Hairy Brush Model Interactive Simulation in Chinese Ink Painting Style
Hairy Brush Model Interactive Simulation in Chinese Ink Painting Style
Hairy Brush Model Interactive Simulation in Chinese Ink Painting Style
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ISBN 978-952-5726-02-2 (Pr<strong>in</strong>t), 978-952-5726-03-9 (CD-ROM)Proceed<strong>in</strong>gs of the 2009 International Symposium on Information Process<strong>in</strong>g (ISIP’09)Huangshan, P. R. Ch<strong>in</strong>a, August 21-23, 2009, pp. 184-188<strong>Hairy</strong> <strong>Brush</strong> <strong>Model</strong> <strong>Interactive</strong> <strong>Simulation</strong> <strong>in</strong>Ch<strong>in</strong>ese <strong>Ink</strong> Pa<strong>in</strong>t<strong>in</strong>g <strong>Style</strong>Tiand<strong>in</strong>g Chen, and Changhong YuInstitute of Communications and Information Technology,Zhejiang Gongshang University, Hangzhou, Ch<strong>in</strong>a 310018E-mail: chentd@sohu.comAbstract—It describes each component element of Ch<strong>in</strong>ese<strong>in</strong>k pa<strong>in</strong>t<strong>in</strong>g <strong>in</strong> detail. Firstly, this paper presents brushemulation based on physical calculation. Then, it proposesthe <strong>in</strong>k pa<strong>in</strong>t<strong>in</strong>g decomposition research technique, andproposes the simulation model system of the Ch<strong>in</strong>ese <strong>in</strong>kpa<strong>in</strong>t<strong>in</strong>g effect. This model had considered the writ<strong>in</strong>gbrush model, as well as rice paper model of the water <strong>in</strong>kproliferation mode m<strong>in</strong>utely. In addition, it proposed thetransfusion mechanical mode which considered thegluewater’s <strong>in</strong>fluence. So it had f<strong>in</strong>ished the <strong>in</strong>k proliferated<strong>in</strong>teractive technology mode fusion physical and <strong>in</strong>kcharacteristic. It conformed to the Ch<strong>in</strong>ese <strong>in</strong>k pa<strong>in</strong>t<strong>in</strong>gunique style, and might carry on the effect accord<strong>in</strong>g to theparameter the control, which caused the <strong>in</strong>k pa<strong>in</strong>t<strong>in</strong>g morevivid.Index Terms—Ch<strong>in</strong>ese <strong>in</strong>k pa<strong>in</strong>t<strong>in</strong>g; brush model; computersimulation; <strong>in</strong>k diffusionI. INTRODUCTIONWhen we start draw<strong>in</strong>g a Ch<strong>in</strong>ese pa<strong>in</strong>t<strong>in</strong>g, fouressential items should be well-prepared for pa<strong>in</strong>t<strong>in</strong>g. Theyare Ch<strong>in</strong>ese pen brush, Ch<strong>in</strong>ese <strong>in</strong>k stick, Rice paper andCh<strong>in</strong>ese <strong>in</strong>k stone. Sometimes we comb<strong>in</strong>e color m<strong>in</strong>eralpigment with orig<strong>in</strong>al Ch<strong>in</strong>ese <strong>in</strong>k to colorize the wholepa<strong>in</strong>t<strong>in</strong>g. Rice paper is made of a special k<strong>in</strong>d of tree sk<strong>in</strong>and its texture has a large difference with other paper used<strong>in</strong> western pa<strong>in</strong>t<strong>in</strong>g arts. Rice paper has good absorbencyof water and <strong>in</strong>k and because of this characteristic of Ricepaper; an artist must conceive a well-composed draft <strong>in</strong>his m<strong>in</strong>d before pa<strong>in</strong>t<strong>in</strong>g. Dur<strong>in</strong>g a pa<strong>in</strong>t<strong>in</strong>g process, anartist should carefully complete the artwork on a paperwithout any wrong strokes at on go. The Ch<strong>in</strong>ese penbrush is composed of a shaft and brush bristles. Bristlesus<strong>in</strong>g different animal’s hair can change the