Hairy Brush Model Interactive Simulation in Chinese Ink Painting Style

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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
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