Review of Computer Models for Fabric Simulation Pregled računalniških modelov za simulacijo tekstilij

3D computer technologies are closely linked to all textile ﬁ elds ranging from the designing and constructing of fabrics and garments, virtual human body presentations, interactive virtual prototyping to virtual fashion shows and e-trading. This paper oﬀ ers a review of frequently used methods for fabric simulation. The review is divided into two parts. The ﬁ rst part of the paper comprises currently used techniques, followed by the presentation of basic terms and fabric parameters required for fabric simulations. The second part discusses the approaches and methods for constructing computer models of fabrics. In conclusion, the list of used techniques and parameters for deﬁ ning a computer fabric model are presented together with given future guidance.


Introduction
Computer-aided technologies are already being used in many areas of the textile industry to improve the effi ciencies of the production processes. Th e main function of computer technology within the textile arena is to help designers when designing new models, textile engineers at the garment development process and retailers of garments at performing their selling activities. Actually computer technology enables all of them to produce more products over shorter duration whilst the development processes  Tekstilec, 2014, letn. 57(4), str. 300-314 Review of Computer Models for Fabric Simulation modelling and animation techniques. Th ese two groups focused on the same problems from diff erent aspects. Th e textile community's research concentrated on three broad categories: modelling the geometric-mechanical structures occurring at yarn crossings, modelling the mechanics of fabric using continuous elastic sheets and rods, and modelling the macroscopic geometric features of fabric [1,2]. In contrast the computer graphics community was motivated towards developing simple fabric models with geometric structures that resemble fabric as well as effi ciently reproducing the virtual appearance of fabric [1−4]. However, both areas present and study the behaviour of fabrics and garments from their own viewpoints. For example, for several years animators have used models with little consideration of the physical laws derived from the real world. Most of the time animation sequences have shown geometric and rigid objects moving and changing according to simple or complex predefi ned transformations [1,5,6]. During that time the simulation of complex fabric behaviour within real environments can only be reached through an optimal combination of modelling techniques for fabric behaviour and numerical methods. Th ey must together combine the high computation effi ciency, stability and visual realism that is required for complex garment forms. However, during further development by textile and computer engineers, the virtual simulations of fabrics and garments necessitated very complex work because of the combination of used techniques involving physical/mechanical simulation, collision detection, and user interface techniques for creating garments [7]. Nowadays, fabric simulation's potential has been developed for use throughout the garment industry. Over the last decade virtual garments for the garment industry have incorporated more and more computer applications not only regarding graphics but also CAD techniques. Nowadays many usable commercial programs for garment simulation and prototyping are provided by the leading CAD/CAM producer, such as Gerber [8], Lectra [9], Assyst-Bullmer [10], and Optitex [11].

Basic terms and defi nitions
At the beginning this paper presents the basic terms and defi nitions commonly used when explaining computer simulations of fabrics and garments. Textile vs. Fabric vs. Cloth: Th e terms fabric and cloth are used within textile assembly trades (such as tailoring and dressmaking) as synonyms for textile. However, there are subtle diff erences in these terms during specialised usages. Textile refers to any material made of interlacing fi bres. Fabric refers to any material made through weaving, knitting, spreading, or bonding that may be used during the production of further goods (garments, etc.). Cloth may be used synonymously with fabric but oft en refers to a fi nished piece of fabric used for a specifi c purpose, for example, tablecloth [12]. Th e term fabric will be used throughout this paper. Fabric model is a term used for a constructed geometrical, physical and mechanical fabric model for simulating fabric within a computer program; usually within the context of 3D computer graphics [12]. Fabric simulation concerns the modelling of fabric for its realistic behaviour simulation [13]. In other words, fabric simulation is the process of replicating the movement and deformation of a piece of fabric or clothing by mimicking how that fabric would react in the real world. Garment simulation: means the physical simulation of cloth-like objects for use in 3D computer graphics. Examples of such objects could be virtual clothing with animated 3D character, a tablecloth, fl ags or curtains etc. [14]. Virtual prototyping of garments: An offi cial defi nition of virtual prototyping regarding fabrics/garments cannot be found in the literature. In respect of this many defi nitions for other application areas are presented [15]. Th e highlights of two of them cover all product types, and they can also be used for virtual fabric/garment prototyping.
Virtual prototyping is a soft ware-based engineer-• ing discipline that entails modelling a mechanical system, simulating and visualising its 3D-motion behaviour under real-world operating conditions, and refi ning/optimising the design through iterative design studies prior to building the fi rst physical prototype [16]. Virtual prototyping or digital mock-up, is a com-• puter simulation of a physical product that can be presented, analysed, and tested from the concerned product's life-cycle aspects such as design/ engineering, manufacturing, service, and recycling as if on a real physical model. Th e constructing and testing of virtual prototype models is called virtual prototyping [17]. Tekstilec, 2014, letn. 57(4), str. 300-314