usage of apen brush. An artist dips few <strong>in</strong>ks on Ch<strong>in</strong>ese pen brush toproduce dry brush effect, or dips more <strong>in</strong>ks to produce <strong>in</strong>kdiffusion effect depend<strong>in</strong>g on style of strokes. <strong>Ink</strong> isgenerated from Ch<strong>in</strong>ese <strong>in</strong>k stick and Ch<strong>in</strong>ese <strong>in</strong>k stoneby add<strong>in</strong>g little water on an <strong>in</strong>k stone and an artist rubs <strong>in</strong>kstick on it. Concentration of <strong>in</strong>k can be controlled <strong>in</strong> theprocess of rubb<strong>in</strong>g an <strong>in</strong>k stick on the <strong>in</strong>k stone and thequantity of water.The Ch<strong>in</strong>ese calligraphy is one of the qu<strong>in</strong>tessence <strong>in</strong>Ch<strong>in</strong>ese art. Calligraphers use the Ch<strong>in</strong>ese brush stroke towrite glamorous characters. As the brush moves, we cansee the affections of the calligrapher/artist and his uniqueartistry. In other words, calligraphers express their attitudeThis research work is supported by Zhejiang Prov<strong>in</strong>ce NatureScience Foundation under Grant Y107411of m<strong>in</strong>d and values by writ<strong>in</strong>g characters. In Ch<strong>in</strong>esecalligraphy, students who want to write beautifulcharacters like that written by famous calligraphers shouldimitate the copybooks first. After practic<strong>in</strong>g repeatedly,they could f<strong>in</strong>d out the extensive knowledge and profoundscholarship of the Ch<strong>in</strong>ese calligraphy, and create theirown styles. The purpose of this thesis is to synthesize thespecific Ch<strong>in</strong>ese calligraphic style of one of the famouscalligraphers mentioned before. Our system also providesa convenient environment for users to imitate copybooksof calligraphy by computer techniques.There are lots of researches that aimed to generaterealistic calligraphic character images. Most of themfocused on the physical properties of the Ch<strong>in</strong>ese brushstroke. Users who want to write a calligraphic characterus<strong>in</strong>g those systems need to have enough basic knowledgeof calligraphy. And some special equipment (<strong>in</strong>clud<strong>in</strong>gthe real Ch<strong>in</strong>ese brush stroke connected to the computers)is also need. Thus, it is not convenient for most users.Ch<strong>in</strong>ese artists and poets use hairy brush to writecalligraphy and draw water <strong>in</strong>k pa<strong>in</strong>t<strong>in</strong>gs. With thedevelopment of computer science, many researchers triedcomputeriz<strong>in</strong>g the hairy brush for convenient, practical,and realistic usage. In this paper, we present a model ofemulat<strong>in</strong>g the hairy brush and synthesize correspond<strong>in</strong>gcalligraphy. It is highly complicate to model a real hairybrush. In Ch<strong>in</strong>ese pa<strong>in</strong>t<strong>in</strong>g and calligraphy, a pa<strong>in</strong>ter orcalligrapher only uses several simple strokes to present hisemotions, feel<strong>in</strong>g, and the artistic spirit. <strong>Model</strong><strong>in</strong>g a 3-Dhairy brush <strong>in</strong> order to satisfy those moves which thepa<strong>in</strong>ter want is very difficult. We only try to model abrush with physical properties like a real brush as much aswe can, based on knowledge from the paper of anefficient brush model construction [1], particularly thebend<strong>in</strong>g property of the brush when we apply a force onthe brush.II. RELATED WORKSThere are a lot of researches that aim to the topic ofbrush model. <strong>Brush</strong><strong>in</strong>g commonly refers to the draw<strong>in</strong>gof curves