DIRECTABLE AND STYLIZED HAIR SIMULATION
Yosuke Kazama, Eiji Sugisaki and Shigeo Morishima
Waseda University, Tokyo, Japan
Keywords: Hair Animation, External Force Field, editing system, hair simulation.
Abstract: Creating natural looking hair motion is considered to be one of the most difficult and time consuming
challenges in CG animation. A detailed physics-based model is essential in creating convincing hair
animation. However, hair animation created using detailed hair dynamics might not always be the result
desired by creators. For this reason, a hair simulation system that is both detailed and editable is required in
contemporary Computer Graphics. In this paper we therefore, propose the use of External Force Field (EFF)
to construct hair motion using a motion capture system. Furthermore, we have developed a system for
editing the hair motion obtained using this process. First, the environment around a subject is captured using
a motion capture system and the EFF is defined. Second, we apply our EFF-based hair motion editing
system to produce creator-oriented hair animation. Consequently, our editing system enables creators to
develop desired hair animation intuitively without physical discontinuity.
1 INTRODUCTION
Recently, virtual humans are being increasingly used
in various CG applications and realistic hair design,
modeling and animation are fundamental elements
required in the creation of virtual humans. However,
simulating natural-looking human hair has proven to
be one of the most difficult and challenging tasks in
CG animation as a result of its complicated motion
characteristics, volume, and fineness. In
entertainment applications, creators hope to not only
achieve
a natural-looking result but also to convey
their taste, intentions, and imagination. Even when
animation is correct from a physics-based
perspective, results can be worthless if the animation
fails to reflect the creators’ artistic intentions. For
these reasons, we have developed a motion capture-
based hair animation system with interactive editing
capabilities.
First, we design a hair simulation model for reed-
shaped hair strands. This easy-to-use structure is
commonly utilized in the entertainment industry. For
example, in (FINAL FANTASY  , 2005) the
characters’ hairstyles were modeled using this type
of structure. At that time, however, a feasible
simulation model for hair structures had not yet been
developed, so it was necessary to apply a clothing
simulation to the hair model in order to create the
desired effect. As a result of this need, we develop a
specialized hair simulation model for this hair
structure. In this paper, this structure is referred to as
the “Hair Object Model”.
Secondly, we capture hair motion using a Motion
Capture System, and then design an External Force
Field (EFF) model based on the captured hair
motion data. Generally, because of the limitations of
captured data, creators need to obtain generous
amounts of motion data by capturing each hair style
when blown by winds from different directions.
Using our method, however, the motion capture data
becomes universal and, consequently, various hair
styles can be animated once creators have captured
the hair motion.
Finally, we develop a hair motion editing system
based on EFF. There is a widespread need for not
only realistic-looking but also artistically meaningful
hair motion, especially in entertainment applications.
To create such animation, creators currently have to
modify almost every frame manually. We, therefore,
develop a system that allows creators to easily
modify hair motion by editing EFF. Consequently,
our system enables creators to intuitively design the
natural-looking hair motions they wish to create
without physical discontinuity.
1.1 Related Work
This overview of related work is limited to previous
work on hair dynamics, which focused on explicit
316
Kazama Y., Sugisaki E. and Morishima S. (2008).
DIRECTABLE AND STYLIZED HAIR SIMULATION.
In Proceedings of the Third International Conference on Computer Graphics Theory and Applications, pages 316-321
DOI: 10.5220/0001095003160321
Copyright
c
SciTePress
hair models. These models handle the shape and
dynamics of each strand and are especially suitable
for long hair. (Anjyo et al., 1992) used a simplified
cantilever beam to model hair, and one-dimensional
projective differential equations of angular
momentum to animate strands. (Rosenblum et al.,
1991) and (Daldegan et al., 1993) reduced
computation time by using sparse representative hair
samples. (Bertails et al., 2006) presented Kirchhoff’s
theory for elastic rods. The mechanical model for
one individual hair strand, called Super-Helices,
handles hair natural curliness. Although these
advances have greatly improved hair animation in
CG, CG creators still hope to create animation that
exactly matches their artistic vision. Moreover, their
hair simulation model is usually applied to a single
hair. However the hair object used in commercial
use is usually modeled as reed-shaped polygons.
Therefore, we develop a specialized motion model
for the hair model.
