Cataloged from PDF version of article.In this paper, a procedural method for the visualization of knitted and woven fabrics is presented. The proposed method is compatible with a mass-spring model and makes use of the regular warp-weft structure of the cloth. The visualization parameters for the loops and threads are easily mapped to the animated mass-spring model. The simulation idea underlying both knitted and woven fabrics is similar as we represent both structures in 3D. As the proposed method is simple and practical, we can achieve near real-time rendering performance with good visual quality. (C) 2007 Elsevier Ltd. All rights reserved

Durupinar, F.

Gudukbay, U.

Computers & Graphics

In this paper, a procedural method for the visualization of knitted and woven fabrics is presented. The proposed method is compatible with a mass-spring model and makes use of the regular warp-weft structure of the cloth. The visualization parameters for the loops and threads are easily mapped to the animated mass-spring model. The simulation idea underlying both knitted and woven fabrics is similar as we represent both structures in 3D. As the proposed method is simple and practical, we can achieve near real-time rendering performance with good visual quality. © 2007 Elsevier Ltd. All rights reserved

Durupinar F.

Güdükbay, U.

Bilkent University Institutional Repository

ARTICLE IN PRESS0097-8493/$ - sedoi:10.1016/j.caCorrespondE-mail addrgudukbay@cs.bComputers & Graphics 31 (2007) 778–783www.elsevier.com/locate/cagShort CommunicationProcedural visualization of knitwear and woven clothFunda Durupınar, Uǧur GüdükbayDepartment of Computer Engineering, Bilkent University, Bilkent 06800, Ankara, TurkeyReceived 11 December 2006; received in revised form 22 May 2007; accepted 14 June 2007AbstractIn this paper, a procedural method for the visualization of knitted and woven fabrics is presented. The proposed method is compatiblewith a mass-spring model and makes use of the regular warp–weft structure of the cloth. The visualization parameters for the loops andthreads are easily mapped to the animated mass-spring model. The simulation idea underlying both knitted and woven fabrics is similaras we represent both structures in 3D. As the proposed method is simple and practical, we can achieve near real-time renderingperformance with good visual quality.r 2007 Elsevier Ltd. All rights reserved.Keywords: Fabric rendering; Knitwear; Woven cloth; Physically-based modeling1. IntroductionModeling the visual appearance of cloth is as importantas the simulation of its draping behavior for the sake ofrealism in computer graphics. There are various methodsto produce fabrics from yarn, such as knitting, weaving,braiding or knotting. Particularly, knitting and weaving arethe most common techniques and they have been studied inthe literature.Meissner and Eberhardt [1] introduce a system thatsimulates the physically correct appearance of knittedfabrics. Zhong et al. [2] propose a method for renderingknitwear on free-form surfaces. Another study that usesfree-form surfaces is presented by Xu et al. [3], wherephotorealistic rendering of knitwear is handled by introdu-cing an element called the lumislice. Later, Chen et al. [4]extend this study to include the realistic animation ofknitwear. A recent study in textile research examines thedynamic draping behavior of woven and knitted fabrics [5].In the case of woven cloth, we cannot do simple texturemapping because occlusion and self-shadowing terms comeinto play due to the structure of the individual threads andtheir interweaving pattern. In [6], woven cloth is simulatede front matter r 2007 Elsevier Ltd. All rights reserved.g.2007.06.002ing author. Tel.: +90 312 290 1386; fax: +90 312 266 4047.esses: fundad@cs.bilkent.edu.tr (F. Durupınar),ilkent.edu.tr (U. Güdükbay).by computing the lighting using a geometrical model of astitch. Then, by sampling the stitch regularly within aplane, a view-dependent texture with per-pixel normalsand material properties is generated. In [7], the weave ofthe texture is simulated by procedural displacements of thegeometry and the loop is represented as a 2D curve. The3D appearance is given by displacing the loop. A recentstudy that supports a wide variety of weave patterns andcaptures the difference in appearance of the front and backsurfaces of woven cloth is presented by Adabala et al. [8].The color texture, BRDF texture and the horizon maps arepre-computed and the rendering of the images using thesetextures is achieved in real time with a good visual quality.In this paper, we propose a simple and efficientprocedural method for the visualization of knitted andwoven textiles. For this purpose, we use rectangular mass-spring meshes and cut out regular garment patternscomposed of quadrilaterals from the meshes. Regularityboth preserves the general cloth behavior such as shearingand bending, thus preserving physical accuracy and