The Visual Computer (1999) 15:159±170� Springer-Verlag 1999 159

A system of 3D hairstyle synthesis basedon the wisp model

Lieu-Hen Chen1, 2, Santi Saeyor1,Hiroshi Dohi1, Mitsuru Ishizuka1

1 Department of Informationand Communication Engineering,School of Engineering, University of Tokyo,7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, JapanE-mail:{chen,santi,dohi,ishizuka}@miv.t.u-tokyo.ac.jp2 Department of Computer Scienceand Information Engineering,National Chi-Nan University, 1, University RD, Puli,Nan-Tou, Taiwan 545, R.O.C.E-mail: lhchen@csie.ncnu.edu.tw

Hair plays an important role in the imageof the human face. However, it is still dif-ficult and time consuming to synthesize re-alistic 3D CG hair images. In this paper, wepresent an integrated system for 3D com-puter graphics (CG) hair image synthesisbased on a trigonal prism wisp model. Byapplying the trigonal prism wisp model,2D hair distribution maps and other CGtechniques to our system, we can success-fully and efficiently synthesize realisticCG hair style images. A 3D hair style edit-ing tool (HET) is incorporated into the sys-tem to support the creation of 3D hairstyles. We have also integrated this systemwith other research results to construct asystem for 3D CG character synthesis.

Key words: 3D CG hair style ± Hair im-age synthesis ± Wisp model ± CG humancharacters ± Anthropomorphic agent

1 Introduction

Hair plays an important role in human face imag-ing. Hair acts as a ªmediumº to express character-istics, conditions, and feelings [1, 2]. When thecomputer graphics (CG) character nods or shakeshis (or her) head to express ªYesº or ªNoº, the mo-tion of hair will affect the realism of the image.The CG characters or faces have been used recent-ly in advanced interfaces with multimedia func-tions, such as in anthropomorphic interfaces. How-ever, it is still difficult and time consuming to syn-thesize realistic 3D CG hair images for these char-acters.The difficulty of hair image synthesis is due tothe inherent properties of hair, such as the ex-tremely huge number of hair strands. This makeshair image synthesis computationally very expen-sive [3]. In addition, one hair strand is very thincompared with the pixel size, and hair strandswithin a wisp are locally parallel. These twoproperties cause an aliasing problem in renderinghair images. Most important of all, there are hugevariations in hair styles, which are determined byextremely complex interactions of many factors.These factors include gravity, friction, static elec-tricity, strand-to-strand and strand-to-head inter-actions, articles such as hair pins, hair bands,mousse, hair grease, and so on. Thus, it is ex-tremely difficult to generate complicated hairstyles with only a physical formula, some mathe-matical formulas and some parameters. All theseproperties of hair make hair image synthesis avery challenging task.The previous approaches to hair image synthesiscan be divided into two categories: the explicitmodel [4±9] and the volume density model [10±13], according to the methods used. The explicitmodel is very intuitive. The modeling and render-ing target of such an approach is each individualhair strand. The rendering target, hair, is treatedin a microscopic way. The particle model for hairsynthesis is classified in this category. In contrast,the volume density model defines the 3D spacedistribution function(s) of the entire hair style,and then applies a ray-tracing technique to calcu-late the color and illumination on the silhouettesurface of hair style. This kind of approach viewshair styles macroscopically. The approach of thevolume density model is more abstract than thatof the explicit model. It is not the purpose of thispaper to judge which method is superior. However,considering the needs of presenting enormous vari-

Correspondence to: L.-H. Chen

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ations of hair styles and animating hair motion, wewould prefer the explicit model for its potentialflexibility.In this paper, we present an integrated system forthe synthesis of 3D CG hair images based on atrigonal prism wisp model. This modeling meth-od, which we use for our system, basically be-longs to the category of the explicit models,though it is more simplified and organized to han-dle the macroscopic properties of hair styles. Byapplying the trigonal prism wisp model, 2D hairdistribution maps, and other CG techniques toour system, we can successfully and efficientlysynthesize realistic CG hair-style images. A 3Dhair style editing tool (HET) is incorporated intothe system to support efficient 3D hair style cre-ation.

