Styling and Animating Human Hair

Keisuke Kishi and Shigeo Morishima

Faculty of Engineering, Seikei University, Musashino, 180-8633 Japan

SUMMARY

Synthesizing facial images by computer graphics

(CG) has attracted attention in connection with the current

trends toward synthesizing virtual faces and realizing com-

munication systems in cyberspace. In this paper, a method

for representing human hair, which is known to be difficult

to synthesize in computer graphics, is presented. In spite of

the fact that hair is visually important in human facial

imaging, it has frequently been replaced by simple curved

surfaces or a part of the background. Although the methods

of representing hair by mapping techniques have achieved

results, such methods are inappropriate in representing

motions of hair. Thus, spatial curves are used to represent

hair, without using textures or polygons. In addition, hair

style design is simplified by modeling hair in units of tufts,

which are partially concentrated areas of hair. This paper

describes the collision decisions and motion repre-

sentations in this new hair style design system, the model -

ing of tufts, the rendering method, and the four-branch

(quadtree) method. In addition, hair design using this hair

style design system and the animation of wind-blown hair

are illustrated. © 2002 Scripta Technica, Syst Comp Jpn,

33(3): 31�40, 2002; DOI 10.1002/scj.1111

Key words: Computer graphics; hair style; tuft

model; animation; GUI.

1. Introduction

Image syntheses of human faces by CG are currently

attracting attention in various fields. In the area of human

communications, for example, human-simulating agents

are being realized and the generation of real human facial

images is required. However, currently hair is represented

by simple curves or replaced by a part of the background,

even though hair is visually important in imaging a human

face. This is due to the fact that hair is difficult to represent

by CG, since the number of hair strands is very large and

their shapes are complicated. However, various attempts

have been made to represent hair by CG, although methods

which are decisively superior from the points of view of

realism, ease of modeling, memory capacity, computing

time, and so on are nonexistent.

In this paper, a hair style design system which repre-

sents and generates an arbitrary hair style in tuft units is

proposed. In addition, a scheme for thinning the ends of hair

using α blending and a scheme for avoiding occlusion of

hair by the head via an accurate collision decision scheme

that includes a collision decision buffer for realizing more

realistic hair animation are presented.

2. Modeling of Hair

The methods for representing hair by CG are broadly

divided into two categories. One consists of methods of

representing hair by anisotropic reflection models [1, 2] or

�texels� [3] by taking the hair as surface texture. and the

other consists of methods of modeling the hair strand by

strand via shape models formed of triangular pyramidal

primitives, for example [4]. Representing wind-blown hair

requires that the motion of hair be represented strand by

strand. Although representing hair by texture can yield

high-quality images, it is not appropriate for representing

motions and the like, since hair is treated as an object.

Although representing hair by shape models is appropriate

© 2002 Scripta Technica

Systems and Computers in Japan, Vol. 33, No. 3, 2002Translated from Denshi Joho Tsushin Gakkai Ronbunshi, Vol. J83-D-II, No. 12, December 2000, p p. 2716�2724

31

for representing motions, if modeling of complicated and

abundant hair is done using polygons, problems associated

with memory capacity and computing arise, since a huge

memory capacity is required to model an entire head of hair.

Considering such problems, methods of approximat-

ing the hair strand by strand via �spatial curves� [5, 6] have

been used. The shapes of the spatial curves are determined

by a number of points in the space, called �shape controlling

points.� Thus, all of the hair can be modeled with a small

memory capacity by storing only the shape control points

as shape data. The spatial curves used in this paper are third-

order B-spline curves and their shapes are shown in Fig. 1.

3. Modeling of Hair

The design system presented in this paper constructs

a head model with about 3400 triangular polygons and

constructs the hair using spatial curves on their surfaces.

The generated hair area consists of about 1300 polygons,

and a strand of representative hair is generated for one

polygon on the modeling tool. Since this system depends

on the head model to a certain degree, a model having a

polygon number of this magnitude is required. In addition,

it is necessary to make the meshes of the generated hair area

fine when using other models.

In modeling hair using shape control points, a huge

number of shape control points must be appropriately

placed. For this purpose, a scheme [7] for determining the

arrangement of the shape control points using an appropri -

ate function and a method of constructing the shape of hair

automatically from the bending state of the hairs [9] have

been proposed. However, a desired hair style cannot be

easily constructed by either method.

