research article the simulation of the brush stroke based

Research ArticleThe Simulation of the Brush Stroke Based onForce Feedback Technology

Chao Guo Zengxuan Hou Guangqing Yang and Shuanzhu Zheng

School of Mechanical Engineering Dalian University of Technology Dalian 116024 China

Correspondence should be addressed to Chao Guo gc35826947maildluteducn

Received 1 September 2015 Revised 30 November 2015 Accepted 1 December 2015

Academic Editor Maria Gandarias

Copyright copy 2015 Chao Guo et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A novel simulation method of the brush stroke is proposed by applying force feedback technology to the virtual painting processThe relationship between force and the brush deformation is analyzed and the spring-mass model is applied to construct the brushmodel which can realistically simulate the brush morphological changes according to the force exerted on it According to thedeformation of the brush model at a sampling point the brush footprint between the brush and the paper is calculated in realtimeThen the brush stroke is obtained by superimposing brush footprints along sampling points and the dynamic painting of thebrush stroke is implemented The proposed method has been successfully applied to the virtual painting system based on the forcefeedback technology In this system users can implement the painting in real time with a Phantom Desktop haptic device whichcan effectively enhance reality to users

1 Introduction

In virtual painting many researchers have focused onJapanese calligraphy and painting [1ndash4] and western painting[5ndash9] These methods yield good results However thesemethods are not suited to Chinese calligraphy and paintingwhich usually consist of typical brush strokes created withvarious painting materials and techniques to convey theartistrsquos deep feelings of a painted object The simulationof brush stroke in Chinese calligraphy and painting hasattracted much attention of researchers [10ndash22]

The brush stroke is defined by the users as a list of positionand pressure samples [1] But the physical model of brush hasnot been considered which has impact on the effects of thebrush stroke

Wong and Ip [12] use a parameterized model to simulatethe physical process of the brush stroke creation Yet in theprocess of stroke generation the brush tip is in the middle ofthe painting stroke and fails to produce the biased-tip strokes

An empirical one-dimensional brush model is proposedin the simulation of the brush stroke [13] Nonetheless theeffects of the first brush footprint and end brush footprintcannot be simulated

Mi et al [15 16] apply the droplet model in theirsimulation of the brush stroke Sun et al [17] propose apractical 3D brush model in the simulation of the brushstroke Zhang et al [18] propose a virtual hairy brush modelbased on triangular mesh to simulate the brush strokeZhang et al [20] propose a statistic-based method to modelthe brush footprints between brush bundles and the paperHowever these methods have not referred to the forcefeedback technology which can effectively enhance reality tousers during the virtual painting process

The force feedback technology is introduced in [6ndash8 21]and theirmethods are described as followsThebrush in [6 7]is modeled with a spring-mass particle system skeleton and asubdivision surface In their feedback forcemodel the stretchspring is used as brush skeletons to deform subdivisionsurface and the force computation is separated from thebrush deformation computation so this approach makeslimited use of the haptic feedback devicersquos ability to recreatean accurate haptic sensation of the virtual brush Baxter andLin [8] focus on generating a wider variety of brushes thatare found in western painting with a versatile multispinemodeling approach They also employ the bending spring toevaluate the force for each brush spine and use the average

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 164821 10 pageshttpdxdoiorg1011552015164821

2 Mathematical Problems in Engineering

as the feedback force They model the brush dynamics basedon energy minimization techniques which are similar to[10] and this method of modeling can simulate small-scaledeformation of the brush instead of large-scale bendingdue to the restriction of constrained energy minimizationBesides differential and derivative operations are needed forthe optimizer which introduce high overhead The brushbristle model in [21] is similar to the algorithm in [6 7]But they use bending springs instead of stretch springs asthe skeletons of the brush in order to simulate the dynamicsof the brush The haptic simulation in [21] is modified fromthe method in [6 7] and the calculations of feedback forceand the brush deformation are splitted so this method hasthe same problem as [6 7] For the characteristics of Chinesebrushes certain feature in Chinese calligraphy and paintingsuch as brush flattening and bristle spreading due to theexerted force on the brush is difficult to simulate by thosemethods and the automatic on-the-fly generation of thebrush stroke has not been studied either

In this paper the relationship between force and thebrush deformation is analyzed and the spring-mass modelis applied to construct the Chinese brush model based onthe force feedback technology In this model a virtual springwhich is perpendicular to the paper plane and deforms alongthe normal of the paper plane is used for calculating theexerted force on the brush and then the deformation of thebrush such as the brush flattening and bristle spreading issimulated According to the deformation of the brush modelat a sampling point the brush footprint between the brushand paper is calculated in real time Then along the sam-pling points the brush stroke is obtained by superimposingfootprints of different sizes and shapes In the meantimeforce information is sent back to the force feedback device tosimulate the feeling that user touches a paper with a Chinesebrush Users also can adjust the painting to the desired effectsaccording to the feedback force The proposed method hasbeen applied to the virtual painting system based on the forcefeedback technology In this system users can paint the brushstroke in real time with a Phantom Desktop haptic device

2 The Brush Model Based onForce Feedback Technology

In the virtual painting process an expressive brush model isbeneficial to the simulation of the brush stroke Accordingto the characteristics of the real Chinese brush we constructthe brush model which includes two components brushgeometry and brush dynamics

21 The Brush Geometry The geometry is closely relatedto the dynamics A well-structured geometry can not onlyreduce the computational complexity and improve the realtime performance but also simulate the deformations ofvarious brushes Like some previous models [10 11] werepresent the geometry (Figure 1) in two layers the skeletonand the surface

The skeleton handles the general bending of the brushWe represent the skeleton as a connected sequence of line

Root node Nn

Spine segment

Outline

planecontrolling

Node Ni

Tip node N0

Brush skeleton

Brush surface

Figure 1 The geometry of the brush

segments (spine segments) that become progressively shortertoward the tip Since the brush tip is usually much softerthan the brush root it bends much more In fact usuallyonly the tip and the belly are used to paint Therefore formodeling efficiency progressively shorter segments are usedtowards the brush tip so as to dedicate higher resolution to tipSuppose the skeleton has 119899+1 nodes119873