with various l<strong>in</strong>e widths <strong>in</strong> bit-mappedgraphical systems. In 1989, Porch and Fellner proposedthe Circle-<strong>Brush</strong> Algorithm [2]. This approach producesconstant l<strong>in</strong>e width by circles of suitable diameter,<strong>in</strong>dependent of the curve’s slope. At the same time,Strassmann’s hairy brushes model [3] was presented. Itprovided a description of physical properties of brushmaterials <strong>in</strong> order to generate hairy brush images of sumiepa<strong>in</strong>t<strong>in</strong>gs – one k<strong>in</strong>d of traditional Japanese art. And the© 2009 ACADEMY PUBLISHERAP-PROC-CS-09CN002184
concept of a collection of bristles was proposed for thefirst time.After that, Horace and Helena [4] proposed the firstmethodology for generat<strong>in</strong>g hairy-brush writ<strong>in</strong>gs. Aparameterized model is built to specify the vary<strong>in</strong>g brushorientation and brush tip pressure, the brush writ<strong>in</strong>g hairproperties and the variation of <strong>in</strong>k deposition along astroke trajectory. From this model, people can simulatethe physical process of brush stroke creation andsynthesize most of the aesthetic features of calligraphicwrit<strong>in</strong>gs. This method is suitable for Ch<strong>in</strong>ese calligraphy.Then, Nelson et al. [5] presented a 3D brush model.The ma<strong>in</strong> feature of this model is its ability to mimicbrush flatten<strong>in</strong>g and bristle spread<strong>in</strong>g due to brushbend<strong>in</strong>g and lateral friction exerted by the paper surfacedur<strong>in</strong>g the pa<strong>in</strong>t<strong>in</strong>g process. S<strong>in</strong>ce the visual feedback issignificant <strong>in</strong> their system, some special equipment isrequired such as a real brush and haptic device.Most researches about Ch<strong>in</strong>ese calligraphy are devotedto image process of the calligraphic documents. Yang etal. [6] proposed a method to vectorize the digital imagesof the Ch<strong>in</strong>ese characters automatically. Thevectorization results can be transformed <strong>in</strong>to a true-typefont for general applications. They also prevent thezigzag phenomena when enlarg<strong>in</strong>g the characters. In thisway, the treasures of the arts of Ch<strong>in</strong>ese culture can bepreserved.A different k<strong>in</strong>d of application on calligraphy andimage process<strong>in</strong>g was suggested by Wei et al [7]. Theyproposed a method to generate scratched look calligraphycharacters by mathematical morphology. By this method,people can decide on number of times of the th<strong>in</strong>n<strong>in</strong>gcomputation and structur<strong>in</strong>g elements, and can also knowwhether the sizes of generated calligraphy characters arethe same as the orig<strong>in</strong>al one <strong>in</strong> theory.A comb<strong>in</strong>ation of brush and image process waspresented by Mi et al [8]. They proposed a virtual brushmodel based on droplet operation and its application onretriev<strong>in</strong>g character outl<strong>in</strong>es and character model<strong>in</strong>g <strong>in</strong>Ch<strong>in</strong>ese calligraphy style. The droplet model helps tocompute stroke area with well-def<strong>in</strong>ed geometry<strong>in</strong>formation and leads to the feasibility of retriev<strong>in</strong>g theoutl<strong>in</strong>es of characters with well-def<strong>in</strong>ed geometryrepresentation.There are many brush models which were designedpreviously. One of the earliest models was developed byStrassmann <strong>in</strong> which he modeled a brush as a onedimensionalarray of bristles swept over a trajectorydef<strong>in</strong>ed by a cubic