Hairy Brush Model Interactive Simulation in Chinese Ink Painting Style

ISBN 978-952-5726-02-2 (Print), 978-952-5726-03-9 (CD-ROM)Proceedings of the 2009 International Symposium on Information Processing (ISIP’09)Huangshan, P. R. China, August 21-23, 2009, pp. 184-188Hairy Brush Model Interactive Simulation inChinese Ink Painting StyleTianding Chen, and Changhong YuInstitute of Communications and Information Technology,Zhejiang Gongshang University, Hangzhou, China 310018E-mail: chentd@sohu.comAbstract—It describes each component element of Chineseink painting in detail. Firstly, this paper presents brushemulation based on physical calculation. Then, it proposesthe ink painting decomposition research technique, andproposes the simulation model system of the Chinese inkpainting effect. This model had considered the writingbrush model, as well as rice paper model of the water inkproliferation mode minutely. In addition, it proposed thetransfusion mechanical mode which considered thegluewater’s influence. So it had finished the ink proliferatedinteractive technology mode fusion physical and inkcharacteristic. It conformed to the Chinese ink paintingunique style, and might carry on the effect according to theparameter the control, which caused the ink painting morevivid.Index Terms—Chinese ink painting; brush model; computersimulation; ink diffusionI. INTRODUCTIONWhen we start drawing a Chinese painting, fouressential items should be well-prepared for painting. Theyare Chinese pen brush, Chinese ink stick, Rice paper andChinese ink stone. Sometimes we combine color mineralpigment with original Chinese ink to colorize the wholepainting. Rice paper is made of a special kind of tree skinand its texture has a large difference with other paper usedin western painting arts. Rice paper has good absorbencyof water and ink and because of this characteristic of Ricepaper; an artist must conceive a well-composed draft inhis mind before painting. During a painting process, anartist should carefully complete the artwork on a paperwithout any wrong strokes at on go. The Chinese penbrush is composed of a shaft and brush bristles. Bristlesusing different animal’s hair can change the usage of apen brush. An artist dips few inks on Chinese pen brush toproduce dry brush effect, or dips more inks to produce inkdiffusion effect depending on style of strokes. Ink isgenerated from Chinese ink stick and Chinese ink stoneby adding little water on an ink stone and an artist rubs inkstick on it. Concentration of ink can be controlled in theprocess of rubbing an ink stick on the ink stone and thequantity of water.The Chinese calligraphy is one of the quintessence inChinese art. Calligraphers use the Chinese 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 Province NatureScience Foundation under Grant Y107411of mind and values by writing characters. In Chinesecalligraphy, students who want to write beautifulcharacters like that written by famous calligraphers shouldimitate the copybooks first. After practicing repeatedly,they could find out the extensive knowledge and profoundscholarship of the Chinese calligraphy, and create theirown styles. The purpose of this thesis is to synthesize thespecific Chinese 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 Chinese brushstroke. Users who want to write a calligraphic characterusing those systems need to have enough basic knowledgeof calligraphy. And some special equipment (includingthe real Chinese brush stroke connected to the computers)is also need. Thus, it is not convenient for most users.Chinese artists and poets use hairy brush to writecalligraphy and draw water ink paintings. With thedevelopment of computer science, many researchers triedcomputerizing the hairy brush for convenient, practical,and realistic usage. In this paper, we present a model ofemulating the hairy brush and synthesize correspondingcalligraphy. It is highly complicate to model a real hairybrush. In Chinese painting and calligraphy, a painter orcalligrapher only uses several simple strokes to present hisemotions, feeling, and the artistic spirit. Modeling a 3-Dhairy brush in order to satisfy those moves which thepainter 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 thebending 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. Brushing commonly refers to the drawingof curves with various line widths in bit-mappedgraphical systems. In 1989, Porch and Fellner proposedthe Circle-Brush Algorithm [2]. This approach producesconstant line width by circles of suitable diameter,independent 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 in order to generate hairy brush images of sumiepaintings – one kind 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 generating hairy-brush writings. Aparameterized model is built to specify the varying brushorientation and brush tip pressure, the brush