Simulation of Chinese Calligraphy

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    M ay 2004, Vo1.19, No.3, pp.39 3-40 4 J. Co mp ut. Sci. Technol.

    D r o p l e t A V i r t u a l B r u s h M o d e l t o S i m u l a t e C h i n e s e C a ll i g ra p h y

    a n d P a i n t i n g

    X iao -Fen g Mi , Min Tan g , an d J i n -X ian g D o n g

    CAD and CG State Key Lab of China, Zhejiang University, Hangzhou 310027, P.R. China

    Artificial Intelligence Institute, Zhejian 9 University, Hangzhou 310027, P.R . China

    E-mail : [email protected] mail .com

    Received July 1, 2002; revised November 15, 2003.

    A bs t r ac t This paper proposes a v i rtua l b rush model based on drople t opera t ion to s imula te Chinese ca l lig raphy

    and trad it ional Chinese painting in real t ime. Two ways of applying droplet m odel to virtual cal l igraphy and

    painting are discussed in detai l. The second droplet model is more elabor ated and can produce m ore vivid

    results while being sl ightly more t ime-consuming. The novel feature of the pro posed droplet v irtual brush model

    successfully enables the simulat ion painting system to overcome the poor expressional abil i ty of virtual brush

    based on part icle system and avoids the complex evaluation of physical brush with solid model . The model ,

    derived from the actua l cal l igraphy and painting experience, due to the simplici ty of the droplet op erat ion and

    its powerful expressive abil i ty, considerably improves the performance of the simulat ion system and maintains

    painting effect com parab le with real brush by suppor t ing special Chinese brush effect such as dry brush, feng and

    stroke diffusion.

    K ey w or ds NPR , v i r tua l b rush, pa in ting system, drople t model

    1 I n t r o d u c t i o n

    Ch in ese ca l l i g rap h y , t h e an c i en t Ch in ese a r t o f

    w r i t i n g , h a s b een a ro u n d fo r so l o n g a s t h e h i s -

    t o r y o f C h i n a . N u m e r o u s c a l l i gr a p h er s h a v e b e e n

    p ro d u c in g co u n t l e s s o f mas t e rp i ec es s i n ce Ch in ese

    ch a rac t e r s ap p ea red . Th e h a i r b r i s t l e b ru sh , w h ich

    h as l o n g s t a rch ed n a tu ra l b r i s t l e s n a r ro w in g t o a

    p o in t ed t i p an d se rv es a s t h e t o o l o f Ch in ese ca l -

    l i g rap h y o r t r ad i t i o n a l Ch in ese p a in t i n g , i s co n v e -

    n ien t to use and has i t s specia l express ive ab i l i ty .

    H o w ev e r , t h i s ch a rac t e r i s t i c o f h a i r b ru s h h as a l so

    imp o sed d i f f i cu l t i e s i n i t s s imu la t i o n b y co mp u te r .

    Mo s t re sea rch e rs imp lemen t t h e i r s imu la t i o n s a s

    so f t b ru sh es , w h ich u su a l l y l ead t o l ack o f t h e ab i l -

    i t y t o ex p re ss so m e sp ec i a l e f fec t s o f Ch in ese b ru s h ,

    su ch a s d ry b ru sh , fen g (ex p l a in ed i n Su b sec t i o n

    2.2), etc.

    1 .1 R e l a t e d W o r k

    V a r i o u s b r u s h m o d e l s h a v e b e e n b u i l t b y m a n y

    resea rch e rs . O n e o f t h e ea r li e s t a t t em p t s i s t h a t o f

    S t ra s sm an n s . In h i s p ap e r [1], h e an a ly z ed t h e e f -

    fec t s a v i r t u a l b ru sh can p ro d u ce an d d ev e lo p ed a

    me th o d fo r d raw in g l i n e s a s b ru sh s t ro k es . H e ac -

    t u a l l y s i m u l a t e d t h e b e h a v i o r o f a b r u s h w i t h w e t

    *Correspondence

    p a i n t o n p a p e r . T h e p a p e r b y H e n m i a n d

    Yoshikaw a [21 descr ib ed som e aspe cts of such k ind

    o f v i r t u a l b ru sh sy s t em. Wo n g an d Ip [3] s imu la t ed

    th e p h y s i ca l p ro cess o f b ru s h s t ro k e c re a t i o n u s in g

    a p a r a m e t e r i z e d m o d e l w h i c h c a p t u r e s t h e w r i t -

    i ng b r u s h s 3 D g e o m e t r i c p a r a m e t e r s , t h e b r u s h

    h a i r p ro p e r t i e s an d t h e v a r i a t i o n s o f i n k d ep o s i-

    t i o n a lo n g a s t ro k e t ra j ec to ry . A n o th e r ap p ro ach i s

    t h a t o f X u an d Tan g s [4 ]. In t h i s m o d e l , c l u s t e r s o f

    h a i r s a re rep re sen t ed a s so l i d mo d e l s an d t h e im-

    i t a t i o n o f t h e ca l l i g rap h y i n c lu d es so m e g eo me t r i c

    o p e ra t i o n s o n t h e mo d e l . N e l so n S . H . Ch u recen t l y

    d ev e lo p ed a s imi l a r 3 D mo d e l [5 ]. Ch an p re sen t ed

    a m e t h o d t o c r e a t e 3 D C h i n e s e p a i n t i n g a n i m a t i o n

    u s in g ex i s t i n g so f tw are p ack ag es b y mo d e l in g an d

    spe cial l ighte ning m ode l [6] .

    Th e re a re a l so h a rd w are ap p ro ach es t o imp le -

    m e n t t h e v i r t u a l b r u s h m o d e l s u c h a s t h e o n e b y

    Gree ne [7] . This mode l , as wel l as Ch u s [5] and Bi l l

    B a x t e r @ s] , p r es e n t e d p a r a d i g m s o f h a r d w a r e - b a s e d

    u se r i n t e r face fo r s t ro k e i n p u t .

    A n o th e r ch a l l en g in g an d c r i t i c a l p ro b l em to ad -

    d re ss i s t h e i n t e rac t i v e mo d e l b e tw een t h e p ap e r

    and ink or p igment . Cu rt i s [9] p res ented an excel -

    l en t mo d e l fo r w a t e rco lo r p a in t i n g , w h ich is ro u g h ly

    th e same a s t h e i n k -b ru sh mo d e l i n Ch in ese ca l l i g -

    rap h y o r t r ad i t i o n a l p a in t i n g . A n e l ab o ra t ed d i s -

    This research is supported b y the National Gr and Fundamental Research 973 Pr ogr am of China (G ran t

    No.2002CB312106), a gran t from Ph.D. Pro gram s Foundation of Ministry of Education of China (No.2000033554), and

    the Na tura l Science Foundation of Zhejiang Province (G ran t Nos.6001107, M603129).

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    J. Co mp ut. Sci. Technol., Ma y 2004, Vo1.19, No.3

    cussion of the ink d if fusion effec t in Chinese ca l-

    l igraphy or pa in t ing is presen ted by J in tae Lee [1~

    Some ink d if fusion models have been proposed for

    different ink spreading effec ts n-13] . Class ica l a r-

    t i f ic ia l in te l l igence , fuzzy logic , and knowledge en-

    gineer ing have been found to be useful in crea t ing

    beau t i fu l ca l l ig raph ic a r twork wi th a v i r tua l ha i ry

    brush[14-16].

