A Virtual Chinese Hairy Brush Model for E-Learning

Transcription

1 A Virtual Chinese Hairy Brush Model for E-Learning Bendu Bai 1,2, Kam-Wah Wong 2, and Yanning Zhang 1 1 Northwestern Polytech University, School of Computer Science, Xi an , China 2 City University of Hong Kong, School of Creative Media, Kowloon, Hong Kong China {baibendu, smkam}@cityu.edu.hk, ynzhang@nwpu.edu.cn Abstract. The increasing demands of education, reduction of study cost and study without location limitation have encouraged developers providing different types of learning and educational systems. This paper presents a virtual Chinese hairy brush painting environment which can be used as a digital tool for learning or creating Chinese calligraphy or Chinese painting. The framework comprises two components: brush geometry model and brush dynamic model. Instead of simulating the brush using bristles, we use points to simulate the whole brush bundle, which can drastically decrease the complexity inherent in the conventional bristle-level approach; our brush dynamic model describes the behavior of the real brush s deformation in terms of the interaction of the external and internal forces with the virtual writing paper. A spring network is derived to calculate the physical deflection of brush according to the force exerted on it. A prototype system has been implemented based on this framework, with which high-quality digital painting and calligraphy artwork can be produced. 1 Introduction Web-based teaching and learning has been explored and studied by many researchers. This paper presents a virtual Chinese hairy brush painting environment which can be used as a digital tool for learning or creating Chinese calligraphy or Chinese painting. The Chinese have been painting with hair brushes and ink on paper over two thousands years. Chinese calligraphy was thought to be the highest and purest form of Chinese painting. Traditional Chinese hair brushes are made from animal hairs and the ink are made from pine soot and animal glue. With the development of modern computers, to design and develop a digital painting environment that simulates Chinese brush has attracted a lot of researchers. Moreover, the increasing demands of education, reduction of study cost and study without location limitation have encouraged developers providing different types of learning and educational systems. However, most of the related researches focus on the visual quality of the output rather than the running efficiency of the system. For a web-based learning H. Leung et al. (Eds.): ICWL 2007, LNCS 4823, pp , c Springer-Verlag Berlin Heidelberg 2008

2 A Virtual Chinese Hairy Brush Model for E-Learning 321 system, the efficiency is relatively important. In this paper we presents a model that is simple and efficient enough for web-based learning purpose. 1.1 Related Work Recently, several physically-based 3D brush models have been proposed and we will review only those are directly related to our work. The first purely physically based 3D brush model was proposed by Saito [6]. Saito used energy optimization to determine the brush deformation. His model accounted for brush stiffness, friction and kinetic energy. However, the model can not simulate brush spreading. Wong et al. [7] modeled a calligraphy brush as an inverted cone, with some ellipses to synthesize Chinese calligraphic writings. Since their model pay no attention to the brush tip while drawing stroke, it fails to produce the biased-tip strokes. Baxter et al. [1] modeled the western brush as spring-mass systems, but the model was still lacking of the effect of brush spreading or splitting. Xu et al. [8][9] presented a more complex geometry which can split into smaller tufts, but the bulk of the brush must penetrate the paper in the drawing process which leads to unrealistic brush footprints. Chu and Tai [2][3][4] delivered a very convincing model for Chinese calligraphy that included factors such as plasticity, tip spreading, and pore resistance. Like Saito, Chu and Tai also used energy optimization for the brush dynamics, but their approach had to solve a static constrained minimization problem by using local sequential quadratic programming(sqp). Although the method of SQP can avoid solving stiff differential equations, it is still complex in computation due to the iterations of SQP. 2 The Brush Model Our aim is to provide a simple but efficient brush model for interactively creating oriental artworks with computer. Since a typical real brush may consist of thousands or even tens of thousands of individual bristles, physically simulating each and every bristle is not practical based on present hardware capability. Inspired by the fact that artists use real brush with elastic bristles to draw strokes, and based on the physical characteristics of the motion of brush, we convert simulating the complex physical deformation of bristles to simulating the footprint variation of brush, since the final effect is determined by the latter. For this purpose, we simplify the geometric representation of brush to be a collection of points instead of hair threads and use it as the basic unit to construct a 3D brush bundle. 2.1 Brush Basic Unit In a real brush, the hairs distribute non-uniformly alone the radius. The density of hairs in the center area is much thicker than that near the boundary. Crowded hairs are obviously found in the center, and loser around the brush boundary.