spl<strong>in</strong>e curve [9]. This model couldaccount for vary<strong>in</strong>g color, width, and wetness. It iseffective approach but not easy to use for non-computerspecialists. Wong and Ip def<strong>in</strong>ed a complex set of<strong>in</strong>terrelated parameters to vary the density, opacity andshade of a footpr<strong>in</strong>t of the current brush draw mark whichtake <strong>in</strong>to account the behavior of a three-dimensionalround calligraphy brush [10]. This represented asubstantial improvement over Strassmann’s <strong>in</strong> term ofusability. Us<strong>in</strong>g the theory of elasticity, Lee [11]modeled a brush as a collection of rods withhomogeneous elasticity along the entire length. Thismodel suffers from unnatural bend<strong>in</strong>g because it assumeshomogeneous elasticity. Saito et al. [12] used a Beziersp<strong>in</strong>e curve and a set of discs centered along the curve tomodel a brush. However, this model doesn’t consider thebrush flatten<strong>in</strong>g and spread<strong>in</strong>g and thus fails to generate arealistic footpr<strong>in</strong>t. In the DAB project [13], a subdivisionsurface is wrapped around a spr<strong>in</strong>g -mass particle systemskeleton to represent the brush geometry. Us<strong>in</strong>g anapproximated implicit <strong>in</strong>tegration method, they were ableto produce a real-time system for do<strong>in</strong>g acrylic- likepa<strong>in</strong>t<strong>in</strong>g. To generate the subdivision surface to modelthe brush head, either <strong>in</strong>terpolation or someapproximat<strong>in</strong>g scheme is used. An <strong>in</strong>terpolated brushhead, however, often cannot deform smoothly because offrequent occurrence of high curvature <strong>in</strong> the brush headsurface, while approximation has the problem of properlyplac<strong>in</strong>g control po<strong>in</strong>ts to yield the desired surface. In thework by Xu et al. [14], general sweep<strong>in</strong>g is employed toestablish the solid geometry model of each hair cluster.The problem however is that general sweep<strong>in</strong>g is a timeconsum<strong>in</strong>goperation. At different stages of pa<strong>in</strong>t<strong>in</strong>g,much computation is needed to apply general sweep<strong>in</strong>goperations to update the model. Also, the solid modelrequires a fair amount of memory for its <strong>in</strong>ternalrepresentation, and after the brush is split many times, thedemand for memory could become a bottleneck. In thework by Chu and Tai [5], a s<strong>in</strong>gle hair bundle is modeledby a geometry model that is mathematically equivalent tothat by Xu et al.’s. Unlike the latter which simulates thespread<strong>in</strong>g and splitt<strong>in</strong>g of the brush tip by a geometryapproach, Chu and Tai use analpha map to implementcluster model<strong>in</strong>g for the split brush. In the recent work ofXu et al. [15], a hierarchical representation is applied ongeometry model, that leads to substantial sav<strong>in</strong>gs <strong>in</strong> everystep of the pa<strong>in</strong>t<strong>in</strong>g process; onl<strong>in</strong>e brush motionsimulation assisted by offl<strong>in</strong>e calibration that guaranteesan accurate and stable simulation of the brush’s dynamicbehavior. They create a new pigment model based on adiffusion process of random molecules which considerdelicate and complex pigment behavior at dipp<strong>in</strong>g time aswell as dur<strong>in</strong>g pa<strong>in</strong>t<strong>in</strong>g. However, their system needs theassistance from offl<strong>in</strong>e calibration, thus choos<strong>in</strong>g theappropriate samples for the brush motion calibrationdatabase which enumerate all the possible motions