Computer simulations of fabrics
Th e qualities of computer models for fabric simulation depends on several predefi ned parameters such as fabric properties, available computer models, schemes for performing mechanical simulation, and fabric surface discretisation [3].

Characterisations of fabrics for computer simulations
Fabrics have by nature special properties that generate interesting shapes when draping or designing 3D shapes of objects. Fabrics can be described as thin, non-homogeneous material in all directions (warp, weft , diagonal) with large deformation under low loading. For successful fabric simulation, the mechanıcal properties are mainly elasticity and viscoelastic parameters, as well as environmental, and need to be defi ned. In the cases of high dynamic situations viscosity parameters should also be precisely defi ned [3]. Among elasticity parameters are important Young modulus, shear and bending rigidity modulus, and the Poisson coeffi cient [1, 18−20]. Initially, researchers focused on input parameters for realistic virtual simulations of real fabrics. Th ey studied a material's behaviour according to its mechanical properties. In the fi rst application of fabric simulations, no measured mechanical and physical properties of fabrics had been used as input parameters. Parameters for diff erent fabric behaviour were set randomly as, for instance, similarly to rubber or they were based on previous experience [3,21]. As input, researchers also used simplifi ed fabric properties as represented by linear and isotropic behaviour assumptions [22]. Furthermore, some simulation systems were tested for their applicability regarding empirical data such by KES-FB (Kawabata Evaluation System) and FAST (Fabric Assurance Simple Tests [2, 17-19, 23−25]. Moreover, besides the KES-FB parameters fabric drape properties were also used for simulation. Furthermore, a simulated fabric also reacts with its environment and also the amount of objects reactions, frictions and self-collision detections between fabrics layers have to be taken into account. Th e most obvious external force exerted on the fabric is universal gravity that should always be taken into account by computer simulation of fabrics. Furthermore, other environmental circumstances should also be included, for instance, if a fabric moves freely in the air or it is in contact with and interacts with the underlying surface i.e. with the human body [3].

Fabric modelling within the textile community
In fabric simulation, the main research key factor is to understand the materials' properties of fabrics. Th e textile community's research was concentrated from the beginning on studying the fabric behaviour from the mechanıcal engineering point of view. Th e research is concentrated on both micro and macro levels when describing the fabric's behaviour [1]: micro level: where the fabric's characteristics are defi ned according to its structure, i.e. interweaving of warp and weft threads in woven fabrics or loops in knitted fabrics, macro level: where a fabric is regarded to as a continuum. It is described on the basis of small particles that are interlinked according to laws of physics. Th e fabric models are presented as geometrical and continuum models.

a) Geometrical model of fabric
Th e fi rst fabric model was the geometrıcal yarn-level model developed by Pierce in 1930 [26] and was later modifi ed several times [1]. Th e model consists of two yam cross-sections constrained by a third yarn segment running perpendicular to the crosssections. Physical phenomena forming amongst the threads were defi ned based on laws of physics and mechanics, Figure 1. Th e results showed that the geometric model was very complex and therefore unsuitable for computer processing at that time. Tekstilec, 2014, letn. 57(4), str. 300-314