0 1198731 119873

119899 with119873

0

as the tip node and119873119899as the root nodeThe length of the line

segment119873119894minus1119873119894is denoted by 119897

119894 1198971 1198972 119897119899form arithmetic

progression and the general formula is shown as follows

119897119894= 1198971+ (119894 minus 1) 119889

119889 =

2 (119871 minus 1198991198971)

[119899 (119899 minus 1)]

(1)

where 119894 is a positive integer and 119894 le 119899 1198971is related to the soft

and hard degree of the brush when the same force is exertedon the brush the softer the brush is the easier the bristlesnear the brush tip deform thus the value of 119897

1is smaller but

on the contrary the value of 1198971is larger The value of 119897

1is

given according to experiments The common difference 119889 isdetermined according to the initial length of the skeleton (119871)and the value of 119897

1

When the brush bends all the spine segments are in thesame plane (Figure 2) The inclination angle of brush holder(the angle between the brush holder and the paper plane)is denoted by 120579 (120579 isin (0 120587)) The angle between the spinesegment 119873

119894minus1119873119894and the paper plane is denoted by 120572

119894(119894 isin

[1 119899]) When the brush is unbent 120572119894= 120579 In the virtual

painting in order to control the outline of the brush strokewhen it is painted with the brush define the cross sectionwhich passes node 119873

119894(119894 isin [1 119899)) as the outline controlling

plane of the brush (the plane bisects the angle between thetwo adjacent spine segments and is perpendicular to the planeof spine segments) The deformation of the brush can besimulated by controlling the positions and sizes of the outlinecontrolling planes

Mathematical Problems in Engineering 3

Brush holder

Paper plane

Outlinecontrolling

plane

120579

Nn

Ni+1

Ni

120572i

li

Niminus1

N0

Figure 2 The skeleton deformation

Di

Dib

Dia

Ni

Figure 3 The deformation of the outline controlling plane whichpasses node119873

119894

The brush surface is represented as a triangular meshsurface defined by the skeleton and the varying outline con-trolling planes of the brush When the brushes are moistenedand unbent the shape of the Chinese brush is similar to acone Therefore the outline controlling planes of the brushare circles along the entire skeletonWe predefine these initialdiameters of circles for various types of brushes In the virtualpainting the brush root connects with the brush holderTherefore the diameter of the circle which passes119873

119899remains

unchanged and the outline controlling plane of the brushtransforms itself into ellipses when the pressure and frictionare exerted on the brush (Figure 3) This representation iscomputationally efficient and does not differ much from thereal brush deformation

In Figure 3 119863119894is the diameter of the circle 119863

119894119886is the

major diameter of the ellipse and 119863119894119887is the minor diameter

of the ellipseThemathematical expression of119863119894119886is shown as

follows

119863119894119886= 119863119894times (1 + 119887119901 + 119888119901

119891) (2)

where 119901 is the pressure factor which is defined as the ratioof the pressure 119865 to the maximum output force of the forcefeedback device In our system the maximum output forceprovided by the Phantom Desktop haptic device is 79NTherefore 119901 = 11986579 The value range is [0 1) in order toadjust the sizes of ellipses in different painting conditions(eg the painting is implemented using brusheswith differentsoft and hard degree) we set the adjustment factors 119887 and 119888which are determined by painting experiments to simulatethe most realistic brush deformations the mathematicalexpression of the frication influence factor 119901

119891is 119901119891= 120583119901

and 120583 refers to the friction factorThe minor diameter (119863

119894119887) of the ellipse is computed

according to the conservation of area

119863119894119887=

1198632

119894

119863119894119886

(3)

22 The Brush Dynamics The aim of the brush dynamic isto simulate brush flattening and bristle spreading due to theforce exerted on the brush during the painting process

A spring-mass model (Figure 4) is adopted to representthe brush dynamics in order to better describe the relation-ship between the force and brush deformation Set a virtualspring between the root node119873

119899and its projection point on

the paper plane (1198731015840119899)The spring is perpendicular to the paper

plane anddeforms along the normal of the paper planeWhenthe brush just contacts the paper plane and it is unbent point1198731015840

119899coincideswith the brush tip node119873

0 and the initial length

of the skeleton is denoted by 119871 The spring moves downwardwhen the pressure is exerted on the brush and the positions ofnodes change while the length of each spine segment remainsunchanged The feedback pressure (119865) is proportional to thedownward displacement of the brush and the mathematicalexpression of 119865 is shown as follows

119865 = 120582119867119883 (4)

In the expression 120582 is the force feedback factor whichis used for controlling the magnitude of 119865 The value of120582 is related to hardware and is determined according toexperimentsThe unit of 120582 is Nmm119867 is the hardness factorof the brush and119867 isin (0 1) The larger the value of119867 is theharder the brush is thus the exerted force is larger when thebrushmoves down the unit displacement119883 is the downwarddisplacement of the brush at a sampling time and is also thedeformation amount of the spring The unit of119883 is mm

In the virtual painting the friction (119865119891) between the

brush and paper is proportional to the pressure and themathematical expression is shown as follows

119865119891= 120583 sdot 119865 (5)

where 119865 is the pressure which is determined by (4) and theunit of 119865 is N


Brush surface

Brush skeleton

F X

L

Brush surface

N0

Nn

Nn

N998400n coincides with N0 N998400

n

Figure 4 The spring-mass model of brush

(a)

Brush holder

Brush skeleton

X

Z

Y

Outlinecontrolling curve

of the brush

The brush footprint

NnSn

Ni

N0

Md120573

MiSiWi

120572i + 120572i+12

Dib

S998400i

W998400i

N998400n

(b)

Figure 5 The brush footprint in the real painting (a) and virtual painting (b)

3 The Simulation of the Brush Stroke

In the painting process when the force is exerted on thebrush the brush footprint is formed between the brush andpaper Then the brush stroke is obtained by superimposingbrush footprints along the painting direction

31 The Control of Force to the Brush Stroke Differenteffects of the brush stroke are simulated by controlling themagnitude and direction of the force which is exerted onthe brush When the painting direction remains unchangedthe brush footprint varies with different magnitude of forceexerted on the brush which will result in different effectsof the brush stroke In the real painting process of theChinese calligraphy and painting themost common paintingtechniques include Zhongfeng Pianfeng and Cefeng In the

virtual painting define the direction of the brush tip (997888997888997888997888rarr