enablesthe definition of complex knit and weave patterns. In mostof the existing systems, woven fabrics are not simulatedphysically; they are simplified as 2D structures. We exploitthe regular structure of cloth models and parametricallydefine the repetitious structure of woven and knitted fabric.The weave and knit patterns can be as complex as desiredand can support any color pattern. As the structure is 3D,ARTICLE IN PRESS1.5x2.5xp1p3 p4p2BP8 BP12BP3BP2BP7 BP11BP1BP5 BP6 BP10 BP4 BP91.5x2.5x4xx 3x x xFig. 1. Bonding points of a knit loop.F. Durupınar, U. Güdükbay / Computers & Graphics 31 (2007) 778–783 779the resulting garments have different appearances for thefront and back surfaces of the fabrics, depending on theweave or knit pattern as in [8]. However, our method doesnot require preprocessing for texture generation; all thecalculations are done on-the-fly. We achieve near real-timerendering and simulation performance with good visualquality.2. Garment visualizationIn this section, the simulation of the two methods offabric production, i.e., weaving and knitting, is introduced.The cloth model used is a mass-spring model [9]. This is aspecific case of a particle system in which the particles areconnected by spring forces. The type and behavior of thecloth is determined by the strength of the spring forces andthe topology of the cloth, which in turn is determined byhow the springs connect the particles. Three types ofsprings are used to reproduce the stretching, shearing andbending behavior of cloth. The mass-spring model isadopted due to its simplicity and efficiency [10]. The initialgrid structure is a rectangular mesh of particles and springsconnecting these particles in horizontal, vertical anddiagonal directions. In addition, contrary to the irregulartriangular meshes, the mesh structures of garment patternsare regular, which is compatible with the warp and weftdirections of the woven cloth. Thus, instead of drawingthe 2D garment pattern and discretizing it by triangulation,we use an initial rectangular mesh composed of quad-rilaterals and cut out the desired shape by preserving theregularity.2.1. KnitwearThe structure of knitwear is complicated compared toother techniques like weaving. This is due to the 3Dgeometry of a knit loop. In our system, we make use of theparticle system and the mass-spring model of our clothmesh in order to consider the interaction of neighboringloops. For this purpose, the cloth mesh must be a regularlattice consisting of quadrilaterals. There are two typesof basic stitches when knitting: left and right loops.The knitwear pattern, which shows the order of the rightand left loops, is read from an input file and canbe changed interactively in the program. Each quadrilat-eral contains one type of loop. The structure of the loopin a quadrilateral is defined by the bonding points (BPs).The positions of the BPs can be determined parametricallyusing the vertices of the enclosing quadrilateral asfollows:BP1 ¼67p3pos þ17p4pos ,BP2 ¼5:521p1pos þ1:521p2pos þ1121p3pos þ321p4pos ,BP3 ¼1:521p1pos þ5:521p2pos þ321p3pos þ1121p4pos ,BP4 ¼17p3pos þ67p4pos ,BP5 ¼ p3pos ,BP6 ¼57p3pos þ27p4pos ,BP7 ¼4:528p1pos þ2:528p2pos þ13:528p3pos þ7:528p4pos ,BP8 ¼67p1pos þ17p2pos ,BP9 ¼ p4pos ,BP10 ¼27p3pos þ57p4pos ,BP11 ¼2:528p1pos þ4:528p2pos þ7:528p3pos þ13:528p4pos ,BP12 ¼17p1pos þ67p2pos , ð1Þwhere BPi is the ith bonding point and pjpos is the 3Dposition of vertex j.Due to the thickness of the yarn, these BPs are movedslightly, taking the normal of that quadrilateral intoconsideration. Then, each bonding point BPi is assignedthe value BPi þ ciN, where N is the surface normal and ci isa constant that is defined according to the type of the loopand BP. Thus, the knitted fabric looks different when frontand back views are considered. Fig. 1 shows the construc-tion of the loops.In order to maintain interactivity, complex volumetricmodels or time-consuming methods like [3,11] for render-ing the yarns in a loop cannot be utilized. Three-dimensionality is achieved by drawing cylinders aroundeach yarn and applying texture mapping on these cylinders(see Fig. 2 for a close-up view of a knitwear). Using theposition information of consecutive BPs, a cylinder ofheight jV!j lying along the positive z-axis is found. Then,the cylinder is transformed by a composite transformationARTICLE IN PRESSF. Durupınar, U. Güdükbay / Computers & Graphics 31 (2007) 778–783780matrix so as to be oriented in the direction of the vectorbetween the two consecutive BPs. The composite transfor-mation matrix M includes a rotation around y-axis, arotation around x-axis, and a translation:M ¼ TðBPiÞ  RxðaÞ  RyðbÞ‘ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðBPiþ1  y BPi  yÞ2þ ðBPiþ1  z BPi  zÞ2qa ¼ arcsinððBPiþ1  y BPi  yÞ=jV!jÞ=‘b ¼ arccosð‘Þ. ð2ÞIn order to optimize the performance, varying levels ofdetail from different viewing distances are shown. For distantviews, since the yarn structure cannot be distinguished,instead of drawing cylinders by performing explicit transfor-mations, we simply draw texture-mapped, antialiased lineprimitives between the BPs by hardware-supported linedrawing. The line size, which is determined by the numberof pixels, is proportional to the proximity of the viewer to theFig. 