    Sim ula t ion of the Chinese t radi t iona l ca l l igra-

    phy o r pa in t ing i s a k ind o f non -pho to rea l i s t i c

    rende r ing [17-19] . Bu t i t is d is t inc t f r om gen era l

    non-pho to rea l i s t i c r ende r ing such a s d ig i ta l pa in t -

    ing , p ic tu re re touch ing , o r i l lu s t ra t ion gene ra t ion .

    Th e m etho ds involve a wide range of colors , r ich

    ed i t ing func t ions , and va r ious b rush pa t te rns , bu t

    gene ra l ly do no t ca re the b rush mode ls tha t a re e s-

    sent ia l in s imula t ion of the hair brush .

    Simula t ion o f the Ch inese t r ad i t ion a l ca l lig ra -

    phy a lso inc ludes the e xtra c t io n of the prof i les of

    the cha rac te r s t rokes . Shamir and Ra ppo por t in -

    t r o d u c e d a p a r a m e t r i c m e t h o d t o c o m p a c t l y re p r e -

    sent exis t ing out l ine-ba sed or ienta l fonts [2~ Wo ng

    and Ip deve loped a f rac ta l -based ou t l ine fon t t ech -

    nology which is ab le to capture the out l ine charac-

    ter is t ics of ca l l igraphy wri t ing [21]. T he y a lso pro-

    posed an a l t e rna t ive me thod in [3 ] to cap tu re the

    s t roke ou t l ine , wh ich i s be t te r than the t r ad i t iona l

    appr oache s[ 12-~41 of expres sing vividness of callig-

    raphy wr i t ing .

    1 .2 O v e r v i e w o f O u r B r u s h M o d e l

    Pu re hard war e approa ches such as G reene 's [7]

    tend to be expens ive and no t gene ra l ly app l ica -

    b le: The mos t s ign i f ican t d rawback o f the cu r re n t

    ha i r b ru sh mode l i s i t s complex i ty due to p ixe l -by-

    pixel evaluat ion . Th e model prop osed in [3] can

    p roduce ra the r v iv id ca l l ig raphy re su l t when s imu-

    la t ing some cases of the dry-br ush effect . How-

    eve r , the s im u la t ion ab i l i ty i s limi ted because o f th e

    mode l ' s coa rseness when s t roke fo rks and the in te r -

    ac t ive mann e r o f the m ode l i s no t so conven ien t and

    s t ra igh t fo rward .

    Th is pape r p roposes a pa rame te r ized phys ica l

    b rush mode l wh ich i s cons i s ten t wi th the rea l p ro .

    cedure o f ca l l ig raphy o r t r ad i t iona l pa in t ing . Th is

    model uses a s implif ied evaluat ion a lgor i thm to ap-

    p rox im a te the e f fec t wh i le ma in ta in ing the ab i l i ty

    to express most of the specia l e ffec ts of Chinese

    ca l l ig raphy . By us ing the app rox ima t ion , the t ime

    needed i s g rea t ly reduced , wh ich enab les ou r m ode l

    to p roduce re su l t in r ea l t ime .

    Tho ugh omi t t ing some o f the minor de ta il s , ou r

    mode l has ac tua l ly enhanced the t r ad i t iona l so ft

    b rush mode l by in t roduc ing a nove l s t roke mode l

    ca l led drople t . This model , d iscussed in de ta i l in

    Sect ions 2 , 3 and 4 , is essent ia l to produce the

    feng effec t , which is a charac ter is t ic fea tur e of

    the Chinese ca l l igraphy. I t a lso helps to pro duce

    the s t roke bounda ry , wi thou t lo s ing the power o f

    exp ress ing the d ry b rush e f fec t and thi s is ve ry

    diff icul t for the previous brush models .

    2 P a r a m e t e r s a n d B r u s h M o d e l

    The b rush mode l p roposed in th i s pape r i s a pa -

    rame t e r ized one . F i r s t , we de f ine a se t o f in te rac -

    t ive ac t ions to s imu la te ac tua l ca l l ig raphy /pa in t ing

    act ions , and th en we def ine a series of brus h pa ram -

    eters , and d iscuss how these ac t ions affec t the var i-

    a t i o n o f t h e p a r a m e t e r s a n d h o w t h e p a r a m e t e r s

    de te rmine the f ina l s t roke mode l .

    2 1 B a s i c A c t i o n s a n d P a r a m e t e r s

    2.1 .1 Basic Act i ons

    The re a re fou r k inds o f bas ic in te rac t ions de -

    f ined in our model . Dipping brush is the in i t ia l

    ac t ion and th i s ac t ion wi l l r e se t the pa rame te r s to

    initial values; Lif t and press the brush is the ac-

    t ion o f mod i fy ing the p re ssu re the b rush imposes

    on the pape r ; B r u s h m o v e m e n t sc ra tches the b rush

    on the pape r and p roduces s t rokes ; Rotate brush-

    holder, the fou r th ac t ion type , i s o f ten pe r fo rmed

    by the ca l l ig raphe rs when they wan t to change the

    d i rec t ion o f the ha i r b rush t ip .

    2 .1 .2 Normal i zed Brush Parame ters

    Bas ic ac t ions dec ide the mod i f ica t ion o f p rope r -

    t i e s o f the b rush , and thu s the s imu la t ion o f ac tua l

    ca l l ig raphy o r Ch inese t r ad i t iona l pa in t ing in ha i r

    b r i s t l e b rush can be pe r fo rmed . Th e mos t impor -

    tant parameters are l is ted as fo l lows.

    1 ) Fundamen ta l b rush pa rame te r s . Th is se t in -

    c ludes b rush leng th L , d iame te r D and ha i r num-

    ber .

    2 ) Brush ve loc i ty V . Th is pa ram e te r deno te s

    the speed o f b rush mo vemen t an d i t i s de tec ted by

    the sys tem th rough use r in te rac t ion .

    3 ) Hum id i ty o f the b rush H . The in i t i a l va lue

    i s g iven by the u se r and i s de tec ted au toma t ica l ly

    by the sys tem when the b rush movemen t ac t ion i s

    pe r fo rmed .

    4 ) Th ickness o f p igmen t T . Th is pa ra me te r de -

    no te s the p ropor t io n o f the am oun t o f ink o r Ch i -

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    Xiao Feng Mi et al.: Droplet: Model fo r Chinese Calligraphy a n d Painting 395

    n e s e t r a d i t i o n a l p a i n t i n g p i g m e n t t o t h e a m o u n t o f

    w a te r . Th i s v a lu e i s imp o r t an t w h en s t ro k es o ve r -

    l ap an d a re b l en d ed .

    5) Brush pressure i s dec ided by the l i f t and press

    b ru s h ac t i o n . Th e p re ss ac t i o n i n c reases b ru s h

    p re ssu re w h e reas t h e l i f t o f b ru sh w i ll d ec rease t h e

    p a r a m e t e r .

