The Droplet Virtual Brush for Chinese Calligraphic Character Modeling

Transcription

1 The Droplet Virtul Brush for Chinese Clligrphi Chrter Moeling Xiofeng Mi Jie Xu Min Tng Jinxing Dong CAD & CG Stte Key L of Chin, Zhejing University, Hngzhou, Chin Artifiil Intelligene Institute, Zhejing University, Hngzhou, Chin mi_xiofeng@yhoo.om.n, tng_m@zju.eu.n Astrt This pper proposes virtul rush moel se on roplet opertion n its pplition on retrieving hrter outlines n hrter moeling in Chinese lligrphy style. In the propose pproh, virtul rush moel se on roplet opertion is pplie to proue vivi hrter outlines. The roplet moel helps to ompute stroke re with well-efine geometry informtion n les to the fesiility to retrieve the outlines of hrters with well-efine geometry representtion. Further more, the vritions of the moel n express vrious Chinese rush styles, so y using the roplet moel, we suessfully overome the poor expressive ility of the previous urve-offset metho. The omplex evlution of stroke re se on physil soli-moel rush is lso eliminte sine the simpliity of the moel. 1. Introution Numerous lligrphers hve een prouing ountless of msterpiees sine Chinese hrters ppere. The hir ristle rush, whih hs long, strhe nturl ristles nrrowing to pointe tip, is onvenient to use n hs its speil expressive ility. This hs lso impose iffiulties to its simultion n retrieving y omputer. Design of Chinese hrter fonts or omputing the outlines of the hrters in eutiful lligrphy styles hs thus ttrte mny reserhes Relte Works Simultions of Chinese lligrphy n e est esrie in terms of rush sweeps long urve trjetories while the rush shpes hnging ynmilly. Designing lligrphi style Chinese hrters in terms of rush sweeps is quite nturl sine it simultes the wy of humn writing hrters. Vrieties of rush moels hve een uilt y mny reserhes. One of the erliest ttempts is tht of Strssmnn s[1]. He tully simulte the ehvior of rush with wet pint on pper n the propose pproh i not suit for font esign. Wong n Ip [2] simulte the physil proess of rush stroke retion using prmeterize moel whih ptures the writing rush s 3D geometri prmeters, the rush hir properties n the vritions of ink eposition long stroke trjetory. Shmir n Rppoport introue prmetri metho to omptly represent existing outline-se orientl fonts[3]. Wong n Ip evelope frtl-se outline font tehnology whih is le to pture the outline hrteristis of lligrphy writing [4]. A most reent pproh is tht of Xu n Tng s[5]. In this moel, lusters of hirs re represente s soli moels n the imittion of the lligrphy inlues some geometry opertions on the moel. The previous virtul rush moels re ll esigne s some kin of soft rushes n nnot express vrious Chinese lligrphy effets, e.g, the effet of ry rush with stroke forks. In tritionl virtul rush moel, the tngent re etween the rush n the pper is ompute pixel y pixel. Though powerful in simulting the tul ry-rush effet, while pplie in retrieving of hrter outlines, this kin of rush moel is inpproprite euse it s too onerne with etil n the tngent re ompute is lk of geometry informtion. An the pproh in moel [4], inherently n imge reognition pproh, is oun to enounter the ilemm when eling with the ry stroke re. Figure 1 shows suh se Overview of the Droplet Moel By omitting some of the minor etils, the propose prmeterize physil rush moel hs tully enhne the tritionl soft rush moel y introuing novel stroke moel lle roplet. This moel, isusse in etil in setion 2, n proue the stroke ounry with well-efine geometry informtion, Stroke outline: Diffiult to retrieve using Imge reognition tehnique Stroke outline: Imposile to retrieve using Imge reognition tehnique Desire stroke outlines with extr inition urves ing to the viviment. Figure 1. It is iffiult to retrieve the outline of the ry strokes n impossile to get the inition urves s the esire results shown on the right in re.