writing hairproperties and the variation of ink deposition along astroke trajectory. From this model, people can simulatethe physical process of brush stroke creation andsynthesize most of the aesthetic features of calligraphicwritings. This method is suitable for Chinese calligraphy.Then, Nelson et al. [5] presented a 3D brush model.The main feature of this model is its ability to mimicbrush flattening and bristle spreading due to brushbending and lateral friction exerted by the paper surfaceduring the painting process. Since the visual feedback issignificant in their system, some special equipment isrequired such as a real brush and haptic device.Most researches about Chinese calligraphy are devotedto image process of the calligraphic documents. Yang etal. [6] proposed a method to vectorize the digital imagesof the Chinese characters automatically. Thevectorization results can be transformed into a true-typefont for general applications. They also prevent thezigzag phenomena when enlarging the characters. In thisway, the treasures of the arts of Chinese culture can bepreserved.A different kind of application on calligraphy andimage processing 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 thinningcomputation and structuring elements, and can also knowwhether the sizes of generated calligraphy characters arethe same as the original one in theory.A combination of brush and image process waspresented by Mi et al [8]. They proposed a virtual brushmodel based on droplet operation and its application onretrieving character outlines and character modeling inChinese calligraphy style. The droplet model helps tocompute stroke area with well-defined geometryinformation and leads to the feasibility of retrieving theoutlines of characters with well-defined geometryrepresentation.There are many brush models which were designedpreviously. One of the earliest models was developed byStrassmann in which he modeled a brush as a onedimensionalarray of bristles swept over a trajectorydefined by a cubic spline curve [9]. This model couldaccount for varying color, width, and wetness. It iseffective approach but not easy to use for non-computerspecialists. Wong and Ip defined a complex set ofinterrelated parameters to vary the density, opacity andshade of a footprint of the current brush draw mark whichtake into account the behavior of a three-dimensionalround calligraphy brush [10]. This represented asubstantial improvement over Strassmann’s in term ofusability. Using the theory of elasticity, Lee [11]modeled a brush as a collection of rods withhomogeneous elasticity along the entire length. Thismodel suffers from unnatural bending because it assumeshomogeneous elasticity. Saito et al. [12] used a Bezierspine curve and a set of discs centered along the curve tomodel a brush. However, this model doesn’t consider thebrush flattening and spreading and thus fails to generate arealistic footprint. In the DAB project [13], a subdivisionsurface is wrapped around a spring -mass particle systemskeleton to represent the brush geometry. Using anapproximated implicit integration method, they were ableto produce a real-time system for doing acrylic- likepainting. To generate the subdivision surface to modelthe brush head, either interpolation or someapproximating scheme is used. An interpolated brushhead, however, often cannot deform smoothly because offrequent occurrence of high curvature in the brush headsurface, while approximation has the problem of properlyplacing control points to yield the desired surface. In thework by Xu et al. [14], general sweeping is employed toestablish the solid geometry model of each hair cluster.The problem however is that general sweeping is a timeconsumingoperation. At different stages of painting,much computation is needed to apply general sweepingoperations to update the model. Also, the solid modelrequires a fair amount of memory for its internalrepresentation, and after the brush is split many times, thedemand for memory could become a bottleneck. In thework by Chu and Tai [5], a single hair bundle is modeledby a geometry model that is mathematically equivalent tothat by Xu et al.’s. Unlike the latter which simulates thespreading and splitting of the brush tip by a geometryapproach, Chu and Tai use analpha map to implementcluster modeling for the split brush. In the recent work ofXu et al. [15], a hierarchical representation is applied ongeometry model, that leads to substantial savings in everystep of the painting process; online brush motionsimulation assisted by offline 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 dipping time aswell as during painting. However, their system needs theassistance from offline calibration, thus choosing theappropriate samples for the brush motion calibrationdatabase which enumerate all the possible motions ofpainting brush will be a problem.III. PROBLEM DESCRIPTIONA. Brush mechanical modelConstruction of a brush model includes the geometricmodel of the building and the construction of mechanicalmodels in two parts. In order to meet the needs of realtimeinteraction in the simulation at the same time to meettwo conditions: first is the computing time required cannot be too long in order to immediately respond to a user'sbehavior, in 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 in this case still must be able to maintainstable operation.Written skeleton brush can be used to simulate particle185