2. The close-up view of a knitwear.Fig. 3. Transition from line primitives to cylinders: (a) distant view with linescylinders. Images at the bottom part show magnified views for each distance.cloth. Another issue to consider is the popping artifacts forthe transition between the two modes of rendering yarns. Thetransition should be gradual and devoid of sudden leaps. Weachieve smooth transition by image blending. For inter-mediate distance ranges, the knitwear is generated with lineprimitives and with cylinders separately. These knitwearimages are blended and the resulting image is rendered. Theblending weights of the two images are determined accordingto the distance of the viewer to the cloth. Blending is handledusing hardware support. The blending operation is illustratedin Fig. 3. In the most distant view, the cloth is rendered withline primitives. Then, at intermediate distance range, theblended image is rendered. The closest view is generated withcylinders. The images at the bottom row demonstratemagnified fragments from each image. The knitwear render-ing algorithms are as follows:Algorithm. RENDERKNITWEAR (cloth, pattern)(1) Compute viewing distance to cloth(2) if viewing distance4 high(3) line width  c/ viewing distance(4) I  GENERATELINETHREADSðcloth; pattern; line widthÞ(5) else if viewing distance 2 ½low, high(6) line width c= viewing distance(7) I  GENERATELINETHREADSðcloth; pattern; line widthÞ(8) I2 GENERATECYLINDRICALTHREADS ðcloth; patternÞ(9) I  (I2  ðviewing distance  lowÞþI1 ðhigh viewing distanceÞÞ=ðhigh lowÞ(10) else(11) I  GENERATECYLINDRICALTHREADS ðcloth, patternÞ(12) Render I; (b) intermediate distance with blended image; and (c) close-up view withARTICLE IN PRESSF. Durupınar, U. Güdükbay / Computers & Graphics 31 (2007) 778–783 781Algorithm. GENERATECYLINDRICALTHREADS (cloth, pattern)Fig. 5. Knitwear garments rendered with line primitives.Fig. 6. The physical behavior of knitwear.(1) for each quadrilateral in cloth(2) Compute bonding points BP using Equation 1 andaccording to pattern(3) for each i 1; . . . ; 11(4) V! BPiþ1BPi(5) Find cylinder of height jV!j lying along the positivez-axis(6) Align cylinder with the direction of V!by thetransformation matrix in Equation 2(7) Draw cylinder in image(8) return imageThe algorithm for GENERATELINETHREADS (cloth, pat-tern, line width) is similar to GENERATECYLINDRICALTH-READS (cloth, pattern) with the exception of drawing lineprimitives of size line width instead of cylinders.Fig. 4 shows a knitted shirt from different distances,where the close-up views are rendered with cylinders andthe distant view is rendered with lines. Fig. 5 showsexamples of knitwear rendered with line primitives. Finally,Fig. 6 demonstrates the physical behavior of knit loops,whereby the correlation between the forces acting on thecloth and the distance between the threads can be observed.2.2. Woven clothIn real life, weaving can be performed by means of aloom. The idea of the loom is to interleave two sets ofperpendicular threads [12]. These threads are the warp andthe weft threads. Warp threads are the vertical ones,whereas weft threads are the horizontal ones. Weavingpatterns can be obtained from two types of interleavingof threads, i.e., warp on weft and weft on warp. Variousweaving patterns can be created by ordering these twoFig. 4. Appearance of a knitted shirt from different distances. Close-upview is rendered with cylinders and distant view is rendered with lines.thread interleaving types. Our system works as follows:(i) we read the patterns from a pattern description file,(ii) draw them in 3D as warp and weft threads bycalculating their positions and (iii) do texture mapping onthem to capture the detailed appearance of the componentfibers. The texture is simply an image of a thread surface,which depicts the twists of the yarn clearly. Texturecoordinates are calculated after the weave pattern is readfrom the file. The 3D structure of each weave unit is shownin Fig. 7.We render the threads one by one at each iteration. Inthis way, our method for rendering woven cloth is similarto the rendering of knitwear since the 3D structure is notignored. The indices of each of the fibers are calculated andthey are moved in the direction normal to the quadrilateralthey are on. Since the weaving structure is definedprocedurally, there is no need to use alpha values for thegaps between the warp and the weft threads. When theweave pattern is read from the file, each quadrilateral inthe cloth mesh is subdivided into smaller quadrilaterals inARTICLE IN PRESSFig. 7. 