Although hair-hair interaction is not the subject
of this paper, we would like to briefly touch upon
innovative approaches to this issue. (Hadap and M.-
Thalmann, 2001) proposed modeling dense dynamic
hair as a continuum by using a fluid model for
lateral hair movement. (Chang et al., 2002) modeled
a single strand as a multi-body open chain expressed
in generalized coordinates. Dynamic hair-to-hair
collision is solved with the help of auxiliary triangle
strips placed among nearby strands. (Bando et al.,
2003) proposed a method in which they model
unordered particles that have only loose connections
to nearby control points. Considering hair-hair
interaction is also making significant contribution to
hair expression in computer graphics (Ward et al.,
2007).
2 HAIR MODEL
In this section, we introduce our Hair Object Model
and explain why we have attempted to handle this
model. Additionally, we describe how our method
controls hair strand motion.
2.1 Hair Object Model
One of the common models used to create realistic
hair is by mapping textures onto reed-shaped
polygons to represent each hair strand. (Figure1).
This model has already been used to realistically
create the hair of human characters in movies and
games. Our hair structure is also based on this model.
The term “hair strand” usually refers to a single thin
Figure 1: Hair Object Model.
hair. In this paper, however, we use the term to refer
to hair of the structure depicted in right image of
Figure 1. Here, we call whole hair strands “Hair
Object Model”. We describe the simulation model
for this Hair Object Model in the following sub-
section.
2.2 Hair Simulation Model
We construct a specific hair motion structure for the
Hair Object Model (Figure 2). This motion structure
is modeled as chains of rigid stick and springs
connected by control points. Each rigid body has 2
degrees of freedom (angles of spherical coordinate)
and the motion of rigid body is represented by the
following equation (Sugisaki et al., 2006).
Where
i
is the number of hair strands,
j
is the
joint number from the hair root,
ji
I
,,1
is the moment
of inertia,
2, ,ij
I
is the air resistance, and
τ
denotes
the strength of the hair’s own force. This force is an
important factor in creating natural-looking hair
motion. Where
ji,,0
Φ
is the initial angle of joints,
and
ji
r
,
is the length of the rigid body. We explain
the external force to hair strands
),( jiH
in section
2.2.1.
2.3 External Forces
The external force to hair
),( jiH
has five
components. The first component is gravity. Gravity,
g
, is a static force. The second component
)(t
Ω
must be the force of wind. To achieve a natural-
looking hair simulation model,
)(tΩ
can be the key
component of our hair simulation model. We explain
how to model the wind force
)(tΩ
in Section 3. The
third component is the force generated by the head
and body moving. The fourth
),( jiS
is a spring
),()(
,,0,,,,2,,,1
jiHII
jijijijijiji
=ΦΦ+Φ+Φ
τ
),,(
,,,, jijijiji
r
φ
θ
Φ
(1)
DIRECTABLE AND STYLIZED HAIR SIMULATION
317
force The last component
)( j
Ψ
is the force caused
by the collision between the hair object and body.
)(),()()(),( jjiSXtgjiH Ψ++Ξ+Ω+=
)),((),(
,,0
jiLLkjiS
ji
=
)(*),(
, ji
EXRX Φ=Ξ
=Ψ
2
2
)(
exp)(
lj
l
j
κ
=Φ
0)cos(0
0)sin()sin(
00)cos(
)(
,
θ
θφ
φ
ji
E
(2)
Where
X
is the distance in movement of the
head,
ji
L
,
is the current state of the spring,
ji
L
,,0
is
the initial state of the spring,
ji
L
,
is the current state
of the spring, and
l
is the joint number that is
detected by the collision.
3 EXTERNAL FORCE FIELD
Wind streams around the head and body are difficult
to simulate. Consequently, defining the force of
wind on hair strands is considered to be one of the
most challenging tasks in hair simulation. Therefore,
we define a vector field that represents the wind
stream, which we call the “External Force Field”
(EFF).
Figure 2: Hair motion structure.
Figure 3: Reproduction from the motion capture data.
In this section, we introduce a novel approach
for hair motion capture and explain how we
construct the EFF.
First, we capture hair motion using Vicon’s
Motion Capture System. Secondly, we apply a wind
force to the hair motion structure, based on the
motion capture data. Finally, we define the EFF
based on actual captured data by the wind force. We
can therefore create animation of the wind blowing
the hair.
3.1 Hair Motion Capture
3.1.1 Setting for Capturing
We obtain 3D hair motion data using an Optical
Motion Capture System.We prepare a wig to be used
during the motion capture by attaching small
reflective markers to 27 hair strands. The
dimensions of the reflective markers were 1.5mm
wide by 3.0mm long. The capture area is
approximately 4000mm wide by 5000mm long by
3000mm high, and a mannequin wearing the wig
with the 27 hair strands is placed in the center of the
capture area.
3.1.2 Capturing Hair Motion
In this section, we detail how we prepare the hair
strands for the motion capture.