b) Continuum model of fabric
Th e observations of fabrics' properties on a continuum level introduced more desirable results. Th e more commonly used were energy-based and elasticity methods. Energy-based methods attempt to model the parameters and structures of fabric by creating and minimising equations that defi ne the strain energy within the fabric. Th ese methods are classifi ed into two groups as low level structural and high-level continuum models. Th e low-level methods were used to model a yarn crossing structure and calculated only a few of the conventional mechanical parameters of woven fabric and some of the geometrıcal parameters focused on fabrıcs' cells. Th e high-level continuum models explored the fabrics' mechanical properties by applying the conventional theory of elastic plates and shells. De Jong and Postle [27] are known as the investigators and developers of low-level models for fabrics. Th ey developed a model based on yarn deformation, and using that model were able to analyse strain energy independent of yarn structure. Th ey separated the total strain energy of yarn structure into four constituents as bending, torsion, lateral compression and longitudinal tension. With their proposed model, they estimated the load-extension, decrimping and bending rigidity properties for various materials. Th eir model was modifi ed by Knoll, Hearle and Shanahan [28−30]. Th e high-level energy-based method for studying fabric properties was fi rst presented by Amirbayat and Hearle [31,32]. Th ey proposed an energy-based method for modelling the large-scale deformations of a thin, fl exible sheet. Th e reason arose because the conventional elasticity-based techniques for fabric modelling had many limitations. Th ey state that the thin shell theory is only a collection of specialcase analyses derived for specifi c, simple three-dimensional geometries, implying that it is unsuitable for modelling the arbitrary and complex geometries of fabrics. Another energy method was presented by Ly [33] who simulated a three-dimensional buckling of a square fabric piece defıned as an anisotropic thin plate under the combined eff ect of tensile and shear forces. Th is model's limitation regarding fabric representation is in its specifi c boundary conditions according to the kinds of fabric. At the same time, another group of scientists developed fabric models based on the theory of elasticity. Kilby [34] fi rstly presented the application of an elasticity theory on woven fabrics. He developed planar stress-strain relationships for a simple trellis using conventional elasticity-based analysis. He assumed that fabric can be modelled with a rectilinear trellis in which the elements are pivoted together at their intersection points but do not pass under and over as is characteristic for fabrics. Lloyd, et al. [35] used this method for investigating fabric behaviour folding in respect to its weight. Th is method was criticised [28] because of the assumption of small strains and deformations. However, in the literature other types of elastic-based methods are reported for fabric modelling. For example Amirbayat [31,32] modelled a sheet of fabric as a thin isotropic rectangular plate in order to determine the strain necessary to produce buckling when opposing concentrated forces are applied to the sheet. Imaoka et al. [55,56] developed a continuum mechanics model of fabric based on the large deformation shell theory. Collier, Govendary, Jevšnik [18,20,36] presented a fi nite element approach to modelling the draping behaviour of fabric. Th ey characterised the deformations of fabric whilst draping as a non-linear small-strain/large-displacement. Gan et al. [37] investigated woven fabric deformation as a large displacement, small strain problem and solve it with a nonlinear fi nite element method. Shell/plate elements are used in woven fabric modelling and when applying them certain points need to be taken into account such as calculations of shell normal, shear elimination, and stress-strain connection determinations [1]. Jevšnik combined the shell-plate theory with the theory of lamina for modelling fused panels. A fused panel was defi ned as a two layer lamina, Figure 2.  [19] Each layers (fabric and interlining) were described with its properties i.e.: specifi c density, fabric thickness and rheological parameters such as Young's and shear modulus in warp and weft directions, and the Poisson ratio. Th e connection between the fabric and fusible interlining was considered as ideal with negligible thickness of thermoplastic. For both fabric and fusible interlinings it was considered that they were a continuum with homogeneous and orthotropic properties [18,36].

Fabric modelling within the computer graphic community
Further development was taking place at the same time within the textile engineering and computer arenas. In garment simulation the main key research factor is to develop a suitable fabric model for studying mechanical and physical legality. In contrast to the textile engineers the computer engineers try to develop fabric models with low computation costs and higher effi ciency [1]. Fabric modelling techniques within the computer graphic community are classifi ed into three categories: geometrical, physical, and hybrid.