system. Will be written as a number of particles in themiddle of spring to connect, and each particle of that partof the representative of the quality of the mid-point.Behavior of particle systems can be used Newton's laws ofmotion to describe. Assume that n particle, particlecoordinates 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, using the following method:The linear part of the edge points so hidden (ImplicitEuler Integration);Non-linear part of the force to do the approaching postcorrection;Adding restrictions to prevent excessiveflexion and extension springs.By using this method of seeking out solutions, althoughnot the most accurate, but because it separated from thelinear 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 integration method with theexplicit integration method (Explicit Euler Integration) thedifference is: in the calculation of the speed of a unit time,the dominant points is used to calculate the force now, andthe hidden points are used the next unit time to calculatethe force.Explicit integration:= + × dt+ (2)Vt 1Vt FtMX = X + V × dt(3)t+ 1 t t+1Implicit integration:dtVt+ 1= Vt + Ft+1× (4)MX = X + V × dt(5)t+ 1 t t+1Although the dominant points is easier to implement, itslack of stability than that. Therefore the use of implicitintegration method, it is necessary to implement thisapproach, first of all to the next time do not know thelocation of the point situation, calculate the next point intime, 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) into (4), let(1)(6)dtV = V { (1 1)}t t+ Ft + H Xt X+ +−t× (7)MThen (5) into (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)Finally, 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 points dominant, so2dt −1( I − H× ) is a constant, you can count in advance,Mand save each time to count the anti-matrix.Aristotle is not due to mechanical inertia of theexistence, meaning that determines 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 systeminto a physical formula:& x = F(10)MBased on Eq. (4), (6) similar hidden derivation process∂Fof integration, 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)Finally:dt −1dtΔ Xt+1= ( I − H× ) × Ft× (12)M MThrough careful observation physical behavior of penhair, we will be found in the fact that it compared the186

characteristics of spring as bending rather than stretchingthe spring. Brush is made of animal hair, while having theflexibility, but it is still hard, and will not change with theforce and length changes, but change the shape byextrusion, there will be trends in restitution. Therefore, thespring bending simulation is used for hair brush pen.Spring bending formula:F = k× ( θ − θ )(13)0dt −1dtΔ θt+1= ( I − H× ) × Ft× (14)M MB. Brush geometry characteristic behaviorThe hairy brushes, used in Chinese painting andcalligraphy, are made from hair of animals, such as horse,deer, and rabbit. According to the kinds of hair, they aregenerally classified into three main types: hard, soft andcombination, each of which has different stiffness andabsorbent. The bristles have different length; shorter onesare inside and longer ones are outside. The brush forms asingle tuft and run into a fine tip when it is moisten. Wewill emulate the brush in moisten state, not in the dry state.A brush is elastic. It bends when some external forceapplied to it and restore to its original shape when theforce is released. Emulating this deformation in 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 in Figure 1. Our emulation includestwo parts: brush geometry and brush dynamic.position of the root spine node, p, from tablet device. Thealgorithm is as follows [5]:a) Calculate the distance between the new position andold position of the root spine node, let O 0 =p, where p isthe new position.b) Determine if there is any spine nodes penetrate thepaper. If yes, set minimization constraints of these spinenodes to be above the paper.c) Solving the energy minimization problem to get θ iand update the new position of spine nodes.Figure 2. Brush dynamic transformationThe energy function is used to demonstrate thedeformation of the brush when there is a force applied onit. Applied the minimum principle of incrementalpotential energy [17], we can predict the shape ofdeformed brush. The incremental potential energy