1198731015840

1198991198730

in Figure 4) as the bending direction of the brush Whenthe bending direction is opposite to the painting direction

the effects of the brush stroke with Zhongfeng are simulatedWhen the bending direction is perpendicular to the paintingdirection the effects of the brush stroke with Pianfeng aresimulated When the brush tip is on one side of the paintingstroke while the brush holder is on the other side the effectsof the brush stroke with Cefeng are simulated

32 The Generation of the Brush Stroke In the real paintingprocess the brush is in contact with the paper surfacewhich forms the brush footprint of the ldquoraindroprdquo shape(Figure 5(a)) Similar to [9ndash11] we suppose that the brushmodel intersects with the paper plane and consider theorthogonal projection of the penetrating portion onto thepaper plane as the brush footprint (Figure 5(b)) Then thecomplete brush stroke is obtained by superimposing thefootprints along the painting direction

The angle between the bending direction of the brush

(997888997888997888997888rarr

1198731015840

1198991198730) and 119911-axis is denoted by 120573 of which the value range


is [0 2120587) The coordinate values of the brush tip node1198730are

determined by

1199091198730= sin120573

119899

sum

119894=1

(119897119894cos120572119894)

1199101198730= 0

1199111198730= cos120573

119899

sum

119894=1

(119897119894cos120572119894)

(6)

The coordinate values of node119873119894are determined by

119909119873119894= sin120573

119899

sum

119905=119894+1

(119897119905cos120572119905)

119910119873119894=

119894

sum

119905=1

(119897119905sin120572119905)

119911119873119894= cos120573

119899

sum

119905=119894+1

(119897119905cos120572119905)

(7)

The points 119878119894and 1198781015840119894(119894 = 1 2 119899) are the endpoints of

the minor diameter (119863119894119887) of the ellipse which passes node119873

119894

and the coordinate values of 119878119894are determined by

119911119878119894= 119911119873119894minus

119863119894119887

2

cos120573 sin(120572119894+ 120572119894+1

2

)

119909119878119894= 119909119873119894minus

119863119894119887

2

sin120573 sin(120572119894+ 120572119894+1

2

)

119910119878119894= 119910119873119894minus

119863119894119887cos ((120572

119894+ 120572119894+1) 2)

2

(8)

where the value range of 119894 is [1 119899 minus 1]The coordinate values of brush root node 119878

119899are deter-

mined by (9) where119863119899is the diameter of circle which passes

the brush root node119873119899 119883 is the downward displacement of

the brush at a sampling time Hence

119911119878119899= minus

119863119899

2

cos120573

119909119878119899= minus

119863119899

2

sin120573

119910119878119899= 119871 minus 119883

(9)

In the plane11987301198731015840

119899119873119899 the outline controlling curve of the

brush is obtained by B-spline fitting according to points 1198730

and 119878119894 The line segment119873

01198731015840

119899which is the projection of the

brush skeleton intersects with the outline controlling curveof the brush at the point119872

119889119872119894is the intersection between

the line segments 1198781198941198781015840

119894and 119873

0119872119889 and the coordinate values

of119872119894are determined by the following equation

119909119872119894= 119909119873119894minus sin120573 sdot tan(

120572119894+ 120572119894+1

2

) sdot 119910119873119894

119910119872119894= 0

119911119872119894= 119911119873119894minus cos120573 sdot tan(

120572119894+ 120572119894+1

2

) sdot 119910119873119894

(10)

Ni

Mi

Si

Wi

S998400i

W998400i

Figure 6 The outline controlling plane which passes node119873119894

The outline controlling plane of the brush which passesnode 119873

119894intersects with the paper plane at the line segment

1198821198941198821015840

119894 In the outline controlling plane (Figure 6) the length

(119908119894) of the line segment119882

1198941198821015840

119894is determined by

119908119894=

119863119894119886

119863119894119887

radic1198632

119894119887minus

41199102

119873119894

cos2 ((120572119894+ 120572119894+1) 2)

(11)

The outline of the brush footprint is symmetric and the

axis of symmetry is997888997888997888997888rarr

1198731015840

1198991198730 Then the coordinate values of

points119882119894and1198821015840

119894are determined by

119909119882119894= 119909119872119894minus

119908119894cos1205732

119910119882119894= 0

119911119882119894= 119911119872119894+

119908119894sin1205732

(12)

1199091198821015840

119894

= 119909119872119894+

119908119894cos1205732

1199101198821015840

119894

= 0

1199111198821015840

119894

= 119911119872119894minus

119908119894sin1205732

(13)

In the paper plane the outline of the brush footprint isobtained by B-spline fitting according to points 119873

0119882119894119872119889

and1198821015840119894

The brush stroke is obtained by superimposing brushfootprints along sampling points In Figure 7 two lines whichare parallel to (the painting direction) are tangent to theoutline of the brush footprint and the tangent points are Aand B Define A and B as the effective points of the footprintAlong the painting direction the brush footprint is dividedinto the front zone (f) and the back zone (b) Since thefootprints cover each other in the real painting process inorder to reduce the computational complexity and improvethe real time performance during the virtual painting the


A

B

b

b

f

f

X

Y

The footprint at the

rarrm

first sampling point

The footprint at thelast sampling point

Figure 7 The brush stroke zone

brush stroke zone is composed of three parts the b zoneof the footprint at the first sampling point the zone formedby sequentially connecting effective points at every samplingpoint and the f zone of the footprint at the last samplingpoint

4 Simulation Experiment and Analysis

Ourmethod is applied to the virtual painting systembased onthe force feedback technology In the system MS VC 2005 isadopted as our integrated development environment (IDE)Qt framework is used for graphical user interface (GUI)Open Inventor is adopted as the graphical kernel library Thehaptics effects are designed with the combination of widelyused standard modules provided by the OpenHaptics libraryfrom SensAble Technologies Inc The hardware componentsinclude HP xw 8600 workstation for graphic and haptics ren-dering and a PhantomDesktop device for haptics interaction

We have developed a novel virtual 3D brush model basedon the force feedback technology With the force feedbackusers can experience the interaction between Chinese brushand paper more realistically The position motion and forceinformation of the virtual brush can be obtained from thePhantom Desktop haptic device to accomplish the brushstroke simulation and the painting stroke also can beadjusted by users to the desired effects through haptic deviceThe schematic diagram of our system is shown in Figure 8 toillustrate how various system components are integrated