2 Basic concepts of our system

We first introduce the five basic design conceptsfor our system:

1. Reality. We must be able to synthesize hair im-ages very realistically.

2. Low cost. We must be able to synthesize real-istic hair images in a much shorter time thanwith previous methods or systems.

3. High flexability. Using one and the same hairmodel, we must be able to create various hairstyles with long or short hair, straight or curlyhair, and so on.

4. Ability to animate hair styles. The ability to in-troduce some kind of physical model and for-mula to emulate the complicated phenomenonof hair is required.

5. Practicality. We want to provide a way to gen-erate and design various 3D hair styles easily.

It is quite reasonable and intuitive to considerthese five concepts as the basic elements thatmake a satisfying system for CG hair style syn-thesis. We have designed our system with theseconcepts. The modeling method, as the core ofthe system, is explained in Sect. 3. Some tech-niques and issues that we consider necessaryfor ªrealisticº hair image synthesis are discussedin Sect. 4. A hair style design and generatingtool, the hair style editing tool (HET), is intro-duced in Sect. 5. The integration of system and

some results of hair style synthesis are discussedin Sect. 6.

3 Trigonal prism wisp model and 2Dhair distribution map

3.1 Trigonal prism wisp model

We define our hair model, the trigonal prism wispmodel, as follows. First, all the hair is divided intoseveral groups of wisps, according to the positionon the skull. Each wisp is constructed by continu-ous trigonal prisms, as shown in Fig. 1. The trigo-nal prisms within one wisp are linked by three 3DB-spline curves. The numbers of control pointsmay differ, basically according to the length ofthe strand of hair.Using curves to implement hair is a very intuitiveidea. It enables our system to create the physicalproperties of hair easily. Furthermore, because hairstrands within a wisp are grouped, we can success-fully reduce the computational time. This model-ing method keeps the hair style data simple and or-ganized. Thus, it is very flexible for the varioushair styles.What has to be noted here is the cross-section ofthe wisp's silhouette: the ªactualº image of onewisp is determined by its 2D distribution map,which we will explain later in this section. Thetrigonal construction of our trigonal prism wispmodel does not affect the real shape of synthesizedwisps. The cross-section of wisp's silhouette doesnot need to be a triangle. Its shape is controlledby the 2D hair distribution maps that we assignto the wisp.The term ªwispº, which is used in the title of ourmodeling method, refers to a group of hair strands.It is a very familiar word to people who study syn-thesizing hair images. However, it is not really pre-cisely defined. In this paper, we will use the termªwispº as the smallest element of a hair style.Within a wisp, there can be 1 to 255 hair strands,which are quite parallel to each other. The 3D ori-entation and shape of one wisp is defined by three3D B-spline curves as shown in Fig. 1. Two wispscan share their edges, which we call control lines,with each other. For us, the wisp is the smallestunit used for calculations of 3D calibration, motionemulation, and illumination.

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1

2

3

Fig. 1. Trigonal prism wisp model

Fig. 2. The relationship between a wispand its 2D hair distribution map

Fig. 3. Two hair style images with thesame wisp model, but using differentlink methods (black hair)

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3.2 Two-dimensional hair distribution map

We use 2D arrays to define the distribution ofhair strands on the cross-section of one wisp, asshown in Fig. 2. Through the continuous trigonalprisms of one wisp, these 2D points are projectedonto screen according to each pair of vectors onthe edges of the two triangles. The position ofeach hair strand within a wisp is actually deter-mined in this 2D way. It is noted that this 2D hairdistribution map can be defined to have hair dis-tribution outside the triangle cross-section of thetriangle prism. This allows us to remove the dis-continuity of hair distribution among wisps.However, we need only calculate the three con-trol lines that we use to control the trigonalprisms. Thus, the 2D hair distribution maps con-tribute to reduce the computational cost of ren-dering hair.There is another important issue: the application ofthe 2D distribution maps to our system for the con-trol of the shape of a wisp's silhouette. For exam-ple, if the hair on the 2D map is randomly distrib-uted within a triangle or a circle, the basic shape ofthe synthesized wisp will be a curved trigonalprism or a curved cylinder, respectively. By con-trolling the shape and distribution density of the2D distribution maps, we can create a naturaland rich effect on 3D hair forms.Depending on the way we link these 2D distribu-tion maps, we can also create some interesting vi-sual effects. As shown in Fig. 3, the two differentwisp images are created from the same wisp model.The left image is created by linking maps withstraight lines, and the right one is linked by sinecurves. Using straight lines makes this linkage pro-cedure simple. However, using curves, such as sinewaves, instead of straight lines to link the 2D distri-bution maps can create some interesting visual ef-fects. Hair images synthesized in this way will havean extremely wavy form, though we use the samethree control lines and one simple wisp structrue.