To prevent miscalculations prior to the
experiment in the captured 3D data, we determine to
use as few hair strands as possible. We therefore
select 27 hair strands to represent the overall hair
motion. We lightly attach 4-10 reflective markers
onto each of the hair strands, depending on its length.
In addition, 8 normalized markers are attached to the
forehead, nose, both cheeks, and the jaw and neck of
the person wearing the experimental wig. Secondly,
we attach the 27 representative hair strands to the
wig, arranging them based on the layer model, a
model hair stylists generally use to design human
hair styles.
Figure 3 shows an example of real hair strands
blown by the wind (right image) and the reproduced
hair animation using captured data from the same
wind (left image). As Figure 3 shows, our method
can reproduce hair motion similar to the reference
animation.
3.2 Applying Wind Force
We apply a wind force based on the motion capture
data obtained from the hair motion structure.
:spring
:rigid-body
:control point
:spring
:rigid-body
:control point
GRAPP 2008 - International Conference on Computer Graphics Theory and Applications
318
Where
ji
X
,
is the position of a motion capture
marker,
s
is the frame number of the motion capture
data.
3.3 External Force Field
In this subsection, we introduce the concept of EFF:
one of the advantages of this paper. The EFF is grid
cubes resembling a voxel around the head (Figure 4).
Each cube has a direction and power of a wind force.
The range of the EFF is 60 cm because the lengths
of most hair styles fall within this range. The EFF is
applied to the control points on our hair motion
structure. When a control point moves into a grid
cube, the force effects a change in the motions of the
control point.
Next, we explain how we define the direction
and power of each grid cube. Firstly, we define the
force existing outside of the grid cubes. Even though
the range of the EFF has been designed, there is still
the possibility that a hair strand may move outside of
the grid cubes. Therefore, we define the direction of
the force from a point where the wind is generated
towards the head. Secondly, we allocate the wind
forces from the motion capture data in grid cubes
based on the difference between hair motion capture
data at a certain time step (arrow 1 in Figure 4).
When motion capture markers do not exist at the
time step in a grid cube, the wind force on the grid
cube is defined by interpolating around the wind
force. There are two methods of interpolation. In the
first, the grid cubes are linearly interpolated by the
nearest two cubes (arrow 2 in Figure 4). In this case,
the subject grid cube is nearer to the head or body
than the grid cube with the defined wind force. The
second case is where grid cubes are interpolated by
the nearest cube and the force existing outside of the
EFF (arrow 3 in Figure 4). This process is
implemented by linear interpolation. Through these
processes, the external force is defined (Figure 4).
Repeating these processes, we are able to design
richer EFF that can achieve more impressive hair
animation.
4 MOTION EDITING SYSTEM
In this section, we introduce our hair motion editing
system based on our hair simulation model and EFF
for natural-looking hair motion described in
sections.
Figure 4: External Force Field.
2 and 3. First, we describe the hair motion editing
process before moving on our editing system’s
motion modification process.
As mentioned previously, hair animation in
entertainment applications, movies and games is
intended to reflect the creators’ intentions and
imagination. This means that hair animation should
be either more stylized depending on the effect
desired by the individual animator. In movies,
especially, animation often contradicts the laws of
physics despite appearing natural. For example, hair
motion tends to be more inordinate in movies than in
the real world.
To create hair animation is a time-consuming
and task requiring great skill, because CG creators
manually control each hair strand in each individual
frame. For this reason, we develop a hair motion
editing system to solve such problems.
4.1 Editing Process
The direction and force of wind is determined by
creators in Sections 2 and 3, so that the hair
animation can be created. As mentioned previously,
however, creators might not be satisfied with the
resulting hair animation. For these cases, our system
provides creators with the option of editing hair
motion intuitively. An overview of the editing
process is shown in Table 1. To achieve an
interactive operation, our system allows creators to
set key frames manually. In other words, when using
our system, it is necessary to set the first key frame
and to choose a target hair strand. Creators are then
required to set the second key frame using a mouse.
This process is repeated until creators are satisfied
with the final result. After setting key frames, hair
motion is automatically re-simulated. We describe
how this automatic process is achieved in the next
sub-section.
