Biomedical Engineering Reference
In-Depth Information
deformation and do not include the deformation inside the volume, so it does not
capture pose-dependent deformations correctly.
The incompressibility of the human skin is realized in mathematical models by
simulating the volume conservation of the deformable bodies. Terzopoulos and
Wa t er s [
24
] used a multi-layered mass-spring structure to yield the volume pre-
serving constraints to simulate the effects of incompressible fatty tissue. However,
the difficulty in handling the volume preservation in a mass-spring system makes
the finite element methods widely used as an alternative approach. The nonlinear
Green-Lagrangian strain tensor can express large deformations correctly whereas
expensive computation is required. However, using a quasi-static approximation, it
is still possible to have a practical character skinning. Teran et al. [
28
] presented a
quasi-static solution for flesh deformation driven by a skeleton. Lee et al. [
5
]useda
similar method to compute the deformation of the soft tissue in their biomechanical
model of the human upper body. Though such quasi-static solutions are much faster
than a fully dynamics simulation with the same model size, they do not capture the
dynamic behaviors of the soft body such as jiggling. Fast simulation also can be
pursued by simplifying the computation using a linearized strain, or infinitesimal
strain under the assumption of small deformation [
29
]. Nonetheless, it causes seri-
ous problems such as inflation of the body especially when the deformation contains
rotational part. To alleviate this shortcoming, many corotational methods (e.g. [
30
,
31
]) are proposed to remove as much of the rigid rotation as possible by using lo-
cal coordinate frames following the global motion of the body. Though corotated
linearized strain has been widely used in interactive graphics applications, it is still
valid only when the deformation is very small.
In deformable character animation, the size of the skin model can be large, and
often requires a lifelike skin deformation, especially in animation film and interactive
graphics application. A high resolution finite element model has to be built with a
large amount of elements, which can eventually be million-scale [
5
]. This makes the
simulation totally impractical by current common computing power.
Methods using modal reduction to reduce the complexity of a finite element
systemhave been investigated, whereas they are not sufficient to capture the nonlinear
deformations. Alternatively, many current techniques called
mesh embedding
use the
concept of spatial embedding, where a relatively low-dimensional coarse volumetric
mesh enclosing the entire deformable body is generated, and it expresses the behavior
of the body and embeds a fine geometry which is also for the visualization of the
skin deformation. One of these techniques relies on a free-form deformation lattice
attached to the skeleton [
32
].
Mesh embedding has been widely used to simulate soft bodies as it reduces the
DOF of the deformable bodies without losing the fine geometry of the characters
and the internal skeleton can be handled more easily in the embedding mesh system
compared to the modal reduction [
33
]. For that reason, Lee et al. [
5
] embed a high-
resolution skin surface as the visualization geometry into the simulation mesh in
their comprehensive upper human body model.
Since in skinning, the realism delivered to observers lies in the visualization
of skin deformation, some frameworks prefer to replace the skin simulation by