2 Rel Moels D2 D3 Droplet Moels D1 1 Initil(Humiity) 2 Initil(Norml) 3 Splitte hirs without losing the power of expressing the ry rush effet whih is rther iffiult for the previous rush moels. When pplie to retrieving lligrphi hrter outlines, the rush prmeters re etermine oring to the lligrphy imge n regenertion of the lligrphy with our moel is just the retrieve result. 4 Lyere hirs 5 Begin to seprte 6 Seprte roplets Figure 2. Vritions of the roplet moels to simulte rel tngent re etween rush n pper tion. 6. Tip iretion V tip. Exept those in the funmentl rush moel prmeter set, ll the prmeters of the rush moel re normlize for the ske of simpliity, tht is, their omins ll lie in the intervl (0, 1). 2. rmeterize Brush Moel The rush moel propose in this pper is prmeterize one. First, we efine set of intertive tions to simulte tul lligrphy/pinting tions, n then we efine series of rush prmeters, n isuss how these tions ffet the vrition of the prmeters n how the prmeters etermine the finl stroke moel Bsi Ations There re four kins of si intertions efine in our moel. Dipping rush is the initil tion n this tion will reset the prmeters into initil vlues; Lift n press the rush is the tion of moifying the pressure the rush imposes to the pper; rush movement srthes the rush on the pper n proues strokes; Rotte rush-holer, the forth tion type, is often performe y the lligrphers when they wnt to hnge the iretion of the hir rush tip Normlize rush prmeters Bsi tions eie the moifition of properties of the rush. The most importnt prmeters re liste s follows: 1. Funmentl rush prmeters. This set inlues rush length L, imeter D n hir numer. 2. Brush veloity V. This prmeter enotes the spee of rush movement n it is etete y the system in user intertion. 3. Humiity of the rush, H. 4. Thikness of pigment T. This prmeter enotes the proportion of the mount of ink or Chinese tritionl pinting pigment to the mount of wter. 5. Brush pressure is eie y the lift n press rush 2.3. Stroke Are Moels In our pproh, we use the roplet moel to simulte the tngent re etween the rush n the pper euse this kin of moel resemles rel moel etter thn previous ones[3, 4, 7]. There re ifferent vritions of the roplet moel esies the stnr roplet shown in figure 2-1. All the roplet moels pply the sme rules in omputing the result n the rules of trnsformtion mong roplets uner the riven of tions re erive from tul rush wieling experiene. The roplet moel is kin of 2D moel. As just mentione, the stnr roplet is the region enlose y two irles, with imeter D 1 n D 2 respetively, n the two ommon tngent lines of them. Both the stnr roplet moel n the vrition 2 ll ontin single roplet, wheres the reminer my onsists of more thn one. The stnr moel n the vrition 2 re two roplets use s the initil moel when the rush is roppe. In ft, vrition 2 is speil form of the stnr moel with D 2 equls 0. The vlue of D 2 is eie y the rush humiity n the funmentl rush prmeters, inluing rush length n imeter. The vrition 4 of the roplet moels is lle lyere roplet. When wieling rush, the frition of the INIT 1 2 H H Rot t e At i on F F = V tip_1 V tip_1 6 Figure 3. Ation-riven moel trnsformtion 3 5 4

3 pper ginst the ottom prt of the rush hirs my e inonsistent with the tip iretion of the upper prt of rush hirs, thus the lyere roplet moel is opte. Exept for the funmentl rush prmeters, ll other prmeters re etermine oring to the rush tions n thus the trnsformtions etween vritions of the moel re riven. The stte mhine is hieve from experiene. The possile trnsformtions etween roplet moel vritions re shown in figure Computtion of Stroke Are Following previous reserhes, the entire stroke re is ssume s the tril the roplets hve swept. The omputtion of the roplet moel n e ivie into two steps: evluting the roplets in its lol oorintion system n then trnsforming it to pper oorintion system. Given the lotion of the rush n the tip orienttion, it is simple to get the trnsformtion T n the sequent work is strightforwr. So in this setion we fous on the evlution of the roplet in its lol oorintion system. Beuse most of the rush prmeters re normlize, we o not intent to n n