ofpa<strong>in</strong>t<strong>in</strong>g brush will be a problem.III. PROBLEM DESCRIPTIONA. <strong>Brush</strong> mechanical modelConstruction of a brush model <strong>in</strong>cludes the geometricmodel of the build<strong>in</strong>g and the construction of mechanicalmodels <strong>in</strong> two parts. In order to meet the needs of realtime<strong>in</strong>teraction <strong>in</strong> the simulation at the same time to meettwo conditions: first is the comput<strong>in</strong>g time required cannot be too long <strong>in</strong> order to immediately respond to a user'sbehavior, <strong>in</strong> order to meet the real-time, this paper usesthe hardware-accelerated system; second one is better thanstability, the user may make a variety of actions, andbrush the model <strong>in</strong> this case still must be able to ma<strong>in</strong>ta<strong>in</strong>stable operation.Written skeleton brush can be used to simulate particle185
system. Will be written as a number of particles <strong>in</strong> themiddle of spr<strong>in</strong>g to connect, and each particle of that partof the representative of the quality of the mid-po<strong>in</strong>t.Behavior of particle systems can be used Newton's laws ofmotion to describe. Assume that n particle, particlecoord<strong>in</strong>ates x, the velocity of particle v, forces on particlesfor F (x, v, F are 3D vector), it is assumed that the weightof each particle equal to M. Can be expressed as two-orderdifferential equations:⎛&x⎞ ⎛v⎞⎜ ⎟=⎜ ⎟⎝&v⎠ ⎝F M ⎠In order to approximate the solution of the differentialequations, us<strong>in</strong>g the follow<strong>in</strong>g method:The l<strong>in</strong>ear part of the edge po<strong>in</strong>ts so hidden (ImplicitEuler Integration);Non-l<strong>in</strong>ear part of the force to do the approach<strong>in</strong>g postcorrection;Add<strong>in</strong>g restrictions to prevent excessiveflexion and extension spr<strong>in</strong>gs.By us<strong>in</strong>g this method of seek<strong>in</strong>g out solutions, althoughnot the most accurate, but because it separated from thel<strong>in</strong>ear part of the direct count, followed by furtheramendments to the rear of the action, so the stability of thefaster and higher, just to meet the real-time requirements.The so-called implicit <strong>in</strong>tegration method with theexplicit <strong>in</strong>tegration method (Explicit Euler Integration) thedifference is: <strong>in</strong> the calculation of the speed of a unit time,the dom<strong>in</strong>ant po<strong>in</strong>ts is used to calculate the force now, andthe hidden po<strong>in</strong>ts are used the next unit time to calculatethe force.Explicit <strong>in</strong>tegration:= + × dt+ (2)Vt 1Vt FtMX = X + V × dt(3)t+ 1 t t+1Implicit <strong>in</strong>tegration:dtVt+ 1= Vt + Ft+1× (4)MX = X + V × dt(5)t+ 1 t t+1Although the dom<strong>in</strong>ant po<strong>in</strong>ts is easier to implement, itslack of stability than that. Therefore the use of implicit<strong>in</strong>tegration method, it is necessary to implement thisapproach, first of all to the next time do not know thelocation of the po<strong>in</strong>t situation, calculate the next po<strong>in</strong>t <strong>in</strong>time, and the use of Taylor's estimate of the value of astart:∂FF = F (1 1)t t+ × Xt X+ +−t∂X∂FH = , ∂ XWill be (6) <strong>in</strong>to (4), let(1)(6)dtV = V { (1 1)}t t+ Ft + H Xt X+ +−t× (7)MThen (5) <strong>in</strong>to (7), acquirability:dtVt+ 1= Vt + ( Ft + H× Vt+1× dt)×M2dtdt⇒ Vt+1× ( I − H× ) = Vt + Ft×MM2 2dt −1 dt −1dt⇒ Vt+1= ( I − H× ) × Vt + ( I − H× ) × Ft×M M M2dt −1dt⇒Δ Vt+ 1= Vt+1− Vt = ( I − H× ) × ( Ft + H× Vt× dt)×MM(8)F<strong>in</strong>ally, the mechanical equation becomes:⎛( Δ Vt+1+Δ Vt)× dt⎞⎛ΔXt+1 ⎞ ⎜ 2⎟⎜ ⎟=dt −1dt⎝ΔVt + 1 ⎠ ⎜( I − H× ) × ( Ft + H× Vt× dt)×⎟⎝ MM ⎠(9)Because only part of the hidden po<strong>in</strong>ts dom<strong>in</strong>ant, so2dt −1( I − H× ) is a constant, you can count <strong>in</strong> advance,Mand save each time to count the anti-matrix.Aristotle is not due to mechanical <strong>in</strong>ertia of theexistence, mean<strong>in</strong>g that determ<strong>in</strong>es the strength of theobjects movement, once the forces disappear, objects willstop. Experiments show that Aristotle than Newton'smechanics better adapted to simulate the mechanicalbehavior of brush written, but also high speed and stabilityadvantages. In Aristotelian mechanics, the particle system<strong>in</strong>to a physical formula:& x = F(10)MBased on Eq. (4), (6) similar hidden derivation process∂Fof <strong>in</strong>tegration, let H = , ∂ XdtXt+ 1= Xt + ( Ft + H× Vt+1× dt)×Mdt dt dt⇒ Xt+1× ( I− H× ) = Xt + Ft× − H× Xt×M M Mdt −1 dt −1 dt dt −1dt⇒ Xt+1= ( I− H× ) × Xt + ( I− H× ) × Ft× −( I− H× ) × Xt×M M M M Mdt −1 dt dt −1dt⇒ Xt+1= ( I− H× ) × ( I− H× ) × Xt + ( I− H× ) × Ft×M M M Mdt −1dt⇒Δ Xt+ 1= Xt+1− Xt = ( I− H× ) × Ft×M M(11)F<strong>in</strong>ally:dt −1dtΔ Xt+1= ( I − H× ) × Ft× (12)M MThrough careful observation physical behavior of penhair, we will be found <strong>in</strong> the fact that it compared the186
characteristics of spr<strong>in</strong>g as bend<strong>in</strong>g rather than stretch<strong>in</strong>gthe spr<strong>in</strong>g. <strong>Brush</strong> is made of animal hair, while hav<strong>in</strong>g theflexibility, but it is still hard, and will not change with theforce and length changes, but change the shape byextrusion, there will be trends <strong>in</strong> restitution. Therefore, thespr<strong>in</strong>g bend<strong>in</strong>g simulation is used for hair brush pen.Spr<strong>in</strong>g bend<strong>in</strong>g formula:F = k× ( θ − θ )(13)0dt −1dtΔ θt+1= ( I − H× ) × Ft× (14)M MB. <strong>Brush</strong> geometry characteristic behaviorThe hairy brushes, used <strong>in</strong> Ch<strong>in</strong>ese pa<strong>in</strong>t<strong>in</strong>g andcalligraphy, are made from hair of animals, such as horse,deer, and rabbit. Accord<strong>in</strong>g to the k<strong>in</strong>ds of hair, they aregenerally classified <strong>in</strong>to three ma<strong>in</strong> types: hard, soft andcomb<strong>in</strong>ation, each of which has different stiffness andabsorbent. The bristles have different length; shorter onesare <strong>in</strong>side and longer ones are outside. The brush forms as<strong>in</strong>gle tuft and run <strong>in</strong>to a f<strong>in</strong>e tip when it is moisten. Wewill emulate the brush <strong>in</strong> moisten state, not <strong>in</strong> the dry state.A brush is elastic. It bends when some external forceapplied to it and restore to its orig<strong>in</strong>al shape when theforce is released. Emulat<strong>in</strong>g this deformation <strong>in</strong> real timeis a tough problem. To make problem simpler, we modelthe brush with a simple skeleton and compute thedeformation of this skeleton and apply it to the wholebrush [16], as shown <strong>in</strong> Figure 1. Our emulation <strong>in</strong>cludestwo parts: brush geometry and brush dynamic.position of the root sp<strong>in</strong>e node, p, from tablet device. Thealgorithm is as follows [5]:a) Calculate the distance between the new position andold position of the root sp<strong>in</strong>e node, let O 0 =p, where p isthe new position.b) Determ<strong>in</strong>e if there is any sp<strong>in</strong>e nodes penetrate thepaper. If yes, set m<strong>in</strong>imization constra<strong>in</strong>ts of these sp<strong>in</strong>enodes to be above the paper.c) Solv<strong>in</strong>g the energy