3D structure of a weave unit.Fig. 8. Examples of woven cloth. The woven cloth in (b) shows thedifference in the appearance of front and back surfaces.Fig. 9. (a) Woven outfit with (a) thick and (b) thin threads for magnified,distant and close-up views.F. Durupınar, U. Güdükbay / Computers & Graphics 31 (2007) 778–783782order to construct the pattern. The input file consistsof a matrix of binary numbers, where 0 denotes wefton warp and 1 denotes warp on weft. Fig. 8 exhibitsexamples of woven cloth. The woven cloth in Fig. 8(b)shows the difference in the appearance of front andback surfaces. Fig. 9 shows a woven shirt with differentthread sizes and from different distances. Transparentcloth can be obtained by simply reducing the thickness ofthe threads.3. Results and conclusionThe implementation is tested on a PC (T2500, 2.00GHz)with 2GB of RAM. The graphics card is NVIDIAGeForce Go 7400 with 256MB memory size. The softwareplatform is Microsoft Visual C++ 6.0 with OpenGLlibraries. The average frame rates for rendering a cloth with5000 loops (threads) are 625 frames per second (fps) fortexture mapping, 42.73 fps for knitwear with line threads,11.22 fps for knitwear with cylindrical yarns, 8.3 fps forblended knitwear, and 70.42 fps for woven cloth. When thesame cloth patch is animated including the gravitationalforce and self-collisions, the average frame rates (includingphysical simulation and rendering) are 35.46 fps for texturemapping, 11.02 fps for simple knitwear, 2.05 fps for knit-wear with cylindrical yarns, 1.72 fps for blended knitwearARTICLE IN PRESSFig. 10. Clothes before and after antialiasing.F. Durupınar, U. Güdükbay / Computers & Graphics 31 (2007) 778–783 783and 12.84 fps for woven cloth. The higher frame rates fortexture-mapped cloth is due to handling texture mappingon GPU. The difference between the rendering times ofknitwear and woven cloth is due to the complexity ofthe knitwear’s threading structure. The correspondenceof the mass-spring system with the warp/weft structure ofthe cloth is more suitable for woven cloth rather thanknitwear.The frame rates for the blended images are lowercompared to the simple and cylindrical knitwear renderingas two images are generated for blending. However, asblending is only applied for a short-distance range, thisdoes not bring much performance overhead on the overall.Due to the thin rendering primitives, some aliasingartifacts occur for distant views. This is prevented byapplying scene antialiasing using the accumulation buffermechanism. The images before and after antialiasing canbe seen in Fig. 10.Owing to the simplicity of the method, the renderingperformance is mostly real time. As a future work,approaches for real-time animation will also be investi-gated. In addition, currently, knitting is only applicable tosimple stitching structures, i.e., left and right loops; thus,further study on complex stitching techniques with aprocedural method can be a future research direction.AcknowledgmentsThis work is supported in part by EC 6th FrameworkProgram under Grant no. FP6-511568 (3DTV Network ofExcellence Project) and the Scientific and TechnicalResearch Council of Turkey (TUBITAK) under Grantno. EEEAG-105E065.References[1] Meissner M, Eberhardt B. The art of knitted fabrics: realistic andphysically based modelling of knitted fabrics. Computer GraphicsForum (Proceedings of Eurographics’98) 1998;17(3):355–62.[2] Zhong H, Xu Y, Guo B, Shum H. Realistic and efficient rendering offree-form knitwear. Journal of Visualization and Computer Anima-tion 2001;12(1):13–22.[3] Xu Y, Lin Y, Zhong CS, Wu E, Shum H. Photorealistic rendering ofknitwear using the lumislice. ACM Computer Graphics (Proceedingsof SIGGRAPH’01), 2001. p. 391–8.[4] Chen Y, Lin S, Zhong H, Xu Y-Q, Guo B, Shum H-Y. Realisticrendering and animation of knitwear. IEEE Transactions onVisualization and Computer Graphics 2003;9(1):43–55.[5] Ji F, Li R, Qiu Y. Simulate the dynamic draping behavior of wovenand knitted fabrics. Journal of Industrial Textiles 2006;35(3):201–15.[6] Daubert K, Lensch H, Heidrich W, Seidel HP. Efficient clothmodeling and rendering. In: Eurographics rendering workshop’01,2000. p. 63–70.[7] Drago F, Chiba N. Procedural simulation of interwoven structures.In: Vince J, Earnshaw R, editors, Advances in modelling, animationand rendering. Berlin: Springer; 2002. p. 123–38.[8] Adabala N, Magnenat-Thalmann N, Fei G. Real-time rendering ofwoven clothes. In: Proceedings of ACM virtual reality software andtechnology, 2003. p. 41–7.[9] Provot X. Deformation constraints in a mass-spring model todescribe rigid cloth behaviour. In: Proceedings of the graphicsinterface (GI’95), 1995. p. 141–55.[10] Witkin A, Baraff D. Physically-based modeling. ACM SIGGRAPHCourse Notes, no. #25, 2001.[11] Meissner M, Eberhardt B, Strasser W. Knit fabrics. In: House D,Breen D, editors, Cloth modeling and animation. A.K. Peters, 2000.p. 123–43.[12] Glassner A. Digital weaving, part 1. IEEE Computer Graphics andApplications 2002; 22(6):108–18.