    6 ) T ip d i rec t i o n ~/'tip

    T o m a k e o u r m o d e l s i m p l e , a l l t h e p a r a m e t e r s

    o f t h e b ru s h m o d e l a re n o rma l i zed ex c ep t t h o se i n

    t h e f u n d a m e n t a l b r u s h m o d e l p a r a m e t e r s e t , t h a t

    i s , the i r dom ain s a l l l ie in the in ter val (0 , 1 ). How

    t o d e r i v e p r o p e r t a n g e n t a r e a b e t w e e n t h e b r u s h

    a n d t h e p a p e r g i v en t h e p a r a m e t e r s is on e o f t h e

    m a i n p u r p o s e s o f t h e p a p e r .

    2 .2 S t r o k e A r e a M o d e l s

    In o u r ap p ro ac h , w e u se t h e d ro p l e t mo d e l t o

    s i m u l a t e t h e t a n g e n t a r e a b e t w e e n t h e b r u s h a n d

    th e p a p e r b ecau se t h i s k in d o f mo d e l re semb les rea l

    mo d e l b e t t e r t h an p rev io u s o n es [1 'a '4 ]. Th e re a re

    d i f feren t v a r i a t i o n s o f t h e d ro p l e t mo d e l b es id es

    th e s t an d a rd d ro p l e t sh o w n in F ig . l ( a ) . A l l t h e

    d ro p l e t mo d e l s ap p ly t h e same ru l e s i n a f fec t i n g

    t h e r e s u lt a n d t h e r u le s o f t r a n s f o r m a t i o n a m o n g

    d ro p l e t s u n d e r t h e d r i v in g o f ac t i o n s a re d e r iv ed

    f ro m ac tu a l b ru sh w ie ld in g ex p e r i en ce .

    Real models

    9 W

    Droplet models

    D2 D3

    a) b) c) d)

    in i t ial In i t ial Spl i t ted hai rs Layered hai rs

    Humidi ty) Normal)

    e) r )

    egin to Sep arate d

    separate droplets

    Fig.1 . Var iat ions of the droplet m odels to s imulate real tangent a rea between brush a nd paper .

    Th e d ro p l e t mo d e l i s a k in d o f 2 D mo d e l . A s

    ju s t m en t io n ed , t h e s t an d a rd d ro p l e t i s t h e reg io n

    en c lo sed b y tw o c i rc l e s , w i th d i ame te rs D 1 an d D 2

    resp ec t i v e ly , an d t h e tw o co mmo n t an g en t l i n e s o f

    t h e m . T h e f in a l r e s u lt o f o u r s y s t e m p r o v e s t h a t

    rep r e sen t a t i o n o f b ru s h i n t h i s mo d e l , i n s t ead o f

    a sof t so lid of a bunc h of ha irs , need s no com plex

    c o m p u t a t i o n a n d s t i l l m a i n t a i n s a s g o o d s i m u l a -

    t i v e r e s u l ts a s o t h e r s. B o t h t h e s t a n d a r d d r o p l e t

    mo d e l an d t h e v a r i a t i o n 2 co n t a in a s i n g l e d ro p l e t ,

    w h e r e a s t h e r e m a i n d e r m a y c o n s i st o f m o r e t h a n

    one.

    T h e s t a n d a r d m o d e l a n d t h e v a r i a t i o n 2 a r e tw o

    d ro p l e t s u sed a s t h e i n i t i a l mo d e l w h en t h e b ru sh

    i s d ro p p ed . In fac t , v a r i a t i o n 2 i s a sp ec i a l fo rm o f

    t h e s t a n d a r d m o d e l w i t h D 2 b e i n g 0 . T h e v a l u e o f

    D 2 i s d ec id ed b y t h e b ru sh h u mid i t y an d t h e fu n -

    d a m e n t a l b r u s h p a r a m e t e r s , i n c l u d i n g b r u s h l e n g t h

    an d d i a me te r . D e t a i l ed d esc r ip t i o n o f t h e ca l cu la -

    t i o n o f t h e m o d e l w i l l b e p re sen t ed i n Su b sec t i o n

    3 1

    T h e d r o p l e t m o d e l i s i m p o r t a n t t o s i m u l a t e t h e

    p ecu l i a r an d imp o r t a n t h a ir b ru sh e f fec t fen g i n

    Chinese ca l l ig raphy . Th ere are d ifferen t s ty les of

    fen g s . Zh o n g fen g , o r t h e cen t ra l cu t t i n g p o w er o f

    t h e b ru sh , re fe r s t o k eep in g t h e b ru sh p o in t a lw ay s

    in th e m id d l e o f t h e s t ro k e an d t h e t i p d i rec t i o n tip

    i s p a ra l l e l t o t h e s t ro k e mo t io n d i rec t i o n ; Ce fen g

    mean s t h e w r i t e r u se s t h e b ru sh p o in t o n e -s id ed ly

    o r in a s id e lo ng man n e r , w i th t h e an g l e b e tw een t h e

    tw o d i rec t i o n s b e in g an o b tu se o n e ; P i an fen g i s a

    sp ec i a l k in d o f Ce fen g w i th t h e an g l e b e in g a r i g h t

    o n e . F ig .2 sh o w s t h ree k in d s o f fen gs co mm o n ly

    u sed i n Ch in ese ca l l i g rap h y o r p a in t i n g .

    Wtip -- --V :ov e

    a) b) c)

    Fig.2. a) Zhon g feng. b) Pla n feng. c) Ce feng. Corre -

    sponding droplet models are al so given.)

    Th e v a r i a t i o n 4 o f t h e d ro p l e t mo d e l s i s ca l l ed

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    396 J. Co mp ut . Sci. Technol., Ma y 2004, Voi.19, No.3

    a layered drople t , which is used when s imula t ing

    the special e ffec t feng . Wh en wie ld ing brush in

    Ce feng o r P ia n feng manner , the f r i c t ion o f the

    pape r aga ins t the b o t t om p a r t o f the b rush ha i rs

    i s incons i s ten t wi th the t ip d i rec t ion o f the u ppe r

    pa r t o f b rush ha i r s , thus the l aye red d rop le t mode l

    is adopted .

    More deta i led explanat ion is g iven in Fig .3 .

    Vmow deno te s the d i rec t ion o f the b rush movemen t ;

    F i s the pape r ' s f r i c t ion aga ins t the bo t t om ha i rs ;

    Vtip_o is the in i t ia l d i rec t ion of the br ush t ip ; Vtip_l

    and Vtip_2 a re t ip d i rec t ions o f the b o t to m and up -

    per ha irs respect ive ly . The fo l lowing formula g ives

    the ca lcu la t ion o f Vt~v_l a n d Vtip_2 T h e p a r a m e -

    ter p is a user-specif ied fac tor which represents the

    user 's in tent ion of wie ld ing brush . Wh en p = 1 ,

    the v i r tua l b r ush exp resses the e f fec t o f P lan feng

    whereas i t expresses Zhong feng when p -+ 0 .

    Vtip_z = no~rnalize(ptip= Vtip_o + ( 1 - p t i p = ) F ) ,

    x = 1,2; Ptip_z E [0, 1]

    Ytip _

    ~nove

    Fig.3. Inconsistence and interaction between

    the directions

    of

    brush tip

    and brush movement.