3 322 B. Bai, K.-W. Wong, and Y. Zhang According to this role, we design the brush basic unit (BU) as shown in Fig.1. Then, a 3D virtual brush in static state can be built using a series of BU (see Fig. 1. The brush basic unit Fig.1) with the different sizes, starting from brush tip to the brush root (see Fig.2). Obviously, the smallest BU may only have one dot. However, for hair brush, a small brush tip including only one dot does not have a practical meaning. Our experiments show that the tip of the brush including four dots is a minimum. Fig. 2. The single brush bundle 2.2 Brush Dynamics Brush dynamic model describes the deformation of the brush bundle at every instance of brush movement. In real-life Chinese calligraphy, a typical stroke usually includes three stages: Qibi (press), Yunbi (move) and Tibi (lift). During different stage the brush dynamic model should have different footprint when the brush is pressed onto or lifted from the paper.

4 A Virtual Chinese Hairy Brush Model for E-Learning 323 A C B Fig. 3. A stroke generated by our model. The moving direction of the brush during a single stroke. Qibi. Fig3. shows a horizontal stroke. As the artist writes the stroke, firstly he presses the brush vertically against the paper until the brush tip reaches the writing paper (see arrow A of Fig3.). Starting from the moment when the brush touched the paper, with the brush continually moving downward(i.e., brush only moves along z-axis), to the moment when the brush is beginning to move on the paper surface (i.e. brush moves along x-axis or y-axis), is the stage of Qibi. During this stage, the brush is dipped with ink. The attractive force between ink and hair molecules holds the hair together. Moreover, in real-life calligraphy writing, usually only the tip of the brush is used to paint in the Qibi stage. Although the force that the brush suffers in the stage is rather complex, such as the external pressure and the internal friction between wet bristles, the footprint in a real-life writing process looks like a circular disk according to our observations. Therefore, our brush model in Qibi stage is designed as a series of concentric circular disks, which are laid to lap over each other onto the cross-sectional plane (as shown in Fig.4. A). This simple representation is computationally efficient and quite similar to the observed reality. A B Fig. 4. The dynamic deformation of our brush during the different stage of a single stroke Yunbi. The stage of Yunbi starts from which the artist drugs the brush along the path of the stroke (see arrow B of Fig3.). At the very beginning of the stage, the artist will continually press the brush against the paper surface, as far as the stroke width reaches certain value which the painter wants the stroke to be.

5 324 B. Bai, K.-W. Wong, and Y. Zhang During this stage, the brush suffers from the pressure and friction with the paper, so that the brush will alter its shape from the invert cone to a bent invert cone (see Fig.4 red line). Moreover, the pressure and the friction also make the circles change as ellipses (see Fig.5. B). Here, we simulate the bent brush through moving the circles with a horizontal displacement along x-axis of the paper plane(see Fig.4 B). In order to maintain the smoothness of the stroke boundaries, the displacement between two adjacent circle should meet the constrain as follows r i r i 1 d i 2(r i r i 1 ) (1) where d i represent the displacement between the ith circle and the (i 1)th circle, r i represents the radii of the ith circle, and r i 1 is the radii of the adjacent of the ith circle nearer to the brush tip. A B C D Fig. 5. The dynamic deformation of our brush. A is the platform of our model. B illustrates brush anamorphosis from circle to ellipse. C illustrates the deformation during the stage of Yunbi. D illustrates the brush deformation of split. The major axis and minor axis of the ith ellipses can be computed by follow equations majoraxis(u i )=r i k u, minoraxis(v i )=r i k v (2) where k u are the deformation constant of major axis, and k v is the deformation constant of minor axis. Typically, k u and k v are from 1.0 to 1.5 and from 1.0 to 0.5, respectively. Tibi. The stage of Tibi describes the process that the brush was lifted from the writing paper, which can be found at the end of the stroke (see arrow C of Fig.3.). During this stage, a moist brush is deformed. In order to return the