4 Rendering hair, shadowing hair,and handling artificial objects

By applying the modeling method discussed in theprevious section, we can establish the model of thehair. The next step is to efficiently render hair im-

ages. To do this, first, we need to calculate the il-lumination on a hair strand.

4.1 Rendering hair

To calculate the illumination of one strand of hair,Ch; we use the following formula [7]:

Ch � LaKa�SLi�Kd cosq�Kssinn q� fÿp� ��;where the subscripts a, d, and s stand for the ambi-ent, diffuse, and specular components, respectively.The Ls are the lightness of the light sources, the Ksare constants, and q and f are angles as defined inFig. 4. For different colors of hair, we need to ad-just the balance of these parameters. Also, produc-ing the visual effects for the various properties ofhair will need more experiment and adjustment.For example, for dry and black hair, we reducethe weight of Ks and Ka; but emphasize Kd: Thislighting model still has its limitations, however,such as the lack of a back light visual effect.No matter what kind of lighting model is appliedto the system, these time-consuming calculationprocedures are only performed along the threecontrol lines of each wisp. The illumination ofeach strand within one wisp is then determinedby interpolating of the previous calculated resultsof the three control lines. With this interpolationprocess, we can save a large amount of time with-out loosing the realism of the hair. The result ofeach wisp is then pixel-blended with the imageof other wisps and background to create the trans-parent visual effect of hair and to remedy the alia-sing problem.

4.2 Shadowing hair

Without taking shadow effects of hair into consid-eration, the synthesized image will lack realismsomehow. To add shadow effects efficiently to ahair image, we modify the traditional shadow Z-buffering method. The modified shadowing meth-od, which we call the shadow mask method, is ex-plained next.The shadow mask method is basically a two-passprocess, just as its parent, the traditional shadowZ-buffer method is. As shown in Fig. 5, the firstpass of these two methods are very similar. All

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wisps are projected to the direction of the lightsource to check whether they are in the shadow ar-ea or not. At this step, the difference between thenew and old methods is that we keep the x, y, z co-ordinates instead of Z-buffer information. Thus,the result of the first pass of our method is a 2Darray that contains the 3D coordinate informationof all points that are ªvisible to the light sourceºon the surface of the hair silhouette. The size of

this 2D array and the radius of each point or ball,will determine the quality of the shadowing ef-fects. As a result of our experiments, we keep thisarray size at the same resolution as that of theviewing window.The second pass of our method is quite intuitive.By assigning an effective radius to every point,we treat these points as balls in 3D space. The un-ion of these balls will then form a masklike area

4

5

Fig. 4. Lighting on the hair model

Fig. 5. The shadow mask method

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that is ªvisibleº to the light source; in other words,it will be outside the dark area. This is the reasonwhy we call this method the ªshadow maskº. Todetermine whether a pixel should be shadowed ornot, at the second rendering step, we need onlyto check whether the Z-buffering value of the ren-dering target is within the Z-range of the relatedpixel on the shadow mask. Figure 6 illustratesthe rendering effect of this showing.As mentioned before, the number of hair strandsis extremely huge. If we apply the traditionalshadowing methods to a target that consists oflots of very small rendering objects, such as hairstrands, the cost will be proportional to the com-

plexity of the objects. Therefore, adding shadoweffects in the traditional way is too expensive forus. Using the shadow mask method, the complex-ity of second rendering pass is basically propor-tional to the resolution of the 2D array. Thus, thismodified shadowing method helps us to createshadow effects for hair in a more efficient man-ner.