termshere account for strain energy and friction force. At eachtime frame, the program update the brush state throughthe deformation of brush skeleton which satisfying allconstraints.Figure 1. Brush elementary geometry modelC. Brush 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 includes conservative anddissipative forces, and can be referred as incrementalpotential energy. To model the brush dynamic, we useenergy minimization method to define the deformed stateof the brush tuft at a certain time frame. With a certainapplied force, we formulate an energy minimizationfunction with Newtonian physics, then solving thisconstraints optimization problem and updating the state ofbrush.First, we will describe the algorithm for brush dynamicproblem in Figure 2. Then we will present energyminimization problem. Let O i (i = 0, 1,… , 6) is theposition of spine 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 using OpenGLbound with Visual C++ in general purpose PC platformwith an Intel dual core 2.4GHz CPU and 1GB RAM.The system architecture includes three phases: inputdata, emulation of the brush, expert system, stroke andbackground environment rendering. The system providesa convenient user interface and service for intelligentdecisions, has full knowledge base and provide.With coordinates of spine nodes at a certain time frame,we can use OpenGL to render the brush model andbackground environment. In the first module, we input thestroke trajectories which can be done with a digitizing penor a mouse to start the calligraphy system.To obtain footprint, we let a part of the brush surfaceintersect the paper plane, and calculate the orthogonalprojection of the penetration. We only need to calculatethe penetration of ellipse cross sections which intersect thepaper line. After getting all cross points, we will have thefootprint of the brush. In the second module, therelationships among all strokes are determined. Finally,when each stroke is allocated with a specific stroke type,as shown in figure 3.187

Figure 3. Simulation resultV. CONCLUSION AND FUTURE WORKSWe have presented a model for 3D hairy brushemulation. This interactive model can real time deformsthe shape of brush tuft when there is a force applied on,based on constrained energy minimization function.However, the main feature of calligraphy system is theintegration of computer graphics and knowledgeengineering. With computer graphics, the graphicalbehavior of calligraphy can be presented in the virtualworld. With knowledge engineering, the aestheticcalligraphic characters can be generated intelligently. Wecombine these two different fields in computer science toachieve better results.EFERENCES[1] Bendu Bai, Kam-Wah Wong and Yanning Zhang, “AnEfficient Physically-Based Model for Chinese Brush”, LectureNotes in 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, “Hairy brushes”, Computer Graphics, Vol.20, pp. 225-232, August 1986.[4] Horace H S Ip, Helena T F Wong, “Calligraphic charactersynthesis using a brush model”, Proceedings of ComputerGraphics International 1997, pp. 13-21.[5] Nelson S.-H. Chu, Chiew-Lan Tai, “An efficient brushmodel for physically-based 3D paingting”, Proceedings of the10 th Pacific Conference on CG&A,pp. 413-418, 2002.[6] Yang His-Ming, Lu Jainn-Jyh, Lee His-Jian, “A Beziercurve-based approach to shape description for Chinesecalligraphy characters”, International conference on documentanalysis and recognition, pp. 276-280, 2001.[7] Wei Li, Ichiro Hagiwara, Takao Yasui, Hu-awei Chen, “Amethod of generating scratched look calligraphy charactersusing mathematical morphology”, Joural of computational andapplied mathematics, pp. 85-90, 2003.[8] Mi Xiaofeng, Xu Jie, Tang Min, Dong Jinxiang, “Thedroplet virtual brush for Chinese calligraphic charactermodeling”, Proceedings of the sixth IEEE workshop onapplications of computer vision, pp. 330-334, 2002.[9] S. Strassmann, “Hairy Brushes”, SIGGRAPH 1986Proceeding, 20(4), pp. 225-232, August 1986.[10] H. T. F. Wong and H. H. S. Ip., “Virtual brush: a model -based synthesis of Chinese calligraphy”, Computer and Graphic,24(1), pp. 99-113, February 2000.[11] J. Lee, “Simulation oriental black-ink painting”, IEEEComputer Graphics and Applications, 19(3), pp. 74-81,May/June 1999.[12] S. Saito and M. Nakajima, “3D physically based brushmodel for painting”, SIGGRAPH99 Conference Abstracts andApplications, pp. 226-233, 1999.[13] B. Baxter, V. Scheib, M. Lin and D. Manocha, “DAB:Interactive haptic painting with 3D virtual brushes”,SIGGRAPH 2001 Proceedings, 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. Poulin, “A layered wispsmodel for simulating interactions inside long hair”, ComputerAnimation and Simulation 2001[17] A. Pandolfi et al., “Time-Discretized VariationalFormulation of Non-Smooth Frictional Contact”, Int’l J.Numerical Methods in Eng., vol. 53, pp. 1801-1829, 2002.188