not lulte the physil moel of the rush preisely. The evlution of the stnr roplet moel is quite simple. D 1 = D pressure, n it mens tht the size of the tngent stroke re vries oring to the vrition of the pressure the lligrpher imposes on the pper. The rnge of D 1 is (0, D). D 2 = D 1 kh, k lies in the intervl (0, 1) n is speifie y the user t the initil time. A reltive igger k mens tht the virtul lligrpher tilts his rush holer to the sie of the rush tip. h = L pressure. See figure 4-. ressure erese h R 1 R 2 Humiity erese (1-s)R 1 The figure 4- shows how the vrition moel 1 or vrition moel 2 trnsforms to vrition 3 or 4. Here, we introue rnom numer s. The irle with rius R on either en of the roplet is ivie into two irles with rius (1-s)R 1 n sr 1 respetively. Figure n in figure 4 shows the roplets when pressure erese. We n see from the figure tht, when the rush is lifte, the roplet vrition 3 or 4 trnsforms to the vrition 6 ultimtely. Note tht in figure 4, ll Rs re hlf the vlue of the sr 1 Figure 4. Evlution of roplets h (1-s)R 1 sr 2 orresponing Ds mentione; R stns for rius n D for imeter. The reunion n merging of the roplets re inverses of roplet seprting n splitting. When the prmeters of the rush moel re moifie, the roplets moel must e reevlute. However, the rush moves ontinuously in rel lligrphy, ut this is impossile in omputer. In our moel, we simply evlute roplets perioilly n use the hull of the two sequentilly evlute roplet moels to pproximte the stroke uring this time. Before further isussion, we first efine some terms. We ll tht eh of the roplet retrieve in the sme evlution re siling roplets with one nother. When evluting roplets moel, eh roplet n e erive y one of the three ses: inheritor from previous roplet, merge one from severl roplets or otherwise one of the resulting roplets from split. In ny se, the previous roplet(s) is(re) the prent(s) of the result roplet n the ltter is lle esennt of the former. After sorting the roplets in roplet moel y the y oorinte vlue in the roplet moel s lol oorintion system, some roplets re lle neighoring ones if there re no other roplets etween them in the sorte sequene. The evlution of the hull is not so strightforwr euse there my e se tht the two roplet moels re topologilly inonsistent. On ourrene of suh inonsistene my e uring the time when roplet moel 1 or 2 trnsforms to moel 3. To voi extreme omplexity, we hol two ssumptions: Assumption 1: Only neighoring siling roplets n e merge into one new roplet n tht the roplets orer of one evlution keeps the sme s the orer of the roplets prents in the previous evlution. For exmple, suppose rop k-1, rop k n rop k+1 re three neighoring roplets, in the next evlution of the roplet moel, the roplet(s) trnsforme from rop k is oun to lies etween the roplets trnsforme from rop k-1 n rop k+1. Assumption 2: In two sequentilly evlute roplets, single roplet n not oth split into severl n in the sme time prt of them merge with other roplets. Now we give the hull rule: eh of the esennts or the prents of roplet prtiiptes to the evlution of the hull with this roplet. the roplets n the hull rule the resulting stoke re Figure 5. Hull rule. The hull of seprte roplets elegntly expresses the ry rush effet.

4 Figure 5 shows n exmple of pplying the hull rule to evlute the stoke re of sh stroke, inluing the se of topologilly ifferene. 3. Clligrphy Reonstrution n Moeling Reonstrution of lligrphi hrters n the moeling-purpose outline lultion n e ivie into two steps: retrieving the rush prmeters from the input lligrphy imge n then regenerting the lligrphy using the virtul rush with the lulte prmeter set Brush rmeters Determintion From figure 3, we n see tht humiity of the roplet virtul rush will rive roplet from vrition 1 or 2 to vrition 3, so, we must etermine the vlue of H long the stroke. Nturlly, we use the vlue of rk-pixel numer ivie y the soure imge y numer of pixels the orresponing roplet overs s the mesurement of stroke humiity. The stroke pth is speifie y user intertively (s the she line in the left sie of figure 6). Drop 2 Drop 1 Drop 31, Drop 32 Drop 4 Drop 5 Drop 6 Drop 71, Drop 72, Drop 