Hairy Brush Model Interactive Simulation in Chinese Ink Painting Style

More documents

Recommendations

Info

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
Page 1: ISBN 978-952-5726-02-2 (Print), 978
Page 5: Figure 3. Simulation resultV. CONCL

Hairy Brush Model Interactive Simulation in Chinese Ink Painting Style

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?