m<strong>in</strong>imization problem to get θ iand update the new position of sp<strong>in</strong>e nodes.Figure 2. <strong>Brush</strong> dynamic transformationThe energy function is used to demonstrate thedeformation of the brush when there is a force applied onit. Applied the m<strong>in</strong>imum pr<strong>in</strong>ciple of <strong>in</strong>crementalpotential energy [17], we can predict the shape ofdeformed brush. The <strong>in</strong>cremental potential energy termshere account for stra<strong>in</strong> energy and friction force. At eachtime frame, the program update the brush state throughthe deformation of brush skeleton which satisfy<strong>in</strong>g allconstra<strong>in</strong>ts.Figure 1. <strong>Brush</strong> elementary geometry modelC. <strong>Brush</strong> dynamicOur brush model has to be bended when it touch thepaper with a given applied force and return to normal statewhen the force release. This <strong>in</strong>cludes conservative anddissipative forces, and can be referred as <strong>in</strong>crementalpotential energy. To model the brush dynamic, we useenergy m<strong>in</strong>imization method to def<strong>in</strong>e the deformed stateof the brush tuft at a certa<strong>in</strong> time frame. With a certa<strong>in</strong>applied force, we formulate an energy m<strong>in</strong>imizationfunction with Newtonian physics, then solv<strong>in</strong>g thisconstra<strong>in</strong>ts optimization problem and updat<strong>in</strong>g the state ofbrush.First, we will describe the algorithm for brush dynamicproblem <strong>in</strong> Figure 2. Then we will present energym<strong>in</strong>imization problem. Let O i (i = 0, 1,… , 6) is theposition of sp<strong>in</strong>e nodes, θ i is the angle between the i-thsegment and the previous segment. We can get the newIV. IMPLEMENTATION AND EVALUATIONWe have rendered the brush model us<strong>in</strong>g OpenGLbound with Visual C++ <strong>in</strong> general purpose PC platformwith an Intel dual core 2.4GHz CPU and 1GB RAM.The system architecture <strong>in</strong>cludes three phases: <strong>in</strong>putdata, emulation of the brush, expert system, stroke andbackground environment render<strong>in</strong>g. The system providesa convenient user <strong>in</strong>terface and service for <strong>in</strong>telligentdecisions, has full knowledge base and provide.With coord<strong>in</strong>ates of sp<strong>in</strong>e nodes at a certa<strong>in</strong> time frame,we can use OpenGL to render the brush model andbackground environment. In the first module, we <strong>in</strong>put thestroke trajectories which can be done with a digitiz<strong>in</strong>g penor a mouse to start the calligraphy system.To obta<strong>in</strong> footpr<strong>in</strong>t, we let a part of the brush surface<strong>in</strong>tersect the paper plane, and calculate the orthogonalprojection of the penetration. We only need to calculatethe penetration of ellipse cross sections which <strong>in</strong>tersect thepaper l<strong>in</strong>e. After gett<strong>in</strong>g all cross po<strong>in</strong>ts, we will have thefootpr<strong>in</strong>t of the brush. In the second module, therelationships among all strokes are determ<strong>in</strong>ed. F<strong>in</strong>ally,when each stroke is allocated with a specific stroke type,as shown <strong>in</strong> figure 3.187