    In the l aye red d rop le t mode l , Vtip_ 1 and Vtip_2

    are specif ied with d if ferent va lues and Ptip_l >>

    Ptip_2. When the b rush moves fa s t , the ink in the

    uppe r ha i r s canno t have enough t ime to depos i t to

    the pap e r and thus the lower d rop let mode l o f va r i-

    a t ion 4 is appl ied; o therwise , the upper model is

    appl ied .

    2 . 3 T r a n s f o r m a t i o n s B e t w e e n D r o p l e t

    V a r i a t i o n s

    va lue o f D2 i s a func t ion o f b rush humid i ty . Wh en

    the pa ram e te r H i s lower tha n a p rede f ined va lue ,

    the ha i r o f b rush canno t be conc en t ra ted in a s in-

    g le bunch and wou ld sp l i t to more than one and

    the mo de l is t r ans fo rmed to 3 . In th is mode l , D3

    i s d e c i d ed b y t h e p a r a m e t e r pressure a n d t h e m a n -

    ne r o f ho ld ing b rush . W hen the s t r e s s po in t o f the

    brush is moved to the t ip area , D3 is increased .

    2) From var ia t ion 3 to var ia t ion 4. As de-

    sc r ibed in Subsec t ion 2 .2 , when the d i rec t ion o f

    b rush movemen t and the t ip d i rec t ion a re no t the

    same ( in Plan feng or Ce feng) , inconsis tence be-

    tween the up pe r a nd lower pa r t s o f the b rush ha i r

    wil l occur .

    3) From var ia t ions 3 , 4 to var ia t ion 5 then 6 .

    When the va lue o f

    pressure

    dec reases , ove r lapped

    drop le t s wi l l a t l a s t become sepa ra ted f rom each

    o the r .

    4 ) From va r ia t ion 5 to va r ia t ions 3 and 4 . Th is

    i s an inve rse t r ans fo rm a t ion o f the p rev ious one .

    Wh en the p re ssu re inc reases , the p rev ious ly sepa -

    ra ted d rop le t s wi l l aga in be ove r lapped .

    5) Fro m var ia t ions 3 , 4 to var ia t ion 2 . W he n

    the ca l l ig raphe r ro ta te s the b rush -ho lde r , the sp l i t

    drople ts wil l uni te in to a s ingle one and the layered

    structure in var ia t ion 4 wil l a lso be e l iminated .

    Fig .4 shows the poss ib le t r ans fo rma t ions be -

    tween the s tanda rd d rop le t mode l and va r ia t ions

    of i t .

    As

    INIT ...~ 8 ~ F=Vtiv_l

    2 action t

    6

    Fig.4.

    Action driven transformation

    of the droplet model.

    In the bru sh mod el und er discussion, except for

    the fund amen tal brush parameters, all other pa-

    rameters are deter mined according to the brush

    actions and thus the transfor mations bet wee n vari-

    ations of the mo del are driven. Th e state ma-

    chine can be achieved from experience. The pos-

    sible transfo rmation s bet wee n droplet mod el varia-

    tions are listed below.

    i) Fr om variations I, 2 to variation 3. Th e re-

    ductior~ of ink is the caus e of this transfer. DI is

    determ ined by the value of brush

    pr ssur

    and the

    3 C o m p u t a t i o n o f S t r o k e A r e a

    The stroke area is the tangent area between the

    brush and the paper when the calligrapher writes

    characters with a brus h and a droplet is the stroke

    area at a given mome nt . Th e entire stroke area is

    ass um ed as the trail the droplets h ave swept.

    3 .1 C o m p u t a t i o n o f t h e D r o p l e t s

    T h e c o m p u t a t i o n o f t h e d r o p l e t m o d e l c a n b e

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    .hfiao-Feng Mi et al.: Droplet: Mo del for Chinese Calligraphy and Pa intin g 397

    divided into two steps: evaluating the droplets in

    its local coordinate system and then transforming

    it to paper co ordinat e system. Given the location

    of the brus h and th e tip orientation, it is simple

    to get the transformation T and the sequent work

    is strai ghtf orward . So in this section we focus on

    the evaluation of the droplet in its local coordinate

    system.

    Because most of the brush p arameters are nor-

    malized, we do not intend to and cannot calculate

    the physical model of the brush precisely. Besides,

    the i ntrod ucti on of various rand om variables into

    the calculations adds to the impossibility. Further-

    more, to give an aesthetically beautiful result, it

    is of no sense being precise. In fact, in our brus h

    model, we have used a lot of simplification of eval-

    uation without loss of expressive power.

    The evaluatio n of the stand ard droplet model

    is qui te simple. D1 = D . p r e s s u r e , and it means

    that the size of the tangent stroke area varies ac-

    cording to the variation of the pressure the callig-

    rapher imposes on the paper. The range of D1 is

    (0, D). De = D I 9 kH , k lies in the interval (0, 1)

    and is specified by the user at the initial time. A

    relatively bigger k means that the virtual calligra-

    pher tilts his brush holder to the side of the brush

    tip.

    h = L .pressure.

    (See Fig.5(a)).

    Humidity decrease

    ( 1 - s ) R I ~ I - s ) R 2

    el (d)

    Fig.5. Evaluation of droplets.

    Fig.5(b) shows how the variation model 1 or

    variation model 2 transforms to variation model 3

    or 4. Here, we introduce a random number s. The

    circle with rad ius R on either end of the droplet is

    divided into two circles with radius (1 - s )R1 and

    sR1 respectively.

    Figs.(c) and (d) in Fig.5 shows the droplets

    when pres sure decreases. We can see from the fig-

    ure that, when the brush is lifted, the droplet vari-

    ation 3 or 4 transforms to variation 6 ultimately.

    Note that in Fig.5, all Rs are half the value of

    the corresponding Ds mentioned; R stands for ra-

    dius and D for diameter.

    The reunion and merging of the droplets are in-

    verses of the course of droplet sep arating and split-

    ting, so we omit explaining the evaluation of the m

    here.

    3 .2 Hul l o f Dropl e t s

    Whe n the parame ters of the brush model are

    modified, for example, lifting or pressing the brush,

    moving the brush etc., the droplet model must be

    reevaluated. The b rush moves continuously in real

    calligraphy, but this is impossible in computer. In

    our model, we simply evaluate droplets periodically

    and use the hull of the two sequentially eval uated

    droplet models to approximate the stroke in this

    interval.

    Before further discussion, we first define some

    terms. We say that the droplets retrieved in

    the same evaluation are sibling droplets with one

    another. When evaluating droplet model, each

    droplet can be derived by one of the three cases:

    inheritor from previous droplet, merged one from

    several droplets or otherwise one of the resulti ng

    drople ts from a split. In any case, the previous

    droplet(s) is(are) the

    parent(s)

    of the result droplet

    and the latter is called a descendant of the former.

    After sorting the droplets in a droplet model by

    the Y coordinate value in the droplet model's local

    coordinate system, where some droplets are called

    neighboring ones if there are no other droplets be-

    tween them in the sorted sequence.