It has previously been confirmed that the motion of

rustling hair blown by the wind can be represented [8] by

modeling the hair strand by strand independently for mo-

tion simulation and applying this dynamic model. However,

since hair consists of a huge number of strands, determining

the hair style by editing spatial curves strand by strand is

impossible in reality. Thus, in this paper, an attempt to make

the design work efficient by treating hair consisting of

multiple strands simultaneously as tuft models for the pur-

pose of designing the hair style and performing the render -

ing and the motion representation separately strand by

strand has been made.

3.1. The tuft model

The elements required in determining the hair style

include the shape of the hair and the correlations between

the head and the hair, as well as between the hairs them-

selves. These elements can be simply treated and the hair

can be approximated to real human hair in a short time by

modeling multiple hair strands simultaneously.

A method of representing hair by tuft models and a

tool for editing have been proposed by Chen and col-

leagues. Their tuft model assigns positions in basic units of

shape, rendering, and motion representation, and has been

shown to reduce the computational load. The tuft model

presented in this paper assigns positions by treating multi -

ple strands simultaneously, and the size of a tuft, the cross-

sectional shape, and the assigned positions on the head can

be designated freely on a GUI, depending on the hair style

to be edited, and thus increases the representability and

flexibility of the method. In addition, rendering and motion

modeling are performed strand by strand as discussed later.

Since third-order B-spline curves are curves approxi-

mating more than seven control points, more than seven

rectangles are defined as tuft models as shown in Fig. 2. The

rectangle is a set of shape control points, and the tuft model

Fig. 1. 3D B-spline curve.

Fig. 2. Tuft model.

32

is edited by rotating, shifting, and transforming the shape

control rectangles. The shape control points are obtained on

the basis of the shape control rectangle to generate spatial

curves.

3.2. Construction of editing system

In this system, hair is constructed by repeating three

procedures: designating the tuft model generation area,

editing the tuft model, and pasting the tuft model onto the

head.

(1) Designation of area

An arbitrary polygon (a pentagon in Fig. 3) is desig-

nated by the mouse and the area for generating the tuft

model is designated. Simultaneously, the following pa-

rameters required for pasting and editing the tuft model are

determined.

(a) Determination of local coordinate system

The local coordinate system of the area is determined,

with the algebraic sum [Fig. 3(a)] of the normal vector of

the polygon designated as the Z axis of the local coordi-

nates.

(b) Shape of shape control rectangle

The initial size of the shape control rectangle is

determined from the maximum and minimum values of the

x and y coordinates of the frame constructed by connecting

the center of gravity of the designated polygon from the

X�Y plane [Fig. 3(b)] of the local coordinate system. The

initial shape of the shape control rectangle is a long rectan-

gle.

(c) Determination of area

Similarly, the relative coordinate values of the hair

generated by the polygon for the shape control rectangle

determined by (b) are determined by projecting the polygon

information of the head model onto the X�Y plane of the

local coordinate system, determining whether the center of

gravity of the projected polygon is contained inside the

frame on the X�Y plane, and taking this polygon as the area

of the tuft model if it is contained. This shape control

rectangle and the control point coordinates on the space are

obtained by obtaining the relative coordinate values with

the center of the shape control rectangle as the origin of the

local coordinate system.

(2) Editing of tuft model

The tuft model is edited by rotating, shifting, and

transforming the shape control rectangle of the tuft model.

More complicated hair styles can be represented by increas-

ing the number of control points or the number of shape

control rectangles. An example of editing the tuft model is

shown in Fig. 4. Since a twisted shape can be represented

by using rotations many times, as shown in Fig. 4(b), and a

wavy shape can be represented by using shifts many times,

as shown in Fig. 4(c), a permanent wave hair style can be

modeled.

Fig. 3. Selected region. Fig. 4. Examples of tuft editing.

33

(3) Pasting

To automate the process of matching the head with a

tuft model, pasting is performed by combining the tuft

model with the local coordinate system of an area. Rota-

tions and shifts are made such that the normal vector of the

first shape control rectangle of the tuft model and the Z axis

of the area coincide. However, since a tuft model is con-

structed from a plane, if a tuft model is pasted unmodified

as shown in Fig. 4, gaps can occur between the tuft models,

resulting in an unnatural hair style, since the head is curved.