Figure 3. <strong>Simulation</strong> resultV. CONCLUSION AND FUTURE WORKSWe have presented a model for 3D hairy brushemulation. This <strong>in</strong>teractive model can real time deformsthe shape of brush tuft when there is a force applied on,based on constra<strong>in</strong>ed energy m<strong>in</strong>imization function.However, the ma<strong>in</strong> feature of calligraphy system is the<strong>in</strong>tegration of computer graphics and knowledgeeng<strong>in</strong>eer<strong>in</strong>g. With computer graphics, the graphicalbehavior of calligraphy can be presented <strong>in</strong> the virtualworld. With knowledge eng<strong>in</strong>eer<strong>in</strong>g, the aestheticcalligraphic characters can be generated <strong>in</strong>telligently. Wecomb<strong>in</strong>e these two different fields <strong>in</strong> computer science toachieve better results.EFERENCES[1] Bendu Bai, Kam-Wah Wong and Yann<strong>in</strong>g Zhang, “AnEfficient Physically-Based <strong>Model</strong> for Ch<strong>in</strong>ese <strong>Brush</strong>”, LectureNotes <strong>in</strong> Computer Science 4613, 2007, pp. 261-270.[2] Porch KC, Fellner WD, “The circle-brush algorithm.”,ACM Transactions on Graphics, Vol. 8, No. 1, pp. 1-24,January 1989.[3] Strassmann S, “<strong>Hairy</strong> brushes”, Computer Graphics, Vol.20, pp. 225-232, August 1986.[4] Horace H S Ip, Helena T F Wong, “Calligraphic charactersynthesis us<strong>in</strong>g a brush model”, Proceed<strong>in</strong>gs of ComputerGraphics International 1997, pp. 13-21.[5] Nelson S.-H. Chu, Chiew-Lan Tai, “An efficient brushmodel for physically-based 3D pa<strong>in</strong>gt<strong>in</strong>g”, Proceed<strong>in</strong>gs of the10 th Pacific Conference on CG&A,pp. 413-418, 2002.[6] Yang His-M<strong>in</strong>g, Lu Ja<strong>in</strong>n-Jyh, Lee His-Jian, “A Beziercurve-based approach to shape description for Ch<strong>in</strong>esecalligraphy characters”, International conference on documentanalysis and recognition, pp. 276-280, 2001.[7] Wei Li, Ichiro Hagiwara, Takao Yasui, Hu-awei Chen, “Amethod of generat<strong>in</strong>g scratched look calligraphy charactersus<strong>in</strong>g mathematical morphology”, Joural of computational andapplied mathematics, pp. 85-90, 2003.[8] Mi Xiaofeng, Xu Jie, Tang M<strong>in</strong>, Dong J<strong>in</strong>xiang, “Thedroplet virtual brush for Ch<strong>in</strong>ese calligraphic charactermodel<strong>in</strong>g”, Proceed<strong>in</strong>gs of the sixth IEEE workshop onapplications of computer vision, pp. 330-334, 2002.[9] S. Strassmann, “<strong>Hairy</strong> <strong>Brush</strong>es”, SIGGRAPH 1986Proceed<strong>in</strong>g, 20(4), pp. 225-232, August 1986.[10] H. T. F. Wong and H. H. S. Ip., “Virtual brush: a model -based synthesis of Ch<strong>in</strong>ese calligraphy”, Computer and Graphic,24(1), pp. 99-113, February 2000.[11] J. Lee, “<strong>Simulation</strong> oriental black-<strong>in</strong>k pa<strong>in</strong>t<strong>in</strong>g”, IEEEComputer Graphics and Applications, 19(3), pp. 74-81,May/June 1999.[12] S. Saito and M. Nakajima, “3D physically based brushmodel for pa<strong>in</strong>t<strong>in</strong>g”, SIGGRAPH99 Conference Abstracts andApplications, pp. 226-233, 1999.[13] B. Baxter, V. Scheib, M. L<strong>in</strong> and D. Manocha, “DAB:<strong>Interactive</strong> haptic pa<strong>in</strong>t<strong>in</strong>g with 3D virtual brushes”,SIGGRAPH 2001 Proceed<strong>in</strong>gs, August 2001.[14] S. Xu, M. Tang, F. C. M. Lau and Y. Pan, “A solid modelbased virtual hairy brush”, Computer Graphics Forum (Proc. ofEurographics 2002), 21(3), pp. 299-308, 2002.[15] S. Xu, M. Tang, F. C. M. Lau and Y. Pan, “Advanceddesign for a realistic virtual brush”, Proc. of Eurographics 2003,22(3), 2003.[16] E. Plante, M.-P. Cani and P. Poul<strong>in</strong>, “A layered wispsmodel for simulat<strong>in</strong>g <strong>in</strong>teractions <strong>in</strong>side long hair”, ComputerAnimation and <strong>Simulation</strong> 2001[17] A. Pandolfi et al., “Time-Discretized VariationalFormulation of Non-Smooth Frictional Contact”, Int’l J.Numerical Methods <strong>in</strong> Eng., vol. 53, pp. 1801-1829, 2002.188