4.3 Handling artificial objects

Artificial objects, such as hair pins, hair bands,ponytails, and braids, are important components

6

7

Fig. 6. Hair style images with andwithout shadow effects (black hair)

Fig. 7. Ponytail hairstyle (red hair)

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8 9

10

Fig. 8. Display of the hair style editing tool (HET)

Fig. 9. Hair style ± sample 1

Fig. 10. Hair style ± sample 2

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that cannot be ignored in handling the variouskinds of hair styles. With our hair model, addinga hair band or ponytail to a hair style is not so dif-ficult. What we need to do is just give somewisps a certain restriction. These wisps are re-quired to pass through a region of 3D space.For example, we can get a ponytail if we let thecontrol lines of a group of wisps pass through alittle circle behind the CG character's head. Ahair style with a ponytail is shown in Fig. 7. Han-dling a braid is a little tricky. A braid is heavierand stiffer than a single hair strand or wisp. It ba-sically consists three wisps. A repeated loopchanges the positions of these three wisps. (How-ever, they do not really have to be three individ-ual wisps. They may be just three branches of onewisp. They may also consist of several wisps sep-arately.)

5 The hair style editing tool (HET)

To make our system really practical, we need lotsof 3D data for various hair styles. However, theprocedure to create these 3D hair styles is a verytime-consuming task. The designer's art senseand technique are also required.We tried to make the design procedure easier. Forthis purpose, we have developed a hair style edit-ing tool (HET) to help users design and generate3D hair styles.As shown in Fig. 8, HET consists of five windows.The command window on the right side containsmost of the command buttons. The view windowlocated in the lower left portion is used to viewthe result in 3D space. We use the other three win-dows to edit the 3D position and orientation of thewisps with a mouse. Users can change their viewangle in these windows whenever they like.Even though we have successfully simplified thehair data structure by grouping hair into wisps, itstill takes lot of effort to position all the wisps in3D space. For example, we can use 256 wisps todefine a hair style which has 256*256=65536 hairstrands within it. To design this hair style, we needto input and edit 3*256=768 3D curves. It will takehours to use the mouse for pointing out all the nec-essary points for these B-spline curves.To resolve this problem, we group the wisps ac-cording to their position on the skull. These groupslook like quarter rings on the skull. We divide the

skull into eight layers. Each layer consists of fourquarter rings. We assume that the shape of thewisps within the same quarter ring are quite simi-lar. Thus, after a designer has designed one or twocontrol lines on a quarter ring, it is reasonable forHET to automatically generate all the other controllines on the same quarter ring, using the line (orlines) that has already been done as an example.The hair style shown in Fig. 9 is generated by in-putting only 14 curves; the other control lines areautomatically generated by HET.This tool helps the user to roughly design a hairstyle with only 10±20 3D B-spline curves, and alsoprovides various functions for editing the details ofa hair style and the ability of exchanging and shar-ing parts between different hair styles. One hairstyle that is a little more complicated than theone in Fig. 9 is shown in Fig. 10. HET also allowsusers to create various visual effects by changingor blending hair colors for a hair style, and by as-signing wavy effects to certain wisps. The timeneeded to design and edit the wisp models wasin total 10 min for Fig. 9, and 30 min for Fig. 10.The rendering time for these CG images is about1 frame/s on a SGI Onyx workstation. (For conve-nience in development and experiment, no hard-ware rendering function, such as line drawing, co-ordinate translation, Z-buffering, etc., is used in thesystem at present.)

6 Integration of the system

We have integrated this system with a face editingtool to combine users' face images that may becaught from a video camera or a digital camera,as illustrated in Fig. 11. With this integrated sys-tem, we can combine a realistic 3D face imagewith any hair style stored in a database.As shown in Fig. 11, a skull is attached to the wireframe of a face like a hat. It can be adjusted to fitthe wire frame. This flexibility is necessary be-cause the head size of each individual human char-acter is usually different.As already mentioned, the motion of hair is toocomplicated to analyze and regenerate completely[14]. It may be caused by an internal force (e.g.,head gesture ) or an external force (e.g., wind ) .We have focused our attention on the case of inter-nal force so far. We have emulated two types ofhair motion that is caused when the CG character