    As for the case shown in Fig.6, in the genera-

    tion o f the shown stroke, there are 5 evalua tions of

    dropl et model, i.e., a - e. As explained in Fig.l ,

    models a, b and e belong to the standard droplet

    model whereas model c or d belongs to variation 6.

    (In interactive calligraphy, the system will execute

    much more than 5 evaluations, and by our model,

    the standard model cannot transform to variation

    6, but this does not affect the explanat ion of the

    terms.) There are more than one droplet in bo th

    c and d. cl, c2 and c3 are siblings wit h one an-

    other , so are dl and d2. c2 and c3 are the pa rent s

    of d2 and t he latt er is a descendant of them . cl, c2

    are neighboring droplets, so are c2 and c3, however,

    this is not true for cl and c3.

    The evaluation of the hull is not so straight-

    forward because there may be case that the two

    drople t models are topologic ally inconsistent . Oc-

    currence of such inconsistence may be during the

    time when droplet model 1 or 2 transforms to model

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    3. To avoid ex t rem e comple :d ty , we hold two as-

    s u m p t i o n s .

    A s s u m p t i o n 1. Only neighboring sibling

    droplets can be merged into one new droplet and the

    droplets' order of one evaluation keeps the same as

    the order of the droplets' parents in the previous

    evaluation.

    a b c1 c2~c3

    dl d2

    a)

    b)

    Fig.6. Hull rule. The h ull of separ ated droplets elegantly

    expresses the "dry brush" effect. (a) The droplets and the

    hull rule. (b) The resulting stroke area.

    F o r e x a m p l e , s u p p o s e dropk_l, dropk a n d

    dropk+l a re t h ree ne ighbo r ing d rop l e t s . In t he

    nex t ev a lua t i on o f t he d rop l e t m ode l , t he d rop l e t ( s )

    t r a n s f o r m e d f r o m dropk i s bound t o l ie be tw een t he

    d r o p l e t s t r a n s f o r m e d f r o m dropk_ 1 a n d dropk+l.

    A s s u m p t i o n 2 .

    In two sequentially evaluated

    droplets, a single droplet cannot split into several

    while in the same t ime part of them merge with

    other droplets.

    N ow w e g ive t he

    hull rule: each of the descen-

    dants or the parents of a droplet partic ipates in the

    evaluation of the hull with this droplet.

    Fig .6 show s an exam ple o f app ly ing t he hu l l ru l e

    to eva lua t e t he s t roke a rea o f a "dash" s t roke , i n -

    c luding the case of topologica l ly d i fference .

    S i m u l a t i o n o f V a r i o u s B r u s h E f f e c ts

    ing s ty le as shown in Fig .6 i s no t good enough as

    far as the rea l "dry brush" or "d i ffusion" effec t i s

    t o be s imu la t ed .

    W h e n t h e v a l u e o f h u m i d i t y d i v i de d b y b r u s h

    ve loc i t y (a s an i nd i ca t i on o f t he depos i t a mo un t o f

    the ink) i s lower th an a predef ined value , the pro -

    duced s t rokes shou ld be rende red i n "d ry b ru sh"

    s ty l e. To exp ress th i s e f fec t, H e l ena T .F . W ong and

    Hor ace H.S. I p [3] have d evelo ped an

    ink deposit ing

    model i n t h e i r v i r t u a l b r u s h s y s t e m t o a t t a c h t h e

    t e x t u r e t o t h e p r o d u c e d s t r o k e p i x e l b y p i x e l a n d

    thr resu l t ing effec t i s fa i r ly v iv id . However , th i s i s

    a t i m e c o n s u m i n g p r o c e s s . I n o u r i m p l e m e n t a t i o n ,

    w e i m p o r t t h e t e x t u r e i m a g e f r o m a p r o p e r p a r t o f

    a p rede f ined t ex tu re l i b ra ry acco rd ing t o t he b ru sh

    humid i ty , ha i r number and t he p re ssu re d i s t r i bu -

    t i on i n t he s t roke a rea .

    In mos t ca se s , t he p re ssu re t he b ru sh imposes

    on t he pape r d i s t r i bu t e s equa l l y a long t he d i rec t i on

    v as show n in Fig .7 . Whi le in som e occasion , th e

    ca l l i g raphe r may choose t o t i l t h i s b ru sh t o s t re ss

    some pa r t o f t he s t roke and l eave t he o the r pa r t

    w h i t e , t hen t he p re ssu re may no t d i s t r i bu t e equa l l y

    a l o n g t h e t a n g e n t a r e a b e t w e e n t h e h a i r b r u s h a n d

    the pape r . F ig .7 show s t he p rocess o f ha t ch ing t he

    s t roke a rea w i th p rede f ined t ex tu re acco rd ing t o

    the humid i ty , p re ssu re and ve loc i t y .

    ~ P ressure

    d i s t r i ~

    distance

    ' 7 ---Y

    t e x t u r e ~ e n s l t y

    p r e s s u r e • h u m i d i t y / v e l o c i t y

    ured stroke area

    T h e d r o p l e t s c o m p u t e d u s i n g t h e a l g o r i t h m d e -

    sc r i bed i n p rev ious sec t i ons rep re sen t t he t angen t

    a r e a s b e t w e e n t h e b r u s h a n d t h e p a p e r . T h e f i n a l

    re su l t a f t e r v i r t ua l "ca l l i g raphy" w i th t h i s mode l

    depends on how to dea l w i th t he t angen t a rea . A s

    the f i r s t app l i ca t i on o f t he mode l , by ha t ch ing t he

    g e n e r a t e d t a n g e n t a r e a s w i t h p r o p e r t e x t u r e s , t o -

    ge the r w i th t he cons ide ra t i on o f i nk d if fu sion , w e

    can re t r i eve fa i r l y good pa in t i ng re su l t s .

    4 .1 H u l l H a t c h i n g

    Pr ope r ha t ch ing o f t he ca l cu l a t ed hu l ls w i ll

    p re sen t v iv id ca l l i g raphy e f fec t . The so l i d ha t ch -

    Fig.7. Th e process of stroke hatching according to th e pres-

    sure, humidity and velocity.

    In t he ca se of F ig .7 , w h en t he va r i a t i on 4 o f t he

    d rop l e t mode l i s app l i ed , due t o t he sca rceness o f

    d e p o s i t e d i n k , w e s h o u l d a p p l y t h e b o t t o m p a r t o f

    t he mode l t o eva lua t e t he s t roke a rea . H ow eve r ,

    w hen t he b ru sh i s w e t enough , t he uppe r l aye r o f

    the drople ts i s appl ied . In th is case , a d i ffusion ef-

    fec t o f t he s t roke i s needed . The d i rec t i ons o f t he

    d rop l e t s a re compu ted acco rd ing t o t he d i scuss ion

    pre sen ted in Subse ct ion 2 .2 . Fig .8 shows the re-

    su i t i ng image and t he de t a i l ed d i scuss ion o f s t roke

    di ffusion i s presented in the next sec t ion .