6 A Virtual Chinese Hairy Brush Model for E-Learning 325 bent brush to its original shape, the flexible force has to overcome the resistance of molecular friction. Due to the effect of this internal frication, the bent brush does not entirety revert to its original shape. We formulate the energy function based on the principle of conservation of energy when the brush was pressed or lifted as follows: E press = E bend + E fric (3) E lift = E bend E fric (4) E press = E lift (5) where E bend is the brush bent energy, and E fric is the internal energy of molecular friction when the brush was pressed or lifted. Then, we deal with the problems by using a spring network to approximate the behavior of the deformations. We use bend springs at each joint point between cone major axis and circles to model the bending deformation of the brush. The relationship between the amount of bent displacement and the spring force can be closely approximated by using Hooke s law [5]: F s = F x = kx (6) where F s is the equal and opposite restoring force of the spring on the stretch node, k is the spring constant, and x is the displacement of a node position under the influence of a force F x. Taking the definition of the Hooke s law (Equation 6) into Equation 3 and 4, we thus have our energy functions as: E press = E bend + E fric = k b d i k f d i (7) E lift = E bend E fric = k b d j + k f d j (8) where k b and k f are the bent spring constant and the internal friction constant, d i (d j ) is the displacement of spring node between the ith (jth) circle and the (i 1)th ((j 1)th) circle. The value of d i, d j should satisfy the constraint of formula (1). 2.3 Splitting Brush The effect of splitting brush results from the brush deformation, the decrease of the volume of the ink, and rapid moving of the brush. With a single brush bundle, it is impossible to achieve the effect of brush splitting. To deal with the problem, Xu [8] proposed a two-level hierarchical brush geometry model. The main advantage of Xu s model lies in modeling the complex geometry of a realistic split brush as several similar cluster using the comparability of the hair macros. We cope with the problem by using a similar approach, with some necessary modifications due to a different primitive model adopted in our framework. According to our brush basic unit (BU), we use a simple algorithm to achieve the splitting effect. Since the amount of ink plays an important role in the process of brush splitting, we firstly set an initial ink value for entire brush bundle(the ink model will be discussed in next section). For every instant t, we

7 326 B. Bai, K.-W. Wong, and Y. Zhang check the decrease of the amount of ink and the deformation of the brush tip. When the ellipse of the brush tip reaches its limit(k u =1.5) and the amount of ink reduce to a threshold, a new primitive brush generates. Then, we use the affine transformations composing the parent brush bundle and the new subbrush bundle together. Each sub-brush bundle can be classified as a collection of vertices as shown in Fig.1. We use the same brush model for the split brush bundle because it can reduce the number of models that need to be generated. This is helpful to build a complex model by a single model, as which allows Graphical Processing Unit(GPU) to work on a smallest set of vertices at a time. Fig.5. D shows a model with one parent brush bundle and two sub-brush bundles. By this method, with less than 6 sub-brush bundles, we have not only modeled the complex geometry of a split brush, but also diminish the computational time. Ink Depositing Model. The ink model describes the process of ink depositing in which brush geometry model is instanced and transformed into a real screen presentation. During the painting process, the brush sweeps paper plane along a stroke path which transfers the brush footprint to the paper plane on each pass. To simulate the decrease of the amount of the ink, we define a parameter c i ( ) for the ink consumption at unit interval of the brush bundle s the ith ellipse. When the single brush bundle split into several bundles, each ellipse of the new sub-brush bundles will have the same value as the ellipse on the same contour line of the main brush bundle. Therefore, the amount of ink of the ith ellipse at instance t is e i,t =1 c i,j. (9) j=1,...,t Here, in terms of efficient computation, we suppose that c i,t = c i,t+1. (10) Suppose we are drawing a stroke, we want to have a brush that gradually adds color so that each points of a footprint contributes a little more ink with whatever is currently in the image. To do so, we simulate the process using alpha blending with OpenGL. The blending functions that use the source and the destination blending factor are GL SRC ALPHA and GL ON MINUS SRC ALPHA. To avoid the alias brush shape, we vary the alphas across the brush to make the brush add more ink in the middle and less on the edges. The process of the ink deposition is optimized by GPU s hardware implementation. As a result, the CPU can offload the rendering processing to do physics simulation, and therefore increase system performance. 3 Implementation Results We have implemented a prototype system based on our brush model. Our system was written in c++ using Microsoft Visual C All graphical rendering