a) Geometrical-based models
Geometrical models were the fi rst techniques to be used in computer graphics for fabric simulation. Th e models were simple geometrical formulations of fabric without the fabrics' physics of dynamic and mechanıcal properties such as wrinkle formulations on local surfaces. Th ese models were unsuitable for complex reproducible fabric simulation. Th ey focused on appearance, particularly folds and creases, which were represented by geometrical equations. Th e geometrical models' characteristics were of high controllability and predictable animation sequences. However, these models were also insuffi cient for responding to situations for exhibiting high variability. Weil presented the fi rst attempt at fabric simulation using a geometrical model in 1986 [38]. At the same time, method was also developed for rendering a fabric's surface once it is in free-hanging shape. Th e surface fabric was described using constraint points by tracing catenaries between each pair. A line between constraint points refers to the (row, column) coordinates through which a line scan-converted from one point to the other would pass within the grid coordinate system. For example, if one constraint point was at grid coordinate (2,3) and another was at (5,3), the line between the two points would include grid coordinates (3,3) and (4,3), Figure 3.  [37,38] A geometrical method for simulating the wrinkles of fabric by rectangular hanging between two points under additional mechanical constraints such as stretching, bending and gravitational forces was developed by Tailler et al. [40]. Th e fi rst attempt at automation of garment manufacturing using the geometrical model for simulating a garment's parts was done by Hints et al. [41]. Th ey constructed the fi rst garment shape adapted to the body by interpolating a user-defi ned set of points. Agui et al. presented the next attempt at computer modelling the sleeve on a bent arm [39]. Th ey constructed the fabric as a hollow cylinder consisting of a series of circular rings. Th e confi gurations of the folds on the sleeve were constructed as a consequence of the diff erences in curvatures between the inner and outer parts of the bent sleeve. Th e researchers Ng et al. [33] used a geometrical approach for developing an animation tool for the quick reproductions of fabric images. Th ey presented the fabric as two layers that consisted of a series of sections with identical numbers of vertices on each layer, Figure 4.   [33] When using the model the folds occurred as a result of the underlying structural formations. Moreover, a set of rules was developed for generating Tekstilec, 2014, letn. 57(4), str. 300-314 Review of Computer Models for Fabric Simulation folds automatically. A fully geometrical approach for non-extensible fabric deformation was developed and simulated by Ming Chen and Kai Tang [22]. Th at model was purely geometrical and did not involve stiff ness coeffi cients or elastic modulus regarding problem formulation. It was able to simulate for example the wrinkles, only theoretically. Th e obtained simulation for a skirt in Figure 5 was achieved for 100% non-extensible fabric [22]. Th e mentioned method has many conservative solutions; therefore their simulations are very artifi cial.
Initial shape Different postures and skirts' shapes All the mentioned models haven't included any mechanical properties but by defi nition the points and their interpolations simulated the imitations of real fabric behaviour. Th e folds' deformations were generated along the lines of a fabric's surface, and the folds could be either automatically determined or manually edited [22]. Th e main interest of the used geometrical models for fabric simulation application is to have a computationally effi cient and highly controllable model which can perform the simulation well within certain predefi ned fabric behaviour. Geometrical models do not consider the physical properties of fabric. Rather they focus on appearance, particularly folds and creases, which they represent by geometrical equations. Geometrical techniques require a considerable degree of user intervention; they can be regarded as a form of advanced drawing tool.

b) Physical-based models
Physically-based models represent the fabric as continuously divided on triangular or rectangular grids. Th e points have defi ned fi nite masses at the intersections. Th e numbers of points are defi ned according to the used problems and techniques. Th e continuum models for computer simulation can fi nd solutions as fabric models based on simple geometry and also for more complex formulations of fabric structure presentation such as models based on energy and elasticity. Th e main continuum mechanical models provide accurate fabric behaviour simulation derived at directly from mechanical laws. In contrast to the geometrical model, the continuum models need to be highly adaptable for accurate computations of the dynamics of objects having well-defi ned mechanical constraints and relatively stable mechanical contexts. Th e continuous models are independent of geometrical representation therefore with them it is possible to solve complex numerical problems by integrating various constraints. Th e complex computation requirements are the reason for their slow performances. Th e Lagrange or fi nite methods are used for fabric behaviour calculations. Th e more common models for interpreting the interactions amongst defi ned points are energy-based models, models based on the theory of elasticity, particle-based and fi nite element models.

c) Energy-based models and models based on the theory of elasticity
Energy-based models and models based on the theory of elasticity are the more common models for interpreting the interactions amongst defi ned points. Th e fi nite element method and Lagrange equations are mainly used for the problem solving of fabric behaviour. Next, very oft en used techniques for modelling are article-based models sometimes referred to as mass-spring models. During this modelling technique an object is assumed to be a collection of mass points that are interconnected by structural, bend and shear springs through a grid structure. Th e mass points (particles)

