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

 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

is the number of hair strands,

is the

joint number from the hair root,

,,1

is the moment

of inertia,

2, ,ij

is the air resistance, and

denotes

the strength of the hair’s own force. This force is an

important factor in creating natural-looking hair

motion. Where

ji,,0

is the initial angle of joints,

and

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,

, is a static force. The second component

)(t

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

=Φ−Φ+Φ+Φ



),,(

,,,, jijijiji

(1)

DIRECTABLE AND STYLIZED HAIR SIMULATION

317

force The last component

)( j

is the force caused

by the collision between the hair object and body.

)(),()()(),( jjiSXtgjiH Ψ++Ξ+Ω+=

)),((),(

,,0

jiLLkjiS

−−=

)(*),(

, ji

EXRX Φ−=Ξ

⎟

⎠

⎞

⎜

⎝

⎛

−

=Ψ

)(

exp)(

⎥

⎦

⎤

⎢

⎣

⎡

=Φ

0)cos(0

0)sin()sin(

00)cos(

)(

θφ

(2)

Where

is the distance in movement of the

head,

is the current state of the spring,

,,0

the initial state of the spring,

is the current state

of the spring, and

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

is the position of a motion capture

marker,

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

),(

jiji

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

: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

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

is the position of the controlled

target hair strand in the second key frame,

is the

number of the key frame,

is the distance between

the target strand and the edited grid cube,

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.

,0,,

2( )

(, ) exp

()

ij ij

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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