
After the reasonable animation, the hierarchical shape matching will restore the
shape to a plausibly deformed state as shown in the figure.
The real world leaves can be separated from the tree by strong external forces.
In our method, the leaves can be easily detached from the tree branches by
invalidating the overlapping properties of the overlapping vertices in the leave
clusters when the force exceeds a given threshold. The global shape matching
will keep the leaves from floating away from the tree. Therefore, we turn off
the initial position based matching when the overlapping property of the leave
cluster is disabled.
5 Experiment
We implemented the proposed method on a system with Intel 3.47 GHz i7 CPU,
24 G DDR3 RAM, and NVidia GTX 590 GPUs running on Windows 7 OS.
The computational performance in the aspect of frame rates is shown in Ta-
ble. 1. As shown in the table, even with the complex model with 211,812 vertices,
the proposed method could generate an interactive animation with the perfor-
mance of 32 frames per second.
Fig. 3 shows the growing of a virtual tree. The L-system based production
rules can generate plausible trees as shown in the figure. By changing the rules
or the initial string, we could generate various types of trees. By the nature of
the exponential growth, a realistic tree could be easily obtained with a few steps
of growth.