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    fo r

    Chinese Ca l l igraphy and Pa in t ing

    399

    Pressure

    dist r ibut ion

    Radial

    dis tance

    Relat ively scarce ~

    ink deposi ted area

    St roke areatangent )

    Diffusio n are a *~

    High density ink AR.esult ing

    "~teoosited area image_

    Fig.8 . The process of s t roke hatching w hen ink i s densely de-

    posi ted a nd the upper layer of droplet var iat ion 4 i s adopted.

    4 .2 S t r o k e D i f f u s i o n

    4.2.1 Basi c Di f fus ion Mo del

    Bas i c d i f fu s ion i s t o be app l i ed w hen t he w ho le

    b rush i s soaked w i th i nk , o r p igmen t and w a te r ,

    equal ly . For th is s imp le model , J in ta e Lee[ 1~ has

    a l ready p roposed a s t roke d i f fu s ion mode l based on

    the co lo r i n t ens i t y obse rva t i on on rea l c i rcu l a r d i f -

    fu s ion images . H e re , w e adop t t h i s d i f fu s ion mode l

    t o o u r s y s te m , e x c e p t t h a t w e o m i t t h e p a p e r m o d e l

    to ge t s imp l i c i t y . Based on ou r expe r imen t on r i ce

    pape r , w e re t r i eve t he p ixe l g raysca l e func t i on o f

    rad i a l d i s t ance f rom the cen t e r o f t he d rop l e t t h a t

    con t r i bu t e s p igm en t t o t ha t p ixe l. F ig .9 (a ) show s

    t h e e x p e r i m e n t a l d a t a f r o m t h e s a m p l e s ho w n i n

    Fig .9 (c ) , and F ig .9 (b ) show s t he re t r i eved func t i on

    cu rves . Th e m ean ing s o f t he re fe rence va lue r0 and

    the va r i ab l e r a re i nd i ca t ed i n F ig .9 (d ) . F rom the

    expe r imen ta l re su l t , t h e d i f fu s ion a rea i s d iv ided

    in to two zones: the d im inish zone , wher e the ink

    (o r p igmen t ) dens i t y g radua l l y dec reases and t he

    ensu ing van i sh zone , w he re t he dens i t y is w eak

    and f l uc tua t e s . The w ho le rende red a rea can be

    d iv ided i n to t he s t roke a rea , w he re t he b ru sh is

    t angen t t o t he pape r , and t he d i f fu s ion a rea , a s

    indica te d in Fig .9(c) . Fol lowing th is mod el , the

    ca l cu l a t ed d imin i sh zone and van i shed zone w hen

    s imu la t i ng t he samp le s t roke i n F ig .9 (c ) a re show n

    in Fig .9(d) , and Fig .9(e) i s the f ina l rend ering re-

    su l t us ing a gradien t brush .

    We use five control points, P0 to/?.4, for the eval-

    ua t i on o f t he sp l ine i n F ig .9 (b ) , w hose coo rd ina t e s

    in t he rad i a l -g raysca l e p l ane a re a s i nd i ca t ed .

    A mong the coo rd ina t e va lues , rd deno te s t he

    wid th of the d i ffusion area ; P2 i s the cr i t ica l po in t

    w here t he g raysca l e beg in s t o dec rease d rama t i ca l l y

    and we record th e graysca le va lue there as G1. G2 is

    t he g raysca l e on t he bounda ry be tw een t he d imin -

    i sh zone and t he van i sh zone . W e g ive t he fo rm u las

    to eva lua t e t he se coo rd ina t e va lues .

    7"d ~ 8pigrnen t 9 pape r " H 9 ro

    G1 = e l G o , G 2 = e 2 G o

    Go = T . Gray scale Cpia m~ t )

    spig,~,~t a n d sp~p~r deno te t he d i f fu s ion ra t i o s o f t he

    p i g m e n t a n d t h e p a p e r r e s p e c t i v e l y a n d t h e v a l u e

    o f t hem i s g iven w hen t he u se r has chosen a k ind

    1.05 Gra y scale

    ~ .,~-~, ~ i ~ i i

    0.0 :

    Ro Radius

    ~ Pixel grayscale

    Po(O, Go)

    . . . .

    G1 = G0q ~ t - 1 (r0, t~0)

    e l xGo ..................~ - ' ~ 2 ( r ~

    DiminishkVanish

    G2 = ~ ione : zone i

    e2x

    Go . .. .. .. .. ~o +2 rd /3 ,

    G2)

    r0 ~ .g 4(r 0 rd , o)

    >;4 d r

    Stroke" Diffusion "i Ra dia l

    distance

    area re

    Vanish \~zone ~,_. :_':_~. /

    L l m l n l S f l

    zone Stroke

    area

    (b) (d)

    (a) (c) (e)

    Fig .9 . (a) Correspond ing exper imen tal densi ty funct ion. (b) Synthesized funct ion curve. (c) Actu al p igment d i f fusion

    images gener ated on r ice paper . (d) Calculated diminish zone and vanish zone. (e) Imi tat io n resul t .

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    400

    J. Com put. Sci. & Technol., Ma y 2004, %1.19, No.3

    of p igme nt a nd a paper , e l a nd e2 are ca l led d if -

    fus ion var iables and the values of the m are 0 .8 and

    0.2 in our system. G0 is the grayscale va lue of

    the center of the s t roke area a nd i ts va lue is de-

    te rmined acco rd ing to the p igmen t co lo r and the

    pigm ent th ickness T. Th e value of r0 is re tr iev ed

    using the a lgor i thm discussed in previous sec t ions .

    The decreasing of the grayscale in d if fus ion is

    based on the phys ica l phenomenon : the wa te r f lows

    more qu ick ly than tha t in the p igmen t pa r t i c le s .

    Thu s i t i s t rue tha t the th ickness o f the ink (o r

    p igmen t ) in the d i f fu s ion a rea i s lower than tha t

    in the s t roke area . We draw the color d is tr ibu t ion

    formula as follows:

    C = Col or( C * Cpigment alpha, Cpia . . . t ' red,

    Cpig,~,~t green, Cp i gm e n t blue) .

    Th e fo rmula imp l ie s tha t the co lo r in the d i f fu -

    s ion area is the same as tha t in the s t roke area but

    more t r anspa r en t s ince the a lpha va lue o f the co lo r

    is lower.

    4 .2.2 N o n - Eq u a l D i f fu s ion

    The discussion in the previous sec t ion is based

    on the a ssumpt ion tha t the ink d i s t r ibu te s equa l ly

    a l l over the brush . However , sometimes, especia l ly

    in the case o f Ch inese t r ad i t iona l pa in t ing , the

    pa in te r may choose to unequa l ly d i spose the p ig -

    men t th ro ughou t the b rush . Fo r example , he may

    le t the p igmen t a round the b rush t ip th icke r than

    tha t o f the o the r pa r t . We use a s imp le s t r a tegy ,

    mult i -pass d if fus ion model , to deal with th is case .

    In th is model , w e es tabl ish a se t of th ickness va l-

    ues {Ti} and a corresp ondin g se t of radius va lues

    {r i} , then app ly the equa l d i f fu s ion mode l to each

    pa i r o f (T i, r i ) and re t r i eve the g raysca le d i s t r ibu -

    t ion Gi . Fo r each (Ti , r i ) , the g raysca le func t ion

    cu rve i s eva lua ted and the eva lua t ion o f the va lue

    Ci a t a g iven po in t i s execu ted wi th the func t ion .