In our system users can implement the painting withdifferent Chinese brush and paper models in real timerather than defining sets of parameters to describe the brushfootprint at any given instant which makes the paintingprocess more natural and spontaneous It means that if aChinese brush and paper model are selected the brushfootprint information will be taken from the Chinese brushmodel directly with the given current state of the dynamicpainting simulation This process is similar to that of the realChinese calligraphy and painting

The parameters in our paper can be classified into theparameters for the geometry of the brush the parameters forthe dynamic of the brush and the parameters between thebrush and paper The parameters for the geometry includethe length (119897

1) of the line segment 119873

01198731 the numbers of

nodes in brush skeleton (119899) the initial length of the skeleton

Table 1 Main parameters in a painting experiment

Parameter 119867 1198971(mm) 119899 120583 119887 119888 119871 (mm)

Value 07 1 9 024 15 075 35

(119871) and initial diameters of circles The parameters for thedynamic of the brush include the hardness factor of the brush(119867) and the adjustment factors (119887 and 119888 in (2)) The frictionfactor (120583) is the parameter between the brush and paper Theinitial length of the skeleton (119871) and initial diameters of circlesare predefined for simulating various types of Chinese brushWhen other parameters remain unchanged the deformationof the brush is more realistic with the increase of thenumbers of nodes in brush skeleton (119899) which will increasethe computation amount on the contrary the computationamount is small Considering the computational complexityand the real time performance during the virtual paintingthe reasonable value range of 119899 is 8ndash13 The value range ofreasonable119867 of Chinese brushes is estimated by consideringthe magnitudes of exerted force on brushes when brushesbend nearly 90∘ and the reasonable hardness factors areabout 03ndash07 With these hardness factors reasonable 119897

1 119887

and 119888 are about 08ndash14 13ndash18 and 06ndash08 respectivelyThe friction factor (120583) is estimated according to differentbrushes and papers and the value range is about 02ndash03Using these values the forces generated for haptic feedbackare also reasonable

In a simulation experiment main parameters are shownin Table 1 The brush deformations and footprints under theactions of different pressure are shown in Figure 9 The areaof brush footprint increases with higher values of the pressurefrom Figure 9

With the same parameters in Table 1 another simulationexperiment is implemented and the effects of the brushstrokes with the pressure of different magnitude and paintingtechniques are shown in Figure 10

In Figure 10 the bending direction of the brush is denotedby red arrow and the painting direction is denoted by greenarrow

Using the Phantom Desktop device users can paint thedesired strokes in real time with the preferred paintingtechnique and some common strokes which are painted inChinese regular script are shown in Figure 11 Some Chi-nese calligraphic characters (Chinese regular script) whichare created with different painting techniques are shownin Figure 12(b) Compared with the Chinese copyright ofrelated characters (Figure 12(a)) we conclude that some realcharacteristics in Chinese characters can be simulated by oursystem

There are two main characteristics that we should con-sider to select an input device for controlling the virtual3D brush the number of input degrees of freedom (DOF)should be as close to the six degrees of freedom of the realChinese brush as possible the magnitude and direction offorce felt by painters give a useful indication of the brushrsquosstate at each moment during the painting process of Chinesecalligraphy and painting thus the input device should pro-vide the haptic sensation which is similar to the real painting


Phantom desktophaptic device

Brush position andmotion

Spring-massmodel

Force feedback

Interactionwith paper

Paintingdirection Rendering

paper andbrush

Brushstroke

Brushfootprint

3D brushsimulator

Figure 8 Architecture of the virtual painting system based on the force feedback technology

F = 189N F = 252N F = 315N F = 378N

Figure 9 The brush deformations and footprints under the actions of different pressure

Zhongfeng

Pianfeng

Cefeng

F = 24N

F = 33N

F = 22N

F = 34N

F = 23N

F = 35N

Figure 10 The effects of the brush strokes with the pressure of different magnitude and painting techniques

Figure 11 Some common strokes which are painted in Chinese regular script are created with our system


(a)

(b)

Figure 12 Some of the Chinese calligraphic characters (a) from Chinese copybook (b) created with our system

Table 2 Some input devices which are commonly used in virtualpainting

Input device Input DOF Output DOF HapticsMouse 2 0 NoneWacom Intuos Tablet 5 0 StaticPhantom Desktop 6 3 Programmatic

process Some input devices which are commonly used invirtual painting are listed in Table 2 The Phantom hapticdevice is able to deliver an arbitrary force to the user underprogrammatic control compared with the Wacom IntuosTablet from Table 2 and our system supports both PhantomDesktop device and mouse as the input device When thebrush stroke is painted with mouse users should input themagnitude of the force through keyboard and control thebending direction and painting direction of the virtual brushthrough mouse in order to implement the painting processIf the brush stroke is not the desired one from observationthey should change the exerted force on the virtual brushand repeat the above steps In the whole process the funof painting would be lost without real time interaction andforce feedback On the other hand when the brush stroke ispainted with the Phantom Desktop device the direction andmagnitude of the exerted force on brush can be input from thePhantom Desktop device If the stroke is not the desired oneusers can change the exerted force through haptic device andthen the deformation and stroke of the brush are displayed inreal time This force feedback process is similar to the realpainting process of Chinese calligraphy and painting

User 1 User 2 User 3 User 4 User 5 User 60

2

4

6

8

10

12

14

16

18

20

The u

sed

time o

f the

pai

ntin

g pr

oces

s (s)

III

Figure 13 The used time of the painting process with the twodevices (I and II)

In order to verify the effectiveness of the haptic feedbacka simulation experiment is implemented by six users thatinclude two art students and four ordinary volunteers Inour system all the users are able to pick up the haptic stylusand start painting immediately with little training or detailedinstruction The Chinese character ldquoqierdquo is painted by theseusers under the same painting condition with two devices(I) mouse and keyboard and (II) Phantom Desktop deviceand the two devices are randomly used in sequenceThe usedtime of the painting process with the two devices is shownin Figure 13 The used time with the mouse and keyboard is


Figure 14 Some of the sample paintings created with our system

more than double that with Phantom Desktop device fromFigure 13

After the experiment six users are also asked to use apen to check which painting manner is more attractive inaccomplishing this task whether it is painted with I or IIThe survey results show that five out of six users expresstheir preference for painting with II (Phantom Desktopdevice) compared to I (mouse and keyboard) From Figure 13and the survey results we can conclude that the paintingprocess of Chinese calligraphy and painting with hapticfeedback is better than that without haptic sensation It wouldbe interesting to conduct a more thorough study over asubstantially larger group of users to confirm our conclusionas well as to evaluate the effectiveness of various parametersin our system