Procedural visualization of knitwear and woven cloth

ARTICLE IN PRESS0097-8493/$ - sedoi:10.1016/j.caCorrespondE-mail addrgudukbay@cs.bComputers & Graphics 31 (2007) 778–783www.elsevier.com/locate/cagShort CommunicationProcedural visualization of knitwear and woven clothFunda Durupınar, Ugˇur Gu¨du¨kbayDepartment of Computer Engineering, Bilkent University, Bilkent 06800, Ankara, TurkeyReceived 11 December 2006; received in revised form 22 May 2007; accepted 14 June 2007AbstractIn this paper, a procedural method for the visualization of knitted and woven fabrics is presented. The proposed method is compatiblewith a mass-spring model and makes use of the regular warp–weft structure of the cloth. The visualization parameters for the loops andthreads are easily mapped to the animated mass-spring model. The simulation idea underlying both knitted and woven fabrics is similaras we represent both structures in 3D. As the proposed method is simple and practical, we can achieve near real-time renderingperformance with good visual quality.r 2007 Elsevier Ltd. All rights reserved.Keywords: Fabric rendering; Knitwear; Woven cloth; Physically-based modeling1. IntroductionModeling the visual appearance of cloth is as importantas the simulation of its draping behavior for the sake ofrealism in computer graphics. There are various methodsto produce fabrics from yarn, such as knitting, weaving,braiding or knotting. Particularly, knitting and weaving arethe most common techniques and they have been studied inthe literature.Meissner and Eberhardt [1] introduce a system thatsimulates the physically correct appearance of knittedfabrics. Zhong et al. [2] propose a method for renderingknitwear on free-form surfaces. Another study that usesfree-form surfaces is presented by Xu et al. [3], wherephotorealistic rendering of knitwear is handled by introdu-cing an element called the lumislice. Later, Chen et al. [4]extend this study to include the realistic animation ofknitwear. A recent study in textile research examines thedynamic draping behavior of woven and knitted fabrics [5].In the case of woven cloth, we cannot do simple texturemapping because occlusion and self-shadowing terms comeinto play due to the structure of the individual threads andtheir interweaving pattern. In [6], woven cloth is simulatede front matter r 2007 Elsevier Ltd. All rights reserved.g.2007.06.002ing author. Tel.: +90 312 290 1386; fax: +90 312 266 4047.esses: fundad@cs.bilkent.edu.tr (F. Durupınar),ilkent.edu.tr (U. Gu¨du¨kbay).by computing the lighting using a geometrical model of astitch. Then, by sampling the stitch regularly within aplane, a view-dependent texture with per-pixel normalsand material properties is generated. In [7], the weave ofthe texture is simulated by procedural displacements of thegeometry and the loop is represented as a 2D curve. The3D appearance is given by displacing the loop. A recentstudy that supports a wide variety of weave patterns andcaptures the difference in appearance of the front and backsurfaces of woven cloth is presented by Adabala et al. [8].The color texture, BRDF texture and the horizon maps arepre-computed and the rendering of the images using thesetextures is achieved in real time with a good visual quality.In this paper, we propose a simple and efﬁcientprocedural method for the visualization of knitted andwoven textiles. For this purpose, we use rectangular mass-spring meshes and cut out regular garment patternscomposed of quadrilaterals from the meshes. Regularityboth preserves the general cloth behavior such as shearingand bending, thus preserving physical accuracy and enablesthe deﬁnition of complex knit and weave patterns. In mostof the existing systems, woven fabrics are not simulatedphysically; they are simpliﬁed as 2D structures. We exploitthe regular structure of cloth models and parametricallydeﬁne the repetitious structure of woven and knitted fabric.The weave and knit patterns can be as complex as desiredand can support any color pattern. As the structure is 3D,ARTICLE IN PRESS1.5x2.5xp1p3 p4p2BP8 BP12BP3BP2BP7 BP11BP1BP5 BP6 BP10 BP4 BP91.5x2.5x4xx 3x x xFig. 1. Bonding points of a knit loop.F. Durupınar, U. Gu¨du¨kbay / Computers & Graphics 31 (2007) 778–783 779the resulting garments have different appearances for thefront and back surfaces of the fabrics, depending on theweave or knit pattern as in [8]. However, our method doesnot require preprocessing for texture generation; all thecalculations are done on-the-ﬂy. We achieve near real-timerendering and simulation performance with good visualquality.2. Garment visualizationIn this section, the simulation of the two methods