Structural Springs Shear Springs
Bend Springs All Springs a b Figure 6: Particle-based model: the simple part of the particle model for fabric simulation (a) and the three types of mass springs (b) [1] Tekstilec, 2014, letn. 57(4), str. 300-314 Review of Computer Models for Fabric Simulation are interconnected by linear springs within the position and velocity at a certain time and mass [1−3]. Th e way the springs are connecting the particles (the topology of the object) and the diff erences in strength of each spring infl uence the behaviour of the object as a whole. A simple particle model for fabric simulation [1][2][3] is shown in Figure 6. Th e fi rst major system for simulating fabric and deformable surfaces was developed by Terzopoulos et al [21]. His model was used based on the elasticity theory and the Lagrange formulation for the calculation of fabric behaviour, Figure 7.   [21] A physical-based model for modelling draped fabric in 3D environmental by a 2D grid was developed by Feynman [42]. He proposed an energy equation from the theory of elastic plates when energy is at a minimum when the fabric is draped: where P ij is energy at point, k s , k b , k g are elasticity, bending, density constants, E elast ij is elasticity energy, E bend ij is bending energy and E grav ij is gravitational energy.
Terzopoulos's model was later extended by Th alaman et. al [3,43]. Th alaman's research team has dealt with the visualisation problems using an analogous approach for the production of a garment by manufacturing. Th is principle of garment prototyping is still a priority during the computer-based garment simulation of fabrics. Her work was mainly focused on collision detection and response, and the designing a complete set of clothing. Her research colleague Volino et al. [44,45] used the theory of elasticity and Newtonian dynamics to simulate fabric, and improved the collision detection of Th alaman`s system. Breen et al. [1] simulated fabric behaviour using the particle-based model. Th is method treats the crossing points of the warp and weft threads as particles. Th e Breen et al. simulation was in two stages. In the fi rst, particles are allowed to fall freely (Figure 8a). In the second stage (Figure 8b), an energy minimisation process is applied to the inter-particle energy functions to generate fi ne detail in the shape of the fabric. Zhang and Yuen [46] presented a fast fabric simulation method using multilevel meshes based on the Provot model [47]. Th e aim of this method was to speed up fabric simulation whilst achieving realistic simulation results. At each phase, the mesh triangular size is smaller than that of the previous phase and therefore calculation is faster. Th e multilevel method provided very good results especially for fabric draping simulation, Figure 9 [46]. a b Figure 9: Draping simulation of a piece of fabric hanging over a disc plate with multilevel meshes: initial position (a), fi nal position aft er simulation phase (b) [46] d) Particle-based approach Th is particle-based approach to fabric modelling was fi rst applied to the problem of computing static drape [2]. A piece of fabric is modelled as a two-dimensional array of particles conceptually representing the crossing points of warp and weft yarns within a plain weave. Th e various inter-crossing strain energies are represented by energy functions parameterised by simple geometrical relationships amongst particles. Th ese energy functions take into account the four basic mechanical interactions of yarn collision, yarn stretching, out-of-plane bending and trellising (in-plane bending) that are shown graphically in Figure 10. Th e model does not consider twisting strain, however. Th e strain energy for crossing particle i is given by equation [2]: where E i is strain energy for crossing article, E repel i is artifi cial energy of repulsion that eff ectively keeps, is E stretch i energies of tensile strain between each particle and its four-connected neighbours, is E bend i energy due to yarns bending out of the local plane of the fabric and E trellis i is energy due to bending around a yarn crossing in the plane.

Bending
Trellising Collision and Stretching Figure 10: Fabric model's energy function [2] Breen [1] simulated the static drape of fabrics and later Eberhardt et al. [48] simulated the fabric drape as dynamic phenomena on the table, on the sphere, and the castle, and the fi nal drape was quick and quite realistic. Particle-based models were used for many applications. Ocabe et al. [49] used visualisation tools focused on automisation of the traditional garment manufacturing processes. Li et a1. [50] simulated fabric immersed within an airfl ow, Gröller et al. [51] modelled the microstructure of the knitted fabrics. Th ey also built a rendering method for the simulation of knitted fabrics (fabric modelling and animation). Th e classic mass-spring model shown in Figure 11 was used by Provot [47].