Some of the sample paintings created with our system areshown in Figure 14

5 Conclusion

In this paper a simulation method of the brush stroke isproposed by applying force feedback technology to the virtualpainting process Firstly a new brush model is adoptedto simulate the brush deformation according to the forceexerted on it Then different effects of the brush stroke aresimulated by controlling the magnitude and direction of theforce exerted on the brush Finally based on the hardwarecomponents HP xw 8600workstation and PhantomDesktopdevice we establish the virtual painting system based on theforce feedback technology and then different effects of thebrush strokes with the pressure of different magnitude and

painting techniques are simulated in real time which caneffectively enhance reality to users

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Natural ScienceFoundation of China (no 51175058)

References

[1] S Strassmann ldquoHairy brushesrdquo Computer Graphics vol 20 no4 pp 225ndash232 1986

[2] J Lee ldquoPhysically-basedmodeling of brush paintingrdquoComputerNetworks and ISDN Systems vol 29 no 14 pp 1571ndash1576 1997

[3] J Lee ldquoSimulating oriental black-ink paintingrdquo IEEE ComputerGraphics and Applications vol 19 no 3 pp 74ndash81 1999

[4] J Shin and M Makoto ldquoInk diffusion simulation for 3D virtualcalligraphyrdquo Journal of AdvancedComputational Intelligence andIntelligent Informatics vol 17 no 4 pp 598ndash603 2013

[5] S DiVerdi A Krishnaswamy and S Hadap ldquoIndustrial-strength painting with a virtual bristle brushrdquo in Proceedingsof the 17th ACM Symposium on Virtual Reality Software andTechnology pp 119ndash126 ACM November 2010

[6] WV Baxter Physically-basedmodeling techniques for interactivedigital painting [PhD thesis] University of North Carolina atChapel Hill Chapel Hill NC USA 2004


[7] W V Baxter Y X Liu andM C Lin ldquoA viscous paintmodel forinteractive applicationsrdquo in Proceedings of the 17th InternationalConference on Computer Animation and Social Agents (CASArsquo04) pp 433ndash441 JohnWiley amp Sons Geneva Switzerland July2004

[8] W V Baxter and M C Lin ldquoA versatile interactive 3D brushmodelrdquo in Proceedings of the 12th Pacific Conference on Com-puter Graphics and Applications (PG rsquo04) pp 319ndash328 IEEESeoul South Korea October 2004

[9] B Baxter V Scheib M C Lin and D Manocha ldquoDAB inter-active haptic painting with 3D virtual brushesrdquo in Proceedingsof the 28th Annual Conference on Computer Graphics andInteractive Techniques (SIGGRAPH rsquo01) pp 461ndash468 ACM LosAngeles Calif USA August 2001

[10] N S H Chu and C-L Tai ldquoAn efficient brush model forphysically-based 3D paintingrdquo in Proceedings of the 10th PacificConference onComputer Graphics andApplications pp 413ndash421IEEE Beijing China October 2002

[11] N S H Chu and C-L Tai ldquoReal-time painting with anexpressive virtual Chinese brushrdquo IEEE Computer Graphics andApplications vol 24 no 5 pp 76ndash85 2004

[12] H T F Wong and H H S Ip ldquoVirtual brush a model-basedsynthesis of Chinese calligraphyrdquo Computers and Graphics vol24 no 1 pp 99ndash113 2000

[13] L X Yao J Z Sun andM J Sun ldquoEmpirically based simulationof brush stroke in Chinese ink wash drawingrdquo ElectronicMeasurement Technology vol 30 no 10 pp 38ndash41 2007

[14] Y S Chua ldquoBezier brushstrokesrdquo Computer-Aided Design vol22 no 9 pp 550ndash555 1990

[15] X-F Mi M Tang J-Z Lin and J-X Dong ldquoAn experiencebased virtual brush modelrdquo Journal of Computer Research andDevelopment vol 40 no 8 pp 1244ndash1251 2003

[16] X-F Mi M Tang and J-X Dong ldquoDroplet a virtual brushmodel to simulate Chinese calligraphy and paintingrdquo Journalof Computer Science and Technology vol 19 no 3 pp 393ndash4042004

[17] M-J Sun J-Z Sun Z Wang and Z-W Ding ldquoPhysicalsimulation of practical 3D brush modelrdquo Journal of TianjinUniversity vol 41 no 3 pp 293ndash299 2008

[18] Z T Zhang J Q Wu and K Yu ldquoChinese calligraphy creationin 3D virtual environmentrdquo Journal of Computer-Aided Designamp Computer Graphics vol 22 no 6 pp 1010ndash1015 2010

[19] H Q Chen J F Luo G H Wen and Z Wu ldquoSimulationof Chinese calligraphy based on physical properties of penpaper and inkrdquo Journal of Computer-Aided Design amp ComputerGraphics vol 24 no 9 pp 1134ndash1138 2012

[20] J S Zhang YMZhang andC L Zhou ldquoSimulating thewritingprocess from Chinese calligraphy imagerdquo Journal of Computer-Aided Design amp Computer Graphics vol 26 no 6 pp 963ndash9722014

[21] J S Yeh T Y Lien and M Ouhyoung ldquoOn the effects ofhaptic display in brush and ink simulation for Chinese paintingand calligraphyrdquo in Proceedings of the 10th Pacific Conferenceon Computer Graphics and Applications pp 439ndash441 IEEEOctober 2002

[22] F L Cai and H S Li ldquoElastic cone for Chinese calligraphyrdquo inFifth International Conference on Graphic and Image Processing(ICGIP 2013) vol 9069 of Proceedings of SPIE p 5 Hong KongOctober 2014