)(
))0()((2
),(
,
2
,,
ji
jiji
E
s
XsX
ji Φ
=Ω
(3)
:Defined from motion capture data
:Interpolated by the nearest two cubes
:Interpolated by the nearest cube and outside of the EFF
:The force existing outside of EFF
1
2
3
:Defined from motion capture data
:Interpolated by the nearest two cubes
:Interpolated by the nearest cube and outside of the EFF
:The force existing outside of EFF
:Defined from motion capture data
:Interpolated by the nearest two cubes
:Interpolated by the nearest cube and outside of the EFF
:The force existing outside of EFF
1
2
3
DIRECTABLE AND STYLIZED HAIR SIMULATION
319
4.2 Dynamics for Editing
The extra force based on the operation in section 4.1
adds to a wind force
)(tΩ
in EFF. As a result, the
target hair strand moves toward the second key
frame without physical discontinuity. The extra
force
),( jia
is provided by the following equation:
Choosing a direction of wind
Simulating hair motion
Setting the first key frame
choosing a target hair strand
Setting the second key frame
controlling the target hair strand
Setting the final key frame
Re-simulating hair motion
Editing system
Animation
:Manual process
:Automatic process
Choosing a direction of wind
Simulating hair motion
Setting the first key frame
choosing a target hair strand
Setting the second key frame
controlling the target hair strand
Setting the final key frame
Re-simulating hair motion
Editing system
Animation
:Manual process
:Automatic process
Figure 5: Edited EFF.
Table 1: Editing process.
Where
ji,,0
Φ
is the position of the controlled
target hair strand in the second key frame,
t
is the
number of the key frame,
l
is the distance between
the target strand and the edited grid cube,
p
is the
distance from the position of the grid cube to the
center of the edited grid cube.
Thus, the extra force required to change the wind
force is applied to the chosen hair strand from the
first to the last key frame (Figure 5).
5 RESULTS
In this section, we present the results of two
animations created using our approach. The pre-
rendered 120-hair strand
simulation runs between
15fps and 20fps on an Intel Core Duo 2.66Hz,
platform with NVIDIA Quadro FX4500.
2
,0,,
2
2
2( )
(, ) exp
()
ij ij
t
l
ij
lp
s
α
Φ−Φ
⎛⎞
=
⎜⎟
⎝⎠
(4)
Figure 6 shows an example of hair motion
applied to a CG character.
Figure 7 shows the animation in Figure 6 after
being modified with our editing system. Both
animations in Figure 6 and 7 are created using the
standard Maya rendering pipeline.
6 CONCLUSIONS
This paper has outlined three advantages of our
approach to hair animation. First, we introduced the
hair simulation model specialized for the Hair
Object Model. Since the Hair Object Model is
adjusted for commercial use, it is not so complicated
to control. Therefore, creators can easily preview
animation almost in real-time. The second advantage
of our system is that it enables users to define EFF
from hair motion capture. Since the captured data is
from an actual motion, the result can be closer to the
real hair motion. Thus, our EFF is created from
captured data, enabling more realistic animation.
The final advantage of our system is that it provides
a way of editing hair motion interactively. This
advantage is associated with the first advantage.
Previewing the animation in real time, our hair
motion model enables creators to edit hair motion
intuitively. Consequently, creators can create hair
animation depending on their taste, intentions, and
imagination. The results produced with our system
highlight our method’s accessibility, convenience
and usability.
As can be seen in Figure 6, our system produces
realistic results which are sufficiently complete for
immediate use. However, by using our editing
system, creators can re-create the resulting hair
animation according to their individual preferences
(Figure 7). This proves our motion editing system
can be used commercially.
7 DISCUSSION AND FUTURE
WORK
Here we discuss the advantages and limitations of
our approach and mention future work. We have
four issues to discuss.
GRAPP 2008 - International Conference on Computer Graphics Theory and Applications
320
First, in this research, the Hair Object Model that
Figure 6: Sample hair motion.
Figure 7: Edited hair motion.
we adopted is one of the most generic polygon
structures used in the creation of CG characters. As
shown in Section 5, our hair simulation model works
successfully, however we have not tried to apply the
hair simulation model to others yet. Therefore we
need to modify our existing system, or develop a
hair simulation model that can be applied to various
hair structures, such as generic hair strands.
Secondly, we have successfully defined EFF
handling of separate winds moving from various
directions, depending on the hair motion capture.
As future work, we plan to capture hair motion
generated by natural wind blowing from several
directions at the same time. Furthermore, if a motion
capture marker is attached to material that is more
lightweight than hair, we will be able to capture
wind streams more precisely and, consequently,
create richer hair animation.
Finally, our hair motion editing system’s GUI
was designed using OpenGL and OpenCV. However,
CG creators often have their own preferences
regarding which 3DCG software they use. We
therefore, need to develop plug-ins for 3DCG
software, such as Maya, 3DMax and so on.
ACKNOWLEDGEMENTS
This research is supported by Japan Science and
Technology Agency, CREST project.
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