Structural Springs
Shear Springs Flexion Springs Figure 11: Classical mass-spring model [47] Furthermore, Baraff and Witkin [52] used a triangulated mesh to represent the fabric structure, using a continuum formulation on a per-triangle basis for in-plane deformation, and the angle between adjacent triangles to measure out-of-plane deformation, Figure 12. Figure 12: Baraff 's and Witkin's simulation using continuum mechanics [52] e) Finite element method Th e fi nite element is a frequently used method for numerical analysis and is based on the usage of matrix algebra. Solving problems was based on discretisation of arbitrary construction into suitable fi nite elements. Th is method is also being developed today as a special scientifi c discipline within the textile area.
Th e development of programs for solving nonlinearity problems is producing very satisfactory results as in the cases when large displacements and small deformations appear that are signifi cant for a fabric. R. Collier et al. were the fi rst to use the fi nite element method for modelling fabric drape [18]. Th e fabric was described as two-dimensional and orthotropic materials with linear properties. He used Young's and shear modules for calculating within warp and weft directions, measured on KES FB system and Poisson's ratio to sum up as per literature. Th e calculated drape coeffi cient was analysed by experimental measurement using a Cusik drape metre. Drapability over the square table was analysed by Govindaray using the fi nite element method [20]. He studied the draping behaviour of fabrics by using a non-linear fi nite element method based on a classical non-linear plate theory. J. Hu et al. [53] used a geometrically nonlinear fi nite-volume method for the numerical simulation and analysis of fabric drape. An initially fl at circular fabric sheet is fi rst subdivided into a number of structured fi nite volumes by mesh lines along warp and weft directions, resulting in rectangular internal volumes and triangular or quadrilateral boundary volumes. Deformation and rotation as a small strain characteristic of using numerical calculations fabric was investigated by Yu [54]. He modelled the fabric using plate and shell elements and the "Alpha" -constant stiff ness matrix iterative method was used to reduce simulation time. Th e advantage of this method is that less computation time is required but the disadvantage is that the degree of non-linearity in the drape problem is incompletely represented by the unknown coeffi cient matrix during iteration. Figure 13: Drape simulations of fused paned using finite elements [36] S. Jevšnik [36] used the fi nite elements method for modelling and simulating fused panel drape, Figure  13. Th e fused panel was treated as a two layer laminate; one lamina was fabric and the other lamina was the fusible interlining, therefore the mechanical model of a fused panel was based on the laminate theory. Th e author also simulated the extension and shear properties according to a measuring process using KES methodology for fabric and fusible interning [19,36].

Hybrid model
Th e hybrid techniques combine the physical and geometrical methods. Th e advantages of combining the physical and geometrical methods were fi rst recognised by Rudomin, Kunii, Taillefer and Tsopelas. Rudomin [55] developed a model that is a combined geometrical-physical model. He developed a method for roughly estimating fabric suspended with a restraint points set. During the same period Kunii [56] developed a hybrid particle model for the simulation of the wrinkles on bent arms. Th e particle system is made up of a grid where each node is linked to its neighbours by springs. Similar wrinkles were modelled by Tsopelas [57]. He treated garments as thin cylindrical tubes under axial loads and simulated garment folds using the deformation theory. Th is process focuses on regions where folds are most likely to appear, that is those regions with large curvatures. Th ese occur at the back of the knees. Taillefer [40] categorised the folds of a hanging fabric into two types, horizontal and vertical, as shown in Figure 14.
Horiyontal folds Vertical folds Figure 14: Simulation of horizontal and vertical types of folds [40] Th e bending properties are one of the most infl uential parameter for realistic fabric simulation especially for presentation involving wrinkling and folding. Pabst et. al. [58] presented bending fabric model that makes use of measured moment-curvature data Tekstilec, 2014, letn. 57(4), str. 300-314 Review of Computer Models for Fabric Simulation and a seam model that signifi cantly improves the realism of garment simulations. Th e effi cient physically-based bending model using hysteresis in fabric simulation was developed also by Wong et al [59].
Th ey compared the bending model with previous methods and plasticity models [1,17,44]. Th e model is not much more complicated than previous models, and experiments showed that with a small extra computation time satisfactory bending hysteresis and plasticity could be obtained [58]. One of the last developed methods for physically-based fabric simulation is Continuum-based Strain Limiting (CSL) method which is suitable for anisotropic biphasic materials [61].