Submit your manuscripts athttpwwwhindawicom

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MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


as the feedback force They model the brush dynamics basedon energy minimization techniques which are similar to[10] and this method of modeling can simulate small-scaledeformation of the brush instead of large-scale bendingdue to the restriction of constrained energy minimizationBesides differential and derivative operations are needed forthe optimizer which introduce high overhead The brushbristle model in [21] is similar to the algorithm in [6 7]But they use bending springs instead of stretch springs asthe skeletons of the brush in order to simulate the dynamicsof the brush The haptic simulation in [21] is modified fromthe method in [6 7] and the calculations of feedback forceand the brush deformation are splitted so this method hasthe same problem as [6 7] For the characteristics of Chinesebrushes certain feature in Chinese calligraphy and paintingsuch as brush flattening and bristle spreading due to theexerted force on the brush is difficult to simulate by thosemethods and the automatic on-the-fly generation of thebrush stroke has not been studied either

In this paper the relationship between force and thebrush deformation is analyzed and the spring-mass modelis applied to construct the Chinese brush model based onthe force feedback technology In this model a virtual springwhich is perpendicular to the paper plane and deforms alongthe normal of the paper plane is used for calculating theexerted force on the brush and then the deformation of thebrush such as the brush flattening and bristle spreading issimulated According to the deformation of the brush modelat a sampling point the brush footprint between the brushand paper is calculated in real time Then along the sam-pling points the brush stroke is obtained by superimposingfootprints of different sizes and shapes In the meantimeforce information is sent back to the force feedback device tosimulate the feeling that user touches a paper with a Chinesebrush Users also can adjust the painting to the desired effectsaccording to the feedback force The proposed method hasbeen applied to the virtual painting system based on the forcefeedback technology In this system users can paint the brushstroke in real time with a Phantom Desktop haptic device

2 The Brush Model Based onForce Feedback Technology

In the virtual painting process an expressive brush model isbeneficial to the simulation of the brush stroke Accordingto the characteristics of the real Chinese brush we constructthe brush model which includes two components brushgeometry and brush dynamics

21 The Brush Geometry The geometry is closely relatedto the dynamics A well-structured geometry can not onlyreduce the computational complexity and improve the realtime performance but also simulate the deformations ofvarious brushes Like some previous models [10 11] werepresent the geometry (Figure 1) in two layers the skeletonand the surface

The skeleton handles the general bending of the brushWe represent the skeleton as a connected sequence of line

Root node Nn

Spine segment

Outline

planecontrolling

Node Ni

Tip node N0

Brush skeleton

Brush surface

Figure 1 The geometry of the brush

segments (spine segments) that become progressively shortertoward the tip Since the brush tip is usually much softerthan the brush root it bends much more In fact usuallyonly the tip and the belly are used to paint Therefore formodeling efficiency progressively shorter segments are usedtowards the brush tip so as to dedicate higher resolution to tipSuppose the skeleton has 119899+1 nodes119873

0 1198731 119873

119899 with119873

0

as the tip node and119873119899as the root nodeThe length of the line

segment119873119894minus1119873119894is denoted by 119897

119894 1198971 1198972 119897119899form arithmetic

progression and the general formula is shown as follows

119897119894= 1198971+ (119894 minus 1) 119889

119889 =

2 (119871 minus 1198991198971)

[119899 (119899 minus 1)]

(1)

where 119894 is a positive integer and 119894 le 119899 1198971is related to the soft

and hard degree of the brush when the same force is exertedon the brush the softer the brush is the easier the bristlesnear the brush tip deform thus the value of 119897

1is smaller but

on the contrary the value of 1198971is larger The value of 119897

1is

given according to experiments The common difference 119889 isdetermined according to the initial length of the skeleton (119871)and the value of 119897

1

When the brush bends all the spine segments are in thesame plane (Figure 2) The inclination angle of brush holder(the angle between the brush holder and the paper plane)is denoted by 120579 (120579 isin (0 120587)) The angle between the spinesegment 119873

119894minus1119873119894and the paper plane is denoted by 120572

119894(119894 isin

[1 119899]) When the brush is unbent 120572119894= 120579 In the virtual

painting in order to control the outline of the brush strokewhen it is painted with the brush define the cross sectionwhich passes node 119873

119894(119894 isin [1 119899)) as the outline controlling

plane of the brush (the plane bisects the angle between thetwo adjacent spine segments and is perpendicular to the planeof spine segments) The deformation of the brush can besimulated by controlling the positions and sizes of the outlinecontrolling planes


Brush holder

Paper plane

Outlinecontrolling

plane

120579

Nn

Ni+1

Ni

120572i

li

Niminus1

N0


Di

Dib

Dia

Ni


119894


119899remains



119894119886is the



follows

119863119894119886= 119863119894times (1 + 119887119901 + 119888119901

119891) (2)


119891is 119901119891= 120583119901




119863119894119887=

1198632

119894

119863119894119886

(3)









119865 = 120582119867119883 (4)




119865119891= 120583 sdot 119865 (5)



Brush surface

Brush skeleton

F X

L

Brush surface

N0

Nn

Nn


n


(a)

Brush holder

Brush skeleton

X

Z

Y


of the brush

The brush footprint

NnSn

Ni

N0

Md120573

MiSiWi

120572i + 120572i+12

Dib

S998400i

W998400i

N998400n

(b)






1198731015840

1198991198730





(997888997888997888997888rarr

1198731015840




determined by

1199091198730= sin120573

119899

sum

119894=1

(119897119894cos120572119894)

1199101198730= 0

1199111198730= cos120573

119899

sum

119894=1

(119897119894cos120572119894)

(6)


119909119873119894= sin120573

119899

sum

119905=119894+1

(119897119905cos120572119905)

119910119873119894=

119894

sum

119905=1

(119897119905sin120572119905)

119911119873119894= cos120573

119899

sum

119905=119894+1

(119897119905cos120572119905)

(7)



119894


119911119878119894= 119911119873119894minus

119863119894119887

2

cos120573 sin(120572119894+ 120572119894+1

2

)

119909119878119894= 119909119873119894minus

119863119894119887

2

sin120573 sin(120572119894+ 120572119894+1

2

)

119910119878119894= 119910119873119894minus

119863119894119887cos ((120572

119894+ 120572119894+1) 2)

2

(8)


119899are deter-




119911119878119899= minus

119863119899

2

cos120573

119909119878119899= minus

119863119899

2

sin120573

119910119878119899= 119871 minus 119883

(9)

In the plane11987301198731015840




01198731015840





119894and 119873




120572119894+ 120572119894+1

2

) sdot 119910119873119894

119910119872119894= 0


120572119894+ 120572119894+1

2

) sdot 119910119873119894

(10)