8 A Virtual Chinese Hairy Brush Model for E-Learning 327 operations are accelerated by using OpenGL on the GPU. In the current implementation, on a 2GHZ Pentium 4 with NVIDIA GeForce FX 5200 display card, our system runs in real-time at 60 frames per second. Figures 6 and 8 show some sample calligraphy and strokes obtained using our prototype system. A calligraphy horizontal stoke shown in Fig 6 was written with a dipped sufficiently ink brush. Fig 6 and (c) illustrate the effect of ink diffusion due to the decrease of the amount of ink and the the amount of the time that the brush spent in contact with the paper. Although the examples shown in the figures 6,,(c) are very simple strokes, it proves that the proposed model is able to simulate the different shading effects along and across the width of a calligraphic stroke, which was not reported by the other systems so far. Fig 6 (d) and (e) illustrate the effect of brush split generated by a dry and multi-tuft brush. Fig 7 to fig 10 show some comparisons between the digitized real calligraphy sample and the imitation artwork created by our prototype system. It proves that very realistic-looking calligraphy artwork can be generated by our brush model. 4 Conclusion and Application We have presented a novel model for virtual brushes that can produce the effects needed by the digital Chinese calligraphy. The model is very simple but efficient, which is essential for a web-based learning system. With the proposed model, realistic Chinese calligraphy artwork can be generated effectively with direct manipulation. Major advantages of our model over previous works are We use a collection of points instead of hair threads as the basic unit to construct a 3D brush bundle, so that we convert simulating the complex physical deformation of bristles (as the way in most previous models did) to simulate the footprint variation of brush, which can efficiently decrease the complexity of physical simulation. We formulate the brush dynamics as a set of energy function according to the force exerted on it. A spring network is derived to calculate those energy function. This method significantly improves the brush s appearance, producing the plastic effect of brush that user expect. Up to now, our research mainly focused on modeling a medium stiff hair brush. It is expected that our model can also mimic other kinds of brushes by modifying the bent spring parameter. Moreover, only a vertical brush dynamic model was simulated presently. In order to simulate a hairy brush in Chinese painting, a slant angle brush dynamic model should also be studied. In Chinese traditional calligraphy, in order to achieve good calligraphic artwork, artist takes a great deal of experimenting and practice. How to control the pressure of the brush and to maintain elasticity during the pressing-downs and raising-ups in moving the brush is indeed a major technique in Chinese art. Speed of the brush is just as important as pressure. Speed affect the flow of the

9 328 B. Bai, K.-W. Wong, and Y. Zhang (c) (d) (e) Fig. 6. Sample calligraphy stoke from our prototype system to illustrate the impact of the variety of the ink. A horizontal stroke with full-inking. A horizontal stroke with medium-inking. (c) Blade-like calligraphic stroke with medium-inking. (d) Made with a drying splitting brush. (e) Character thousand made with a drying splitting brush. ink and the texture of a line; it creates the feeling of motion within a line (see Fig 6 (d) and (e)). This takes arduous labor and long practice before full control is gained, especially the changing of pressure while doing one stroke, such as press-lift-press, or vice versa. In learning to write, school children were usually taught to practice it by facsimile the artwork of famous artistes. Fig 8 is the facsimile template of the stroke Ti, which illustrates the flow of the stroke Ti. Beginner put a paper on the template, then facsimile the stoke again and again. Nowadays, computer are widely used in our daily life. Base on our system we can develop a Chinese calligraphy learning and practice system, which not only is convenient for learning writing, but also economizes on paper, which has practical significance.

10 A Virtual Chinese Hairy Brush Model for E-Learning 329 Fig. 7. Digitized image of a real art work. The image generated by our prototype system. Fig. 8. Digitized image of a real art work. The image generated by our prototype system. Fig. 9. Digitized image of a real art work. The image generated by our prototype system.

11 330 B. Bai, K.-W. Wong, and Y. Zhang Fig. 10. Digitized image of a real art work. The image generated by our prototype system. Acknowledgments The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China [Project No. CityU ] References 1. Baxter, B., Scheib, V., Lin, M., Manocha, D.: DAB: Interactive haptic painting with 3D virtual brushes. In: SIGGRAPH 2001 Proceedings (2001) 2. Chu, N.S., Tai, C.L.: An efficient brush model for physically-based 3D painting. In: Proc. of Pacific Graphics (2002) 3. Chu, N.S., Tai, C.L.: Real-Time Painting with an Expressive Virtual Chinese Brush. IEEE Computer Graphics and Applications 24(5), (2004) 4. Chu, N.S., Tai, C.L.: MoXi: Real-Time Ink Dispersion in Absorbent paper. In: SIG- GRAPH 2005 Proceedings (2005) 5. Landau, L.D., Lifshitz, E.M.: Theory of Elasticity, Course of Theoretical Physics, vol. 7. Pergamon Press, Oxford (1986) 6. Saito, S., Nakajima, M.: 3D physically based brush model for painting. In: SIG- GRAPH 1999 Conference Abstracts and Applications, p. 226 (1999) 7. Wong, H.T.F., Ip, H.H.S.: Virtual brush: A model-based synthesis of Chinese calligraphy. Computers and Graphics 24(1), (2000) 8. Xu, S., et al.: A Solid Model Based Virtual Hairy Brush. In: Eurographics 2002 Proceedings, Saarbrucken, Germany, pp Blackwell Publishers, Oxford (2002) 9. Xu, S., Tang, M., Lau, F., Pan, Y.: Advanced Design for a Realistic Virtual Brush. Computer Graphics Forum 22(3), (2003)