offabric production, i.e., weaving and knitting, is introduced.The cloth model used is a mass-spring model [9]. This is aspeciﬁc case of a particle system in which the particles areconnected by spring forces. The type and behavior of thecloth is determined by the strength of the spring forces andthe topology of the cloth, which in turn is determined byhow the springs connect the particles. Three types ofsprings are used to reproduce the stretching, shearing andbending behavior of cloth. The mass-spring model isadopted due to its simplicity and efﬁciency [10]. The initialgrid structure is a rectangular mesh of particles and springsconnecting these particles in horizontal, vertical anddiagonal directions. In addition, contrary to the irregulartriangular meshes, the mesh structures of garment patternsare regular, which is compatible with the warp and weftdirections of the woven cloth. Thus, instead of drawingthe 2D garment pattern and discretizing it by triangulation,we use an initial rectangular mesh composed of quad-rilaterals and cut out the desired shape by preserving theregularity.2.1. KnitwearThe structure of knitwear is complicated compared toother techniques like weaving. This is due to the 3Dgeometry of a knit loop. In our system, we make use of theparticle system and the mass-spring model of our clothmesh in order to consider the interaction of neighboringloops. For this purpose, the cloth mesh must be a regularlattice consisting of quadrilaterals. There are two typesof basic stitches when knitting: left and right loops.The knitwear pattern, which shows the order of the rightand left loops, is read from an input ﬁle and canbe changed interactively in the program. Each quadrilat-eral contains one type of loop. The structure of the loopin a quadrilateral is deﬁned by the bonding points (BPs).The positions of the BPs can be determined parametricallyusing the vertices of the enclosing quadrilateral asfollows:BP1 ¼67p3pos þ17p4pos ,BP2 ¼5:521p1pos þ1:521p2pos þ1121p3pos þ321p4pos ,BP3 ¼1:521p1pos þ5:521p2pos þ321p3pos þ1121p4pos ,BP4 ¼17p3pos þ67p4pos ,BP5 ¼ p3pos ,BP6 ¼57p3pos þ27p4pos ,BP7 ¼4:528p1pos þ2:528p2pos þ13:528p3pos þ7:528p4pos ,BP8 ¼67p1pos þ17p2pos ,BP9 ¼ p4pos ,BP10 ¼27p3pos þ57p4pos ,BP11 ¼2:528p1pos þ4:528p2pos þ7:528p3pos þ13:528p4pos ,BP12 ¼17p1pos þ67p2pos , ð1Þwhere BPi is the ith bonding point and pjpos is the 3Dposition of vertex j.Due to the thickness of the yarn, these BPs are movedslightly, taking the normal of that quadrilateral intoconsideration. Then, each bonding point BPi is assignedthe value BPi þ ciN, where N is the surface normal and ci isa constant that is deﬁned according to the type of the loopand BP. Thus, the knitted fabric looks different when frontand back views are considered. Fig. 1 shows the construc-tion of the loops.In order to maintain interactivity, complex volumetricmodels or time-consuming methods like [3,11] for render-ing the yarns in a loop cannot be utilized. Three-dimensionality is achieved by drawing cylinders aroundeach yarn and applying texture mapping on these cylinders(see Fig. 2 for a close-up view of a knitwear). Using theposition information of consecutive BPs, a cylinder ofheight jV!j lying along the positive z-axis is found. Then,the cylinder is transformed by a composite transformationARTICLE IN PRESSF. Durupınar, U. Gu¨du¨kbay / Computers & Graphics 31 (2007) 778–783780matrix so as to be oriented in the direction of the vectorbetween the two consecutive BPs. The composite transfor-mation matrix M includes a rotation around y-axis, arotation around x-axis, and a translation:M ¼ TðBPiÞ  RxðaÞ  RyðbÞ‘ ¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃðBPiþ1  y BPi  yÞ2 þ ðBPiþ1  z BPi  zÞ2qa ¼ arcsinððBPiþ1  y BPi  yÞ=jV!jÞ=‘b ¼ arccosð‘Þ. ð2ÞIn order to optimize the performance, varying levels ofdetail from different viewing distances are shown. For distantviews, since the yarn structure cannot be distinguished,instead of drawing cylinders by performing explicit transfor-mations, we simply draw texture-mapped, antialiased lineprimitives between the BPs by hardware-supported linedrawing. The line size, which is determined by the numberof pixels, is proportional to the proximity of the viewer to theFig. 