Ni

Mi

Si

Wi

S998400i

W998400i




1198821198941198821015840



1198941198821015840


119908119894=

119863119894119886

119863119894119887

radic1198632

119894119887minus

41199102

119873119894

cos2 ((120572119894+ 120572119894+1) 2)

(11)



1198731015840


points119882119894and1198821015840


119909119882119894= 119909119872119894minus

119908119894cos1205732

119910119882119894= 0

119911119882119894= 119911119872119894+

119908119894sin1205732

(12)

1199091198821015840

119894

= 119909119872119894+

119908119894cos1205732

1199101198821015840

119894

= 0

1199111198821015840

119894

= 119911119872119894minus

119908119894sin1205732

(13)


0119882119894119872119889

and1198821015840119894



A

B

b

b

f

f

X

Y


rarrm














Parameter 119867 1198971(mm) 119899 120583 119887 119888 119871 (mm)

Value 07 1 9 024 15 075 35


1 119887










Spring-massmodel

Force feedback



paper andbrush

Brushstroke

Brushfootprint

3D brushsimulator


F = 189N F = 252N F = 315N F = 378N


Zhongfeng

Pianfeng

Cefeng

F = 24N

F = 33N

F = 22N

F = 34N

F = 23N

F = 35N




(a)

(b)






2

4

6

8

10

12

14

16

18

20

The u

sed

time o

f the

pai

ntin

g pr

oces

s (s)

III








5 Conclusion





Acknowledgment


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Brush holder

Paper plane

Outlinecontrolling

plane

120579

Nn

Ni+1

Ni

120572i

li

Niminus1

N0


Di

Dib

Dia

Ni


119894


119899remains



119894119886is the



follows

119863119894119886= 119863119894times (1 + 119887119901 + 119888119901

119891) (2)


119891is 119901119891= 120583119901




119863119894119887=

1198632

119894

119863119894119886

(3)









119865 = 120582119867119883 (4)




119865119891= 120583 sdot 119865 (5)



Brush surface

Brush skeleton

F X

L

Brush surface

N0

Nn

Nn


n


(a)

Brush holder

Brush skeleton

X

Z

Y


of the brush

The brush footprint

NnSn

Ni

N0

Md120573

MiSiWi

120572i + 120572i+12

Dib

S998400i

W998400i

N998400n

(b)






1198731015840

1198991198730





(997888997888997888997888rarr

1198731015840




determined by

1199091198730= sin120573

119899

sum

119894=1

(119897119894cos120572119894)

1199101198730= 0

1199111198730= cos120573

119899

sum

119894=1

(119897119894cos120572119894)

(6)


119909119873119894= sin120573

119899

sum

119905=119894+1

(119897119905cos120572119905)

119910119873119894=

119894

sum

119905=1

(119897119905sin120572119905)

119911119873119894= cos120573

119899

sum

119905=119894+1

(119897119905cos120572119905)

(7)



119894


119911119878119894= 119911119873119894minus

119863119894119887

2

cos120573 sin(120572119894+ 120572119894+1

2

)

119909119878119894= 119909119873119894minus

119863119894119887

2

sin120573 sin(120572119894+ 120572119894+1

2

)

119910119878119894= 119910119873119894minus

119863119894119887cos ((120572

119894+ 120572119894+1) 2)

2

(8)


119899are deter-




119911119878119899= minus

119863119899

2

cos120573

119909119878119899= minus

119863119899

2

sin120573

119910119878119899= 119871 minus 119883

(9)

In the plane11987301198731015840




01198731015840





119894and 119873




120572119894+ 120572119894+1

2

) sdot 119910119873119894

119910119872119894= 0


120572119894+ 120572119894+1

2

) sdot 119910119873119894

(10)

Ni

Mi

Si

Wi

S998400i

W998400i




1198821198941198821015840



1198941198821015840


119908119894=

119863119894119886

119863119894119887

radic1198632

119894119887minus

41199102

119873119894

cos2 ((120572119894+ 120572119894+1) 2)

(11)



1198731015840


points119882119894and1198821015840


119909119882119894= 119909119872119894minus

119908119894cos1205732

119910119882119894= 0

119911119882119894= 119911119872119894+

119908119894sin1205732

(12)

1199091198821015840

119894

= 119909119872119894+

119908119894cos1205732

1199101198821015840

119894

= 0

1199111198821015840

119894

= 119911119872119894minus

119908119894sin1205732

(13)


0119882119894119872119889

and1198821015840119894



A

B

b

b

f

f

X

Y


rarrm














Parameter 119867 1198971(mm) 119899 120583 119887 119888 119871 (mm)

Value 07 1 9 024 15 075 35


1 119887










Spring-massmodel

Force feedback



paper andbrush

Brushstroke

Brushfootprint

3D brushsimulator


F = 189N F = 252N F = 315N F = 378N


Zhongfeng

Pianfeng

Cefeng

F = 24N

F = 33N

F = 22N

F = 34N

F = 23N

F = 35N




(a)

(b)






2

4

6

8

10

12

14

16

18

20

The u

sed

time o

f the

pai

ntin

g pr

oces

s (s)

III








5 Conclusion





Acknowledgment


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Brush surface

Brush skeleton

F X

L

Brush surface

N0

Nn

Nn


n


(a)

Brush holder

Brush skeleton

X

Z

Y


of the brush

The brush footprint

NnSn

Ni

N0

Md120573

MiSiWi

120572i + 120572i+12

Dib

S998400i

W998400i

N998400n

(b)






1198731015840

1198991198730





(997888997888997888997888rarr

1198731015840




determined by

1199091198730= sin120573

119899

sum

119894=1

(119897119894cos120572119894)

1199101198730= 0

1199111198730= cos120573

119899

sum

119894=1

(119897119894cos120572119894)

(6)


119909119873119894= sin120573

119899

sum

119905=119894+1

(119897119905cos120572119905)

119910119873119894=

119894

sum

119905=1

(119897119905sin120572119905)

119911119873119894= cos120573

119899

sum

119905=119894+1

(119897119905cos120572119905)

(7)



119894


119911119878119894= 119911119873119894minus

119863119894119887

2

cos120573 sin(120572119894+ 120572119894+1

2

)

119909119878119894= 119909119873119894minus

119863119894119887

2

sin120573 sin(120572119894+ 120572119894+1

2

)