Thus, rotations and transformations are performed on the

hair strand by strand, taking the state of bending of the head

as a cylinder as shown in Fig. 5.

3.3. Replication method

Approximately 50 to 60 tuft models per hair style are

constructed and about 1300 strands of hair, one strand per

polygon, are generated. A hair image is created by a render -

ing module by increasing the number of strands of hair if

this number is too small. In addition, the width of repre-

sentation is broadened by using two different replicating

methods.

In representing a hair style with small collections of

tufts as hair with permanent waves, a representative shape

is replicated, increasing the number of strands of hair, with

the head polygon as one unit. In contrast, in representing a

uniform hair style such as straight hair, a new shape is

obtained from a shape control rectangle, increasing the

number of strands, with a tuft model as one unit. A hair style

having smooth highlights can be generated by this ap-

proach. In addition, variations are imparted to the hair ends

by using representative shapes determined by the modeling

tools and random numbers in both replication methods.

Although about 100,000 strands of hair exist on the

human head, about 50,000 strands are considered in order

to obtain sufficient quality without the head surface show-

ing, considering the processing time in real rendering.

However, about 90,000 strands are considered in animation.

3.4. Interface

The screen for hair style construction is constructed

in a GUI and all stages can be controlled by the mouse. This

interface screen, shown in Fig. 6, is composed of four

components: an entire screen (lower left) on which the head

model and hair are shown, a tuft model editing screen

(lower right), a shape control rectangle editing screen (up-

per right), and a control panel (upper left).

Since a hair style is constructed from tuft models and

a tuft model is constructed from a shape control rectangle

in this system, editing can be done for each constructing

element. Specifically, the editing of the hair style is done

on the whole screen, the editing of the tuft model is done

on the tuft model editing screen, and the editing of the shape

control rectangle is done on the shape control rectangle

editing screen. Since individual editing results are fed back

onto all editing screens instantaneously, interactive editing

is possible. In addition, the hair generated on the head is the

representative hair.

4. Rendering

4.1. Cylindrical pipe model

In reproducing the real texture of hair by rendering,

a normal vector must be determined at all points on theFig. 5. Pasting tuft model.

Fig. 6. Interface.

34

spatial curves. However, the values obtained by the spatial

curves mentioned earlier are only coordinate values in

space, and local structures are not defined. In this paper,

rendering of spatial curves is made possible [5] by comput-

ing a normal vector for an arbitrary point on the spatial

curves, assuming that the spatial curve line is a very thin

tube as shown in Fig. 7. In this method, the spatial curve is

divided evenly into 100 parts, the luminance at 101 points

is obtained, and color compensation is performed.

Lambert�s model is used in computing the diffuse

reflection components and Phong�s model is used in com-

puting the specular reflection components.

4.2. Antialiasing

Since a very thin object such as hair is treated in this

paper, aliasing occurs very frequently. Thus, eliminating

aliasing is very important. Since a hidden surface is elimi -

nated by using a Z buffer algorithm, using an antialiasing

method suitable for the Z buffer method is important.

Thus, in this paper, a Z buffer, a color buffer having

a resolution several times that of the actual CRT is prepared,

an image with resolution is synthesized using this Z buffer,

and then an image with low resolution is generated by

assigning the average number of pixels to one picture.

4.3. Thinning of hair ends

The thickness of a strand of hair is not constant, and

thinning the hair ends is considered. Thus, it is considered

that the thinner the object observed, the harder it is to

recognize, since it assimilates with objects behind it or the

background. Thus, considering this phenomenon, thinning

of hair ends approximated by spatial curves without three-

dimensional structures is achieved by using α blending,

which produces gradations of the α value from points

before dividing into 100 parts, with α = 0 at the hair end as

shown in Fig. 8.

5. Hair Motion Control

The positions of the shape control points may be

obtained by certain methods to control the motion of a

curve. The contraction or elongation of hair by external

forces can be ignored compared with the overall shape

changes. Thus, in this paper, the motions of segments are

simulated by connecting the shape control points estab-

lished in a space by a rod-shaped rigid body and obtaining

numerical solutions of an equation of motion that takes

account of the external forces acting on each rigid body and

the restoring forces acting between neighboring rigid bod-

ies. Figure 9 shows the shape control points connected by

a rigid body rod.