2. The close-up view of a knitwear.Fig. 3. Transition from line primitives to cylinders: (a) distant view with linescylinders. Images at the bottom part show magniﬁed views for each distance.cloth. Another issue to consider is the popping artifacts forthe transition between the two modes of rendering yarns. Thetransition should be gradual and devoid of sudden leaps. Weachieve smooth transition by image blending. For inter-mediate distance ranges, the knitwear is generated with lineprimitives and with cylinders separately. These knitwearimages are blended and the resulting image is rendered. Theblending weights of the two images are determined accordingto the distance of the viewer to the cloth. Blending is handledusing hardware support. The blending operation is illustratedin Fig. 3. In the most distant view, the cloth is rendered withline primitives. Then, at intermediate distance range, theblended image is rendered. The closest view is generated withcylinders. The images at the bottom row demonstratemagniﬁed fragments from each image. The knitwear render-ing algorithms are as follows:Algorithm. RENDERKNITWEAR (cloth, pattern)(1) Compute viewing distance to cloth(2) if viewing distance4 high(3) line width  c/ viewing distance(4) I  GENERATELINETHREADSðcloth; pattern; line widthÞ(5) else if viewing distance 2 ½low, high(6) line width c= viewing distance(7) I  GENERATELINETHREADSðcloth; pattern; line widthÞ(8) I2 GENERATECYLINDRICALTHREADS ðcloth; patternÞ(9) I  (I2  ðviewing distance  lowÞþI1 ðhigh viewing distanceÞÞ=ðhigh lowÞ(10) else(11) I  GENERATECYLINDRICALTHREADS ðcloth, patternÞ(12) Render I; (b) intermediate distance with blended image; and (c) close-up view withARTICLE IN PRESSF. Durupınar, U. Gu¨du¨kbay / Computers & Graphics 31 (2007) 778–783 781Algorithm. GENERATECYLINDRICALTHREADS (cloth, pattern)Fig. 5. Knitwear garments rendered with line primitives.Fig. 6. The physical behavior of knitwear.(1) for each quadrilateral in cloth(2) Compute bonding points BP using Equation 1 andaccording to pattern(3) for each i 1; . . . ; 11(4) V! BPiþ1BPi(5) Find cylinder of height jV!j lying along the positivez-axis(6) Align cylinder with the direction of V!by thetransformation matrix in Equation 2(7) Draw cylinder in image(8) return imageThe algorithm for GENERATELINETHREADS (cloth, pat-tern, line width) is similar to GENERATECYLINDRICALTH-READS (cloth, pattern) with the exception of drawing lineprimitives of size line width instead of cylinders.Fig. 4 shows a knitted shirt from different distances,where the close-up views are rendered with cylinders andthe distant view is rendered with lines. Fig. 5 showsexamples of knitwear rendered with line primitives. Finally,Fig. 6 demonstrates the physical behavior of knit loops,whereby the correlation between the forces acting on thecloth and the distance between the threads can be observed.2.2. Woven clothIn real life, weaving can be performed by means of aloom. The idea of the loom is to interleave two sets ofperpendicular threads [12]. These threads are the warp andthe weft threads. Warp threads are the vertical ones,whereas weft threads are the horizontal ones. Weavingpatterns can be obtained from two types of interleavingof threads, i.e., warp on weft and weft on warp. Variousweaving patterns can be created by ordering these twoFig. 4. Appearance of a knitted shirt from different distances. Close-upview is rendered with cylinders and distant view is rendered with lines.thread interleaving types. Our system works as follows:(i) we read the patterns from a pattern description ﬁle,(ii) draw them in 3D as warp and weft threads bycalculating their positions and (iii) do texture mapping onthem to capture the detailed appearance of the componentﬁbers. The texture is simply an image of a thread surface,which depicts the twists of the yarn clearly. Texturecoordinates are calculated after the weave pattern is readfrom the ﬁle. The 3D structure of each weave unit is shownin Fig. 7.We render the threads one by one at each iteration. Inthis way, our method for rendering woven cloth is similarto the rendering of knitwear since the 3D structure is notignored. The indices of each of the ﬁbers are calculated andthey are moved in the direction normal to the quadrilateralthey are on. Since the weaving structure is deﬁnedprocedurally, there is no need to use alpha values for thegaps between the warp and the weft threads. When theweave pattern is read from the ﬁle, each quadrilateral inthe cloth mesh is subdivided into smaller quadrilaterals inARTICLE IN PRESSFig. 7. 