Accuracy of fabric computer simulations
Th e accuracy of computer processing fabric simulation is, besides the selected model, the next important parameter. However, the accuracy of computer simulation depends on the selected model of a fabric according to the phenomenon of its deformation. In the case of 2D textile products (fl ags, curtain) the simplest mathematical models are chosen for calculation (linear mathematical models). For garments and other 3D textile forms, more complex models have to be selected such as polynomial models, interval models, and discrete models. Th e discrete model is seldom interesting for fabric simulation models [3], Figure 15. Continuum mechanics studies the states of fabrics' surfaces and volumes through quantities varying continuously within space and time. Each physical parameter of the material is represented by a scalar or vector value continuously varying according to position and time. Mechanical laws can then be represented as a set of partial diff erential equations which hold throughout the volume of the material. Particle systems discretise the material itself as a set of point masses ("particles") that interact with a set of "forces" that approximately model the behaviour of the material [3]. Computational time for fabric simulation depends on the fabric object's discretisation. Th e density of discretisation depends on the method of numerical simulation, the shapes and motions of the fabrics, as well as the available computer hardware. Triangular meshes are the more common representations for complex fabric objects [3]. Th e mechanical computer models of fabrics have to provide the simulation of fabric properties rapidly and realistically. Th e performance of fabric simulation depends on adequate implementation of algorithms and numerical methods. In the literature, there are many ways of compiling computer systems for fabric simulation and their performances are improving from year to year [1,3]. Ultimately, the rendering process of the fabric should also be included for the desired end-look of Figure 15: A particle system and continuum mechanics [3] the simulated fabric. Volino and Magnenat-Th almann in their book pointed out four parameters having a signifi cant infl uence on the success of fabric simulation [3]: scope: -the simulation system should support the mechanical behaviour and the properties to be simulated. accuracy: -the mechanical system should be simulated in a very accurate way within whatever possible context. robustness: -the simulation system should be able to compute the mechanical system whatever the context, which can vary along the simulation regarding accuracy, and no particular situation should cause the simulation to fail. speed: -speed is obviously one of the major values of a good mechanical simulation system. Th e speed is validated by offl ine computation systems, interactive applications, and real-time applications. Table 1 collates and presents some of the used models and techniques for fabric simulation. Th e collected data based on literature reference [39] and authors' literature studies and own research experiences. Certain of better known models are also described in the previous paragraphs.

Comparisons between used methods
Th e geometrical techniques for constructing the computer models of fabrics have not include the measured fabric parameters, because they were constructed on the same assumptions of fabric parameters. Th e advantage of this is that the computation time is faster than by other modelling techniques. Physical techniques are the most commonly used for modelling fabric models because of reasonable computation time and quite good realistic presentations of virtual fabric behaviour. Th e simulation of fabrics' behaviour using the hybrid models provides very good realistic presentations of fabrics within a virtual environment but the computation time is very time-consuming.

Conclusions
Visualisation of a garment within a virtual environment is an exciting branch for textiles as well as for computer graphics engineers. Th e correct selection of a fabric model for virtual simulation is a very important issue during the designing of an effi cient fabric simulation system. Nowadays developed fabric models for obtaining realistic fabric behaviour are still insuffi cient even though many already complex applications have been presented for virtual clothing simulation. From the presented review it can be concluded that over the past decades within the textile engineering and computer arenas new signifi cant solutions of models for fabric simulations have not been forthcoming. Th e development of fabric models for computer simulation was mostly focused on physically-based models or their hybrids. Th eir main advantage is good realistic presentations of simulated fabrics. Th e geometrical techniques are based on the appearance of the fabric sample without the mechanical and physical properties of fabric. Researchers have presented more or less upgraded or modifi cations of existing methods. Th e reasons are probably in the necessity of developing highly effi cient computer performances that can simulate fabric on the micro level with the least possible limitations regarding fabric characteristics.