Each rod is expressed in a polar coordinate system

and its motion can be considered as consisting of rotational

motion in two directions, θ and φ. Letting the sum of all the

forces applied to a segment, such as the wind force and

gravitational force, be F and the positional vector of the

Fig. 7. Cylindrical pipe.

Fig. 8. Thinned down hair tip. Fig. 9. Segment model.

35

center of gravity of the segment be r, the rotational moment

is represented as N = F × r, so that the equation of motion

of an arbitrary segment becomes

where m, l, and ω are the mass, length, and angular velocity

of a segment. The end point of Segn becomes the beginning

point of Segn+1 and the computation is repeated from the

root to the tip of hair.

6. Collision Decision and Avoidance of

Occlusion

In modeling hair, the shapes of the spatial curves are

determined in such a way that hair is not present inside the

head. However, if simulation of motion is done while

ignoring the existence of the head, hair ends up being buried

inside the head. To avoid this problem, a scheme using

simulated external forces [9] and a scheme using a collision

decision buffer in a cylindrical coordinate system [10] have

been proposed. The former scheme prevents hair from

being stuck inside the head by the simulated external forces

by establishing a simulated external force area that sur-

rounds the head. Although the computing rate is increased

to the extent that special collision processing is not required

by the former scheme, rigorous collision decisions may not

be made by this scheme. In addition, the simulated external

forces must be empirically established so as to prevent hair

from getting stuck inside the head. On the other hand, in the

latter scheme, collisions are detected by comparing the

shape control points transformed into a cylindrical coordi -

nate system with a table storing the distances from the

center of an object to the object surface in a cylindrical

coordinate system which has been constructed in advance.

However, since a collision decision buffer is expressed in a

cylindrical coordinate system in this scheme, a buffer must

be used for each object and the node coordinate conversions

must be computed for each object. The computing time is

expected to increase with this scheme in an environment in

which a number of objects coexist, as in the case of arms,

for example. Although a scheme [12] using collision deci-

sion buffers is adopted in this paper, object groups are not

detected and the points on an object are detected by the

scheme described here.

6.1. Collision decision

In this paper, high-speed decision based only on

comparison operations is performed by computing the in-

tersection points between the polygon and the vertical line

in advance, as discussed below. First, as shown in Fig. 10,

a virtual plane not intersecting all objects, which has a size

allowing all objects associated with collision to be pro-

jected in parallel, is established. Here, a plane parallel with

the x�y plane is considered. Next, a two-dimensional ar-

rangement corresponding to this plane is used. In the ele-

ments [xn, yn] of the arrangement, the coordinates of the

points intersected by a vertical line dropped from point

(xn, yn) corresponding to the plane are stored in the inter-

section order, as shown in Fig. 10. Here, the arrangement

established on the virtual plane is such that the places where

objects do not exist are made sparse by using a quadtree.

As shown in Fig. 11, the virtual plane is divided into four

regions, and the areas are further divided into four regions

if an object of collision exists, but are not divided if such

an object does not exist.

Letting the coordinates of the control point deciding

the shape of the hair be represented by (xp, yp, zp) in colli-

sion decision, the element closest to (xp, yp) is referenced

from the arrangement constructed in advance. Since the

virtual plane is established so as to contain all objects

initially when the coordinates of the control point exceed

the range of the arrangement, objects are nonexistent in this

case. Since the coordinate values z1, z2, z3 . . . of all of the

points of intersection with the polygon at the same xp, yp are

stored in this element, if it is assumed that an object is all

closed and that the coordinate value zp of the control point

z is in the range of

this control point necessarily exists outside all objects.

6.2. Avoiding occlusion

Occlusion of hair inside the head cannot be avoided

by collision decision alone. In avoiding the occlusion of

hair, a certain procedure must be performed on the hair at

(1)

Fig. 10. Collision decision buffer.

36

the time of collision to prevent it from sticking inside the

head.

Observing the actual movement, if hair collides with

the head, the hair is considered to flow along the head

surface as it comes in contact with the head. Here this

phenomenon is simulated by the following method in order

to represent more natural hair movement. As shown in Fig.