    Th e f ina l va lue G a t a po in t i s the ma x im um o f the

    se t {Gi} on tha t po in t .

    F ig .10 shows ou r non-equa l d i f fu s ion mode l an d

    the rende r ing re su l t in th i s mode l .

    4 .3 M o r e E l a b o r a t e d D r o p l e t s

    The hul l-ha tching ru le and d iffusion using a gra-

    d ient brush have advantages in eff ic iency. Appling

    these models , we can in terac t ive ly s imula te ca l l ig-

    raphy us ing the in t roduced v i r tua l b rush . However ,

    the re su l t s a re somehow no t a s good a s expec ta t ion

    compared wi th the re su l t u s ing the mode l p roposed

    by [3] or [10]. Imp rovin g the qual i ty of rea l sam-

    p l ing s t roke tex tu re fo r hu l l ha tch ing can improve

    the re su l t s to some ex ten t ; however , to ge t more

    rea l i s t i c r e su l t s , we mus t cons ide r e labo ra t ing the

    d rop le t s , though th i s wi ll cost m ore t ime fo r s t roke

    gene ra t ion .

    To mimic a rea l brush in var ious aspects , we

    e labo ra te the d rop le t s wi th b r i s t l e s a r ranged some-

    wha t r andomly wi th in the d rop le t a rea a s shown

    in Fig .11 . This m odel takes the de nsi ty of br is t les

    in to accoun t and can gene ra te s t rokes more v iv id ly .

    Ins te ad of drople t hul l ing , to v isual ize the s t rokes

    on the pape r , th i s mode l on ly d raws l ines f rom the

    se lec ted br is t les with previous drople ts to the se-

    lec ted co r re spond ing ones wi th the i r descendan ts .

    Th e co lo r and t r ansp a renc y o f the l ine are dec ided

    b y t h e a m o u n t o f w a t e r a n d w h e t h e r t o d r a w t h e

    l ines is dec ided by the hum id i ty o f the d rop le t s .

    a)

    (b/

    , ]~ ~ d~176 Io lo lo ]oJ

    , [oFoIo Io Io Iol o lol o[o Io Io Iv IolO I

    o l ~ I o lo {o I O l o l

    op o ~ t~ I , I * J , l * t , [~ * i * i ~

    Io l

    1/,t~

    ~17 6 ~176 17 6 ~ [~l ~

    ~ * 1 - [ , ~ , I , l - i . I, [ , t ' l - l ' ~ l o l

    o I .l ~' l -L %. l- I 1 ,[~ Eo I

    Olo lot r ~ o ~ . ; . ' , o ~ . ~ ~ ~176 < ~ G e n e r a t e d

    olo [ .~ I?A~ .I .~- tot .I . l~ I '~ Io[ol dr op le t

    o I ololo la4~176-I .[ ~ .; ~176~lo V I Uns e le c te d

    o lOlo lOl Olop~4~. , .4~l op [ol o

    olo I o[O Io Iol o[ololol o I olo[olo I ol br is tl e

    , o o o o o o oplo[ol olO[ ao[o[ . Se le ct ed

    oOo~o o~ r o oo l~

    b r i s t l e

    (c)

    F i g . 1 1 . E l a b o r a t e d d r o p l e t w i t h b r i s t l e s . ( a ) D e n s e l y d i s -

    t r i b u t e d b r i s t l e s . ( b ) S p a r s e l y d i s t r i b u t e d b r i s t l e s . ( c ) E l a b -

    o r a t e d d r o p l e t w i t h b r i s t l e s .

    2 r 2

    F i g . 1 0 . N o n - e q u a l d i f f u s i o n u s i n g m u l t i - p a s s d i f f u s i o n m o d e l .

    The c r i t e r ia o f whe the r to d raw the l ine a re im-

    por t an t fo r exp ress ing some spec ia l ha i r b rush e f-

    fec ts . One of such examples is f ly ing white (or

    fe i ba i in Chinese) . A drop le t with h igh speed

    and lack of ink wil l g ive the s t roke so me k inds of

    f ly ing white . We express th is e ffec t by decrease

    the possib i l i ty of drawing t he l ines of the d rople ts .

    Ano th e r improvem en t o f the d rop le t s i s to ap -

    ply Lee 's mode l to the dropl e t hul ls[ l~ to express

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    Xiao Feng Al l et al . : Droplet: Model for Chinese Cal l igraphy and Paint ing 401

    a) b) c) d)

    Fig.12. (a) Norm al version of a calligraphy. (b) Result of a brush w ith more sparsely distribute d bristles. (c) Stroke stress

    with flying white. (d) Highly diffused calligraphy. (T he virtua l brush used in (a), (b) and (e) has a diam eter of 65 pixel

    equivalent, and in (d), we use a brush with a diameter of 50 to give the space for ink diffusion.)

    ~H . . . . . . . l i ~ f , ~ i l l ~ r - - ' -

    Fig 13 User interface of the Sinobrush system

    s t r o k e d i f f u s io n . S i n c e th e d r o p l e t s h a v e w e l l d e -

    f i n e d g e o m e t r i c a l b o u n d a r y , h i s a l g o r i t h m c a n e a s -

    i l y b e a p p l i e d .

    F i g . 1 2 g i v e s 4 v e r s io n s o f t h e C h i n e s e c h a r a c t e r

    " w i n e " , t h e f i r s t t w o o f w h i c h h a v e a l r e a d y b e e n

    s i m u l a t e d i n [3]. H o w e v e r , t h a t m o d e l is s o m e h o w

    n o t s o c o m p e t e n t f o r t h e l a t t e r t w o e f f e c t s , w h i c h

    n e e d a w e ll d e f in e d s t r o k e b o u n d a r y a n d m o r e e l a b -

    o r a t e d s t r o k e a r e a d e f i n i t i o n .

    5 I m p l e m e n t a t i o n a n d R e s u l t

    5 . 1 I m p l e m e n t a t i o n

    A p p l y i n g t h e i d e a s a n d a l g o r i t h m s d i s c u s s e d

    a b o v e , w e h a v e d e v e l o p e d a n i n t e r a c t i v e s y s t e m

    w i t h t h e p r o p o s e d v i r t u a l b r u s h m o d e l . T h e s y s -

    t e m ' s w o r k f t o w i s g i v e n b e l o w :

    Brush.Ini t ial ize0;

    Begin: Retrieve Brush Parameters() ;

    Calc New Stroke Model();

    Calc Tangent Area(); / /h ul l calculat ion

    Fi l l Tangent Area (brush parameters);

    Adjust brush parameters() ; / / i nk decreasing, etc.

    while ( Trigger Initialize())

    got o Begin; / /m ov e act ion

    go to Brush.Ini t ial ize(); / /b ru sh dipping

    In the evaluation of two sequential droplet mo d-

    els r an dom factors are introdu ced into the decision

    of droplet m ergi ng and splitting an d into the loca-

    tion of the droplet in the pape r space to add vivid-

    ness to the imitational result. In the calculation

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    402

    J. Com put. Sci. & Technol., M ay 2004, Vo1.19, No.3

    o f t h e b r u s h m o d e l i n e a c h lo o p , t h e i n k r e d u c t i o n

    m o d e l c a n b e a n i t e r a t i v e p r o c e d u r e :

    I N K i + I = I N K i - I N K i . Sst~ok~ 9 f ( t , A p )

    o

    wi th -~-

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    X i a o - F e n g M i e t al.: D r o p l e t : M o d e l f o r C h i n e s e C a l l i g r a p h y a n d P a i n t i n g

    403

    b ru sh . S in ce t h e i n t e rac t i v e ma n n e r i s t h e k ey -

    b o a rd an d t h e mo u se cu rso r , t h e sy s t em h as a l so

    p ro v id ed ex t ra t o o l s an d t h e u se r can ed i t t h e p a th ,

    t h e p re ssu re e t c . o f t h e s t ro k es t h ro u g h t h em .