3D structure of a weave unit.Fig. 8. Examples of woven cloth. The woven cloth in (b) shows thedifference in the appearance of front and back surfaces.Fig. 9. (a) Woven outﬁt with (a) thick and (b) thin threads for magniﬁed,distant and close-up views.F. Durupınar, U. Gu¨du¨kbay / Computers & Graphics 31 (2007) 778–783782order to construct the pattern. The input ﬁle consistsof a matrix of binary numbers, where 0 denotes wefton warp and 1 denotes warp on weft. Fig. 8 exhibitsexamples of woven cloth. The woven cloth in Fig. 8(b)shows the difference in the appearance of front andback surfaces. Fig. 9 shows a woven shirt with differentthread sizes and from different distances. Transparentcloth can be obtained by simply reducing the thickness ofthe threads.3. Results and conclusionThe implementation is tested on a PC (T2500, 2.00GHz)with 2GB of RAM. The graphics card is NVIDIAGeForce Go 7400 with 256MB memory size. The softwareplatform is Microsoft Visual C++ 6.0 with OpenGLlibraries. The average frame rates for rendering a cloth with5000 loops (threads) are 625 frames per second (fps) fortexture mapping, 42.73 fps for knitwear with line threads,11.22 fps for knitwear with cylindrical yarns, 8.3 fps forblended knitwear, and 70.42 fps for woven cloth. When thesame cloth patch is animated including the gravitationalforce and self-collisions, the average frame rates (includingphysical simulation and rendering) are 35.46 fps for texturemapping, 11.02 fps for simple knitwear, 2.05 fps for knit-wear with cylindrical yarns, 1.72 fps for blended knitwearARTICLE IN PRESSFig. 10. Clothes before and after antialiasing.F. Durupınar, U. Gu¨du¨kbay / Computers & Graphics 31 (2007) 778–783 783and 12.84 fps for woven cloth. The higher frame rates fortexture-mapped cloth is due to handling texture mappingon GPU. The difference between the rendering times ofknitwear and woven cloth is due to the complexity ofthe knitwear’s threading structure. The correspondenceof the mass-spring system with the warp/weft structure ofthe cloth is more suitable for woven cloth rather thanknitwear.The frame rates for the blended images are lowercompared to the simple and cylindrical knitwear renderingas two images are generated for blending. However, asblending is only applied for a short-distance range, thisdoes not bring much performance overhead on the overall.Due to the thin rendering primitives, some aliasingartifacts occur for distant views. This is prevented byapplying scene antialiasing using the accumulation buffermechanism. The images before and after antialiasing canbe seen in Fig. 10.Owing to the simplicity of the method, the renderingperformance is mostly real time. As a future work,approaches for real-time animation will also be investi-gated. In addition, currently, knitting is only applicable tosimple stitching structures, i.e., left and right loops; thus,further study on complex stitching techniques with aprocedural method can be a future research direction.AcknowledgmentsThis work is supported in part by EC 6th FrameworkProgram under Grant no. FP6-511568 (3DTV Network ofExcellence Project) and the Scientiﬁc and TechnicalResearch Council of Turkey (TUBITAK) under Grantno. EEEAG-105E065.References[1] Meissner M, Eberhardt B. The art of knitted fabrics: realistic andphysically based modelling of knitted fabrics. Computer GraphicsForum (Proceedings of Eurographics’98) 1998;17(3):355–62.[2] Zhong H, Xu Y, Guo B, Shum H. Realistic and efﬁcient rendering offree-form knitwear. Journal of Visualization and Computer Anima-tion 2001;12(1):13–22.[3] Xu Y, Lin Y, Zhong CS, Wu E, Shum H. Photorealistic rendering ofknitwear using the lumislice. ACM Computer Graphics (Proceedingsof SIGGRAPH’01), 2001. p. 391–8.[4] Chen Y, Lin S, Zhong H, Xu Y-Q, Guo B, Shum H-Y. Realisticrendering and animation of knitwear. IEEE Transactions onVisualization and Computer Graphics 2003;9(1):43–55.[5] Ji F, Li R, Qiu Y. Simulate the dynamic draping behavior of wovenand knitted fabrics. Journal of Industrial Textiles 2006;35(3):201–15.[6] Daubert K, Lensch H, Heidrich W, Seidel HP. Efﬁcient clothmodeling and rendering. In: Eurographics rendering workshop’01,2000. p. 63–70.[7] Drago F, Chiba N. Procedural simulation of interwoven structures.In: Vince J, Earnshaw R, editors, Advances in modelling, animationand rendering. Berlin: Springer; 2002. p. 123–38.[8] Adabala N, Magnenat-Thalmann N, Fei G. Real-time rendering ofwoven clothes. In: Proceedings of ACM virtual reality software andtechnology, 2003. p. 41–7.[9] Provot X. Deformation constraints in a mass-spring model todescribe rigid cloth behaviour. In: Proceedings of the graphicsinterface (GI’95), 1995. p. 141–55.[10] Witkin A, Baraff D. Physically-based modeling. ACM SIGGRAPHCourse Notes, no. #25, 2001.[11] Meissner M, Eberhardt B, Strasser W. Knit fabrics. In: House D,Breen D, editors, Cloth modeling and animation. A.K. Peters, 2000.p. 123–43.[12] Glassner A. Digital weaving, part 1. IEEE Computer Graphics andApplications 2002; 22(6):108–18.

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Procedural visualization of knitwear and woven cloth

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