12, the velocity and acceleration of node P on the object

surface can be divided into the components normal and

tangential to the object surface. The tangential component

is considered to be unrelated to occlusion of hair inside the

head. Thus, by preserving only the tangential components

of the velocity and the acceleration of this node, the node

can continue a flowing movement on the object surface and

occlusion inside the object can be prevented. In Fig. 12, N

is the normal vector to the object surface. This vector is

obtained by preparing one right-angled parallelepiped for

each polygon constituting an object in advance and decid-

ing with which right-angled parallelepiped or polygon the

colliding decided node has collided. In addition, if the node

belongs to multiple right-angled parallelepipeds, the poly-

gon that minimizes the distance between the node and the

center of gravity of the polygon is taken as the colliding

polygon.

Although the tangential direction vectors of the ob-

ject exist in an infinite number and form tangential planes,

letting the velocity vector of node P be f, the tangential

component of f has the direction of the line of intersection

of the plane formed by the normal vector N and f and its

tangential plane. Thus, the tangential direction component

vector of f is expressed as

where fN is the unit vector of f and can be obtained as

fN = f / |f|. Thus, the tangential components of f are given

by

Similarly, the tangential direction of the acceleration of

node P can be obtained. These components realize the

natural movement of hair by being specified as the new

velocity and acceleration of node P.

Fig. 11. Collision decision buffer by quadtree. (2)

Fig. 12. Collision detect.

(3)

Fig. 13. Loose waves.

37

7. Hair Style Image Synthesis

A permanent wave hair style called �loose waves�

obtained by the scheme proposed in this paper is shown in

Fig. 13. The hair image created by the hair style design

system using a real model shown in Fig. 14(a) is shown in

Fig. 14(b). A hair style called a doll bob is created and part

of an animation sequence is shown in Fig. 15. The respec-

tive numbers of hair strands and of tuft models were 55,616

and 58 in the image shown in Fig. 13, and 78,834 and 49 in

the images in Fig. 14; the number of hair strands was

89,724, the number of tuft models was 61, and the wind

force was sinusoidal with an amplitude value of 1.3 in the

images in Fig. 15. The highlights are just along the head in

Fig. 14(b). In addition, a permanent wave hair style, which

had been difficult to image up to now, has been madeFig. 14. Comparison with real image.

Fig. 15. Example of animation.

38

possible as shown in Fig. 13. Comparing Figs. 14(a) and

14(b) reveals that a very close impression could be realized.

Hair naturally blown by wind could be represented by

animation as shown in Fig. 15.

About 7 minutes was required for the construction of

one frame, using a Silicon Graphics IRIS 02 (R5000, 180

MHz).

8. Conclusions

In this paper, a scheme for modeling hair in tuft units

is proposed and a hair style design system which can

construct the shape of a complicated hair style graphically

and by dialogs is proposed. A hair image can be generated

by representing a large number of strands with a small

amount of shape data by assuming a spatial curve to be a

cylindrical pipe. The thinness and smoothness of hair,

which could not be reproduced in the past, can be realized

by rendering with an image buffer whose degree of resolu-

tion is several times that of the display, or by α blending.

In addition, an algorithm for performing accurate judgment

of collisions between the human head and the hair is pro-

posed, and also a scheme for avoiding occlusion of hair

inside the head by realistic modeling.

The realism of animation and imaging of hair will be

further improved in the future by improving the perform-

ance of the motion control algorithm and the rendering

algorithm. The algorithms must be made simple and effi -

cient to make real-time syntheses possible, and optimal

trade-offs between quality and synthesis time must be

found.

In designing hair having a realistic look, a system

allowing hair styles rich in variations is required. In order

to develop such a system, modeling tools considering hair

decorations, and the like are being developed, seeking

realistic representations of loose hair, stray hair, and so on.

Tools for adjusting hair styles to represent an existing hair

style cut by scissors or partially curled are also essential.

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39

AUTHORS (from left to right)

Keisuke Kishi received his B.E. degree from the Department of Electrical and Electronic Engineering of S eikei University

in 1998, and is currently in the master�s program. His research interests include represent ation of hair by computer graphics.

Shigeo Morishima (member) received his B.E., M.E., and D.Eng. degrees from the Department of Electronic Engin eering

of the University of Tokyo in 1982, 1984, and 1987. He is now an associate professor in the Department of Electrical and

Electronic Engineering of Seikei University. He was a visiting research fellow at the Univ ersity of Toronto in 1994�95. His

research interests include computer graphics, computer vision, and multimodal interface s. He received a 1992 IEICE

Achievement Award, and is a member of IEEE, ACM, the Acoustic Society of Japan, the Televisi on Society, and others.

40