119910119878119894= 119910119873119894minus

119863119894119887cos ((120572

119894+ 120572119894+1) 2)

2

(8)


119899are deter-




119911119878119899= minus

119863119899

2

cos120573

119909119878119899= minus

119863119899

2

sin120573

119910119878119899= 119871 minus 119883

(9)

In the plane11987301198731015840




01198731015840





119894and 119873




120572119894+ 120572119894+1

2

) sdot 119910119873119894

119910119872119894= 0


120572119894+ 120572119894+1

2

) sdot 119910119873119894

(10)

Ni

Mi

Si

Wi

S998400i

W998400i




1198821198941198821015840



1198941198821015840


119908119894=

119863119894119886

119863119894119887

radic1198632

119894119887minus

41199102

119873119894

cos2 ((120572119894+ 120572119894+1) 2)

(11)



1198731015840


points119882119894and1198821015840


119909119882119894= 119909119872119894minus

119908119894cos1205732

119910119882119894= 0

119911119882119894= 119911119872119894+

119908119894sin1205732

(12)

1199091198821015840

119894

= 119909119872119894+

119908119894cos1205732

1199101198821015840

119894

= 0

1199111198821015840

119894

= 119911119872119894minus

119908119894sin1205732

(13)


0119882119894119872119889

and1198821015840119894



A

B

b

b

f

f

X

Y


rarrm














Parameter 119867 1198971(mm) 119899 120583 119887 119888 119871 (mm)

Value 07 1 9 024 15 075 35


1 119887










Spring-massmodel

Force feedback



paper andbrush

Brushstroke

Brushfootprint

3D brushsimulator


F = 189N F = 252N F = 315N F = 378N


Zhongfeng

Pianfeng

Cefeng

F = 24N

F = 33N

F = 22N

F = 34N

F = 23N

F = 35N




(a)

(b)






2

4

6

8

10

12

14

16

18

20

The u

sed

time o

f the

pai

ntin

g pr

oces

s (s)

III








5 Conclusion





Acknowledgment


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











determined by

1199091198730= sin120573

119899

sum

119894=1

(119897119894cos120572119894)

1199101198730= 0

1199111198730= cos120573

119899

sum

119894=1

(119897119894cos120572119894)

(6)


119909119873119894= sin120573

119899

sum

119905=119894+1

(119897119905cos120572119905)

119910119873119894=

119894

sum

119905=1

(119897119905sin120572119905)

119911119873119894= cos120573

119899

sum

119905=119894+1

(119897119905cos120572119905)

(7)



119894


119911119878119894= 119911119873119894minus

119863119894119887

2

cos120573 sin(120572119894+ 120572119894+1

2

)

119909119878119894= 119909119873119894minus

119863119894119887

2

sin120573 sin(120572119894+ 120572119894+1

2

)

119910119878119894= 119910119873119894minus

119863119894119887cos ((120572

119894+ 120572119894+1) 2)

2

(8)


119899are deter-




119911119878119899= minus

119863119899

2

cos120573

119909119878119899= minus

119863119899

2

sin120573

119910119878119899= 119871 minus 119883

(9)

In the plane11987301198731015840




01198731015840





119894and 119873




120572119894+ 120572119894+1

2

) sdot 119910119873119894

119910119872119894= 0


120572119894+ 120572119894+1

2

) sdot 119910119873119894

(10)

Ni

Mi

Si

Wi

S998400i

W998400i




1198821198941198821015840



1198941198821015840


119908119894=

119863119894119886

119863119894119887

radic1198632

119894119887minus

41199102

119873119894

cos2 ((120572119894+ 120572119894+1) 2)

(11)



1198731015840


points119882119894and1198821015840


119909119882119894= 119909119872119894minus

119908119894cos1205732

119910119882119894= 0

119911119882119894= 119911119872119894+

119908119894sin1205732

(12)

1199091198821015840

119894

= 119909119872119894+

119908119894cos1205732

1199101198821015840

119894

= 0

1199111198821015840

119894

= 119911119872119894minus

119908119894sin1205732

(13)


0119882119894119872119889

and1198821015840119894



A

B

b

b

f

f

X

Y


rarrm














Parameter 119867 1198971(mm) 119899 120583 119887 119888 119871 (mm)

Value 07 1 9 024 15 075 35


1 119887










Spring-massmodel

Force feedback



paper andbrush

Brushstroke

Brushfootprint

3D brushsimulator


F = 189N F = 252N F = 315N F = 378N


Zhongfeng

Pianfeng

Cefeng

F = 24N

F = 33N

F = 22N

F = 34N

F = 23N

F = 35N




(a)

(b)






2

4

6

8

10

12

14

16

18

20

The u

sed

time o

f the

pai

ntin

g pr

oces

s (s)

III








5 Conclusion





Acknowledgment


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










A

B

b

b

f

f

X

Y


rarrm














Parameter 119867 1198971(mm) 119899 120583 119887 119888 119871 (mm)

Value 07 1 9 024 15 075 35


1 119887










Spring-massmodel

Force feedback



paper andbrush

Brushstroke

Brushfootprint

3D brushsimulator


F = 189N F = 252N F = 315N F = 378N


Zhongfeng

Pianfeng

Cefeng

F = 24N

F = 33N

F = 22N

F = 34N

F = 23N

F = 35N




(a)

(b)






2

4

6

8

10

12

14

16

18

20

The u

sed

time o

f the

pai

ntin

g pr

oces

s (s)

III








5 Conclusion





Acknowledgment


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Spring-massmodel

Force feedback



paper andbrush

Brushstroke

Brushfootprint

3D brushsimulator


F = 189N F = 252N F = 315N F = 378N


Zhongfeng

Pianfeng

Cefeng

F = 24N

F = 33N

F = 22N

F = 34N

F = 23N

F = 35N




(a)

(b)






2

4

6

8

10

12

14

16

18

20

The u

sed

time o

f the

pai

ntin

g pr

oces

s (s)

III








5 Conclusion





Acknowledgment


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(a)

(b)






2

4

6

8

10

12

14

16

18

20

The u

sed

time o

f the

pai

ntin

g pr

oces

s (s)

III








5 Conclusion





Acknowledgment


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra














5 Conclusion





Acknowledgment


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article the simulation of the brush stroke based

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