73 Drop 81, Drop 82, Drop 83, Drop 84 Totl Drk Rtio D % D % D % D % D % D % D % D % D /0% D % Figure 6. ixel smpling from soure imge to etet roplet ink eposit mount Figure 7. lligrphy reonstrution n moeling of the one shown in figure 6. Figure 6 lso shows the rk-pixel rtio of some lulte roplets. We n see from the t liste on the right tle tht when the rk rio of roplet rops, it my e ivie into severl smller ones. Given stroke imge, the lgorithm of the roplet omputing n e s follows: Input: I: Clligrphy imge soure S: Stroke pth v1,v2: two vlve humiity vlue, 1 v2>v1 0 Initiliztion: i = 0 ; // the strt point of S D = stroke_with ( i );V = stroke_tngent ( i ); lulte_roplets(d, i, V) {Drop ij }; A lulte roplets to finl roplet set Itertion: for eh lulte Drop ij, o egin if rk_rtio(rop ij ) < v1 erese rop size of Drop ij ; else if rk_rtio(rop ij )>v2 set Drop ij mergle; else split Drop ij ; en Merge mergle roplets; Inrese size of remining merle roplets; i = mrh_on(s, i ) // go to next segment of S; D = stroke_with ( i );V = stroke_tngent ( i ); roplet_just(d, V, Drop ij ); roplet hull with the prents using hull rule if(one) exit; else go to Itertion. The roplet vlve humiity vlues, v1 n v2, re etermine intertively. If v1 is lose to 0 n v2 lose to 1, then no roplet splitting or merging will our Stroke Regenertion n Exmples After the roplets long the stroke pth re retrieve, ifferent use of the roplets n get ifferent results. One pplition tht n e one on the roplets is simply to hth eh of the roplets with proper lligrphy texture oring to the ink-eposit mount of the given roplet. Unlike the tngent re ompute vi tritionl virtul rush moel, the tngent re in our moel hs ontine omplete geometry informtion, whih mkes geometry opertion on them possile. By union of the roplets retrieve, my lso generte in virtul lligrphy, we n retrieve profiles of rt hrters in lligrphy or sript style with extr outlines to inite the stroke forks or ry rush effets. Figure 7- is the retrieve roplets n is the result imge fter texturiztion of them. The figure in is the union of the roplets. After the profiles re ompute, the genertion of 3D hrter moel is strightforwr. A simple extrue lgorithm works quite well. Figure 7- is the extrue soli moel using the profile in with mrle texture, whih n e use in virtul relity.

5 Figure 8- shows two Chinese hrters (mens orient ) generte y our pinting system, shows the ompute roplets n the profile in is the union of them. Sine the lulte outlines re not smooth, we use ui uniform B-spline to pproximte eh loop of the generte stroke outlines. Figure gives the result. We n see tht the merge roplets in figure 8 express the stoke forks, most importnt spet of ry-rush effet orretly n elegntly. Figure 10. is the extrue soli moel of the lligrphy shown in, is the virtul lligrphy using the roplet rush moel 4. Referene Figure 8. The lultion of the stroke outlines As isusse in previous setions, our rush moel is prmeterize one, so y justing the funmentl rush prmeters we n get vritions of sme font. Figure 9 [1] S. Strssmnn, Hiry rush. roeeing of SIGGRAH 1986, , [2] H.T.F. Wong n H.H.S. Ip, Virtul rush: moel-se synthesis of Chinese lligrphy, Computers & Grphis, 24(1):99 113, [3] R. Shmir n A. Rppoport, Qulity enhnements of igitl outline fonts, Computers & Grphis, 21(6): , [4] H.H.S. Ip, H.T.F. Wong, Frtl oing of Chinese slle lligrphi fonts, Computers & Grphis, 18(3): , [5] Songhu Xu, Min Tng, Frnis Lu n Yunhe n, A Soli Moel Bse Virtul Hiry Brush, roeeings of Eurogrphis Figure 9. thin n ol version of shows suh n exmple. The tehnique esrie hs vrious pplitions. Beuse urves of the hrter profiles n e preisely retrieve, we n exports NC oes n signifintly enhne the ility of existing lettering mhine, whih urrently n only el with preefine set of true type hrters. This tehnique lso introues new prigm of 3D hrter moeling, n my e pplie in vrious CAD systems. Figure 10- shows nother exmple, whih is soli moel of the lligrphy in. Dry rush effet is wiely use in this piee of work n outlines lulte from tritionl soft rush nnot work well for suh kin of lligrphy, however, our metho is quite ompetent.