    5 . 2 E x a m p l e s

    Fig .14 i s a p iece of ca l l ig ra phy w ork by Sino-

    b ru sh . In t h i s w o rk , t h e di f fus io n an d d ry b ru sh

    e f fec t s a re ex ceU en t ly ex p re ssed i n so me p a r t o f

    ch a rac t e r s . Th e w o rk sh o w n in F ig .1 5 is a t y p i -

    ca l pi ece o f Ch in ese t rad i t i o n a l p a in t i n g , an imi t a -

    t i o n of R u n n i n g h o r s e , o n e of X u B e i h o n g ' s m a s -

    t e rp i eces an d X u i s o n e o f t h e g rea t e s t a r t i s t s i n

    m o d e r n C h i n a . I n t h is i m i t a t io n , m o s t o f t h e t y p -

    ica l e ffec ts o f ha i r b rush , i .e . , the dry -bru sh and

    the d i ffus ion effec t, a re wel l expressed . Fig .16 an d

    Fig . 1 7 sh o w a n o th e r tw o p i eces o f imi t a t ed p a in t i n g

    p r o d u c e d b y o u r S i n o b r u s h s y s t e m .

    6 D i s c u s s i o n a n d F u t u r e W o r k

    Th e re su l t o f ca l l i g rap h y o r p a in t i n g i n v i r t u a l

    b r u s h r e l i e s o n t h e f u n d a m e n t a l p a r a m e t e r s a n d

    th e ac t i o n s i n t e rac t i v e ly ex ecu t ed . Th i s p ap e r p ro -

    p o sed a s imp l if i ed an d e f fect i ve v i r t u a l b r u sh m o d e l

    w h ich fo cu ses t h e co n ce rn o n to t h e re su l t . Th e i n -

    t r o d u c t i o n o f v a r i a t io n s o f d r op l e t m o d e l a n d t h e

    hul l ru le i s the e ssen t ia l fea ture of the m odel .

    T h e p r o p o s e d m o d e l p r o p e r l y s i m u la t e s t h e s p e -

    c ia l e ffec t o f Chines e ca l l ig raphy , such as the dry-

    b ru sh e f fect an d t h e d i f fu sio n i n mu ch l e ss t ime

    w h ereas su ccess fu l l y ma in t a in s g o o d ren d e r in g re -

    su i t .

    Th e re i s s t i l l w o rk t o d o , fo r ex amp le :

    1 ) A d o p t a n e l a b o r a t e d i n k - p a p e r i n t e r a c t i o n

    mo d e l a f t e r t h e i n t e rac t i v e ca l l i g rap h y o r p a in t i n g

    w i th t h e v i r t u a l b ru sh h as f i n ish ed, fo r w h ich t h e

    mo d e l co n t r i b u t ed b y L ee [1~ i s g o o d en o u g h ;

    2 ) So me mo re co n v en i en t u se r - i n t e rac t i v e man -

    n e r sh o u ld b e co n s id e red a n d imp ro v ed . U se o f n eu -

    ra l n e tw o rk i s an o p t i o n , w h ich can l ea rn f ro m th e

    p o s t - i n t e r a c t i v e p a r a m e t e r a d j u s t m e n t w h e n u s i n g

    t h e S i n o b r u s h s y s t e m ;

    3 ) D u e t o t h e w e l l -d ef in ed g eo m e t ry p ro p e r t i e s

    o f t h e d r o p l e t s , w e can ea s i ly p ro d u ce t h e o u t l i n e s

    o f t h e re su l t i n g s t ro k es i n ca l l i g rap h y s ty l e w i th -

    o u t l o s in g t h e v iv id n ess i n d ry s t ro k e a rea b y au to -

    ma t i ca l l y ad d in g so me in d i ca t i n g cu rv es t o t h e re -

    su i t i n g p ro f i l e s . Th i s b en e f i t s 3 D ca l l i g rap h y -s ty l e

    c h a r a c t e r m o d e l i n g . W e h a v e a lr e a d y d e ve l o p e d a n

    3 D - ch a r ac t e r mo d e l i n g sy s t em f ro m rea l i s ti c cal l ig -

    rap h y u s in g t h e d ro p l e t mo d e l [2s ]. H o w ev e r , mo r e

    can b e d o n e , fo r ex amp le , 3 D -sea l mo d e l i n g , ep ig -

    rap h y mo d e l in g , e t c .

    A c k n o w l e d g m e n t s W i t h o u t w is e a n d p ro -

    fe ss io n a l ad v i ce f ro m Zh an g Y an , w h o i s an ex -

    ce l len t a r t i s t f ro m th e Ch in ese A cad em y o f A r t ,

    t h e re su l t o f o u r w o rk mig h t b e a mess . Th e au -

    th o rs w o u ld l i k e t o t h an k Miss Zh an g fo r h e r g en -

    e ro u sn ess an d v a lu ab l e ad v i ces . Th an k Pro f . To n g

    Ru o fen g fo r h i s en co u rag emen t an d i n sp i ra t i o n .

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    Xiao-Feng Mi was born in

    1978. He received the B.S. de-

    gree in co mpu ter science in 2000

    and is expected to receive the

    M.S. degree in the spring of

    2003. Now he is a research assis-

    tant in the CAD CG State Key

    Lab of China, Zhejiang Univer-

    sity. His research interests in-

    clude computer graphics, com-

    puter vision and distributed solid modeling.

    M in Ta ng was born in 1974. He received the B.S.,

    M.S., and Ph.D. degrees all in computer science from

    Zhej iang Univ ers ity in 1994, 1996, an d 1999, respec-

    tively. Now he is an associate professor at the Depart-

    ment of Computer Science and Engineering, Zhejiang

    University. His research interests include solid model-

    ing, surface modeling, and computer graphics.

    Ji n- Xi an g D on g was born in 1945. He is a re-

    search professor and Ph.D. supervisor in the Depart-

    ment of Computer Science and Engineer ing of Zhejiang

    University. In the years from 1993 to 1994 he worked as

    an adjunct associate professor at Department of Com-

    puter Science in the University of Souther n California,

    USA. Now he is the vice direct or of the Ins tit ut e of Arti-

    ficial Intelligence and the vice directo r of the CA D CG

    State Key Lab of China, Zhejiang University. His re-

    search interests include comput er graphics, CAD a nd

    CIMS.