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nods ªyesº or shakes his/her head ªnoº. The mo-tion is achieved by simulating hair as a pendulumresting on a cone as shown in Fig. 12. When acharacter's head shakes, it gives the pendulum anangular momentum. This angular momentummay or may not be big enough to lift the pendulumfrom the slope. It also makes the pendulum oscil-late along the slope of the cone. The emulation re-

sult is shown in Fig. 13. The pendulum model is anextremely simple model and is only suitable foremulating certain motion patterns. To simulatemore complicated and general hair motion, moreresearch effort is needed.We also propose a system of 3D character synthe-sis as shown in Fig. 14, in which the system of hairstyle synthesis serves as one of the basic modules.

11

12

Fig. 11. Integration of a hair style image anda face image

Fig. 12. Pendulum model

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Fig. 13a±c. Animation (black hair)

a

b c

In this system, not only CG hair styles, but alsoface expression emulation, speech synthesis, andartificial intelligence (AI) components to generatemotions based on a scenario script are to be includ-ed. The integration of all these functions will make

an intelligent life like agent with a realistic figureavailable; this agent will serve as one importantstyle of advanced interface close to daily face-to-face communication.

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7 Conclusion

We have proposed a new hair modeling method,i.e., a trigonal prism wisp model with 2D hair dis-tribution maps, and developed a prototype systemto synthesize and animate various kinds of 3D hairstyles. This system is integrated to combine faceimages with the hair styles. Further work is expect-ed to improve the quality of hair images, and toachieve better system performance. There is a planto introduce the concepts of virtual reality into thenext version of HET to allow users to ªdirectlyºedit a hair style by hand in a virtual space. The de-velopment of the scenario maker will help in iso-lating the animation module and the AI module.This independence will make our system of 3DCG character synthesis, serving as a platform to in-corporate with various AI modules through a stan-dard interface, a scenario maker. Though there arestill lots of research issues left for future work inour entire project (Fig. 14), our system has beenproven to be an efficient and practical system forcreating 3D hair styles, synthesizing realistic hairimages, animating hair motion, and manipulatingvarious hair styles.

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LIEU-HEN CHEN is currentlyan Assistant Professor of Com-puter Science and InformationEngineering at the NationalChi-Nan University, Taiwan.His current research interests in-clude interactive 3D graphicsand virtual reality. He receiveda BS in Computer Science andInformation Engineering fromthe National Taiwan Universityin 1989, and his MS and PhD de-grees in Electrical and ElectronicEngineering from the Universityof Tokyo, in 1994 and 1998, re-spectively.

SANTI SAEYOR is a PhD stu-dent at the Department of Infor-mation and Communication En-gineering at the University ofTokyo, Japan. He received hisBE in Electronic Engineeringfrom King Mongkut's Instituteof Technology Ladkrabang,Bangkok, Thailand, in 1993,and his ME in Electrical Engi-neering from the University ofTokyo, in 1996. His current re-search interests are in the areasof autonomous informationagents, mobileagents, and Inter-net technology.

HIROSHI DOHI is a ResearchAssociate at the Department ofInformation and CommunicationEngineering of the University ofTokyo, Japan. He received hisBS and MS degrees in ElectricalEngineering from KEIO Univer-sity, Japan, in 1985 and 1987, re-spectively. His current researchinterests are the Anthropomor-phic Intelligent Agent Interfaceand Internet-based multimodalsystems. He ia a member of theACM and IPS Japan.

MITSURU ISHIZUKA is a Pro-fessor of the Department of In-formation and CommunicationEngineering of the University ofTokyo. Previously, he worked atthe NTT Yokosuka Lab. and theInstitute of Industrial Science,University of Tokyo. He receivedhis BS, MS, and PhD degrees inElectronic Engineering from theUniversity of Tokyo. His re-search interests are in the areasof artificial intelligence, hypo-thetical reasoning mechanisms,multimodal human interfaces,and intelligent WWW informa-

tion space. He is a member of the IEEE, AAAI, IEICE Japan,IPS Japan, and Japanese Society for AI.