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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 : xiaofeng_mi@hot 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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Xiao-Feng Mi e t a l . : Drop le t : Model
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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8/17/2019 Simulation of Chinese Calligraphy
11/12
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.