Pregled računalniških modelov za simulacijo tekstilij

300 Simona Jevšnik1, Fatma Kalaoğlu1, Sena Terliksiz1 and Jure Purgaj2 1Istanbul Technical University, Textile Technologies and Design Faculty, Istanbul, Inon. Cad. No. 65, 34437, Turkey 2Pädagogische Hochschule Wien, Institut für Berufsbildung, Mode- und Designpädagogik, Grenzakcerstraße 18, A-1100 Wien, Austria Review of Computer Models for Fabric Simulation Pregled računalniških modelov za simulacijo tekstilij Scientific Review/Pregledni znanstveni članek Received/Prispelo 10-2014 • Accepted/Sprejeto 11-2014 Abstract 3D computer technologies are closely linked to all textile fields 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 offers a review of frequently used methods for fabric simulation. The review is divided into two parts. The first 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 defining a computer fabric model are presented together with given future guidance. Keywords: CAD/CAM in textiles, fabric simulations, fabric models Izvleček Računalniške 3D tehnologije so čedalje bolj prisotne na različnih tekstilnih področjih, od konstruiranja in izdelave tkanin in oblačil, virtualne predstavitve človeškega telesa, interaktivnega virtualnega prototipiranja, do virtualnih modnih revij in e-trgovanja. Prispevek podaja pregled pogosteje uporabljenih računalniških metod za simulacijo tekstilij. Razdeljen je na dva dela: v prvem je opisano trenutno stanje uporabe računalniških modelov za simulacijo tekstilij, temu sledi razlaga osnovnih pojmov in potrebnih parametrov za njihovo simulacijo. V drugem delu so predstavljeni pristopi in metode za njihovo izgradnjo. V zaključkih je podan pregled najznačilnejših uporabljenih tehnik in parametrov, potrebnih za definiranje računalniških modelov tekstilij ter smernice nadaljnjega razvoja. Ključne besede: CAD/CAM v tekstilstvu, simulacije tekstilij, modeli tekstilij 1 Introduction Computer-aided technologies are already being used in many areas of the textile industry to improve the efficiencies of the production processes. The 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 Corresponding author/Korespondenčna autorica: Assoc. Prof. D.Sc. Simona Jevšnik E-mail: [email protected] are geographically dispersed. In addition, computer technologies enable all participants (engineers, designers, and sellers) to adopt quick responses to market requirements and perform quick fabric and garment design modifications thus allowing their garments to be sold more globally. Garment simulation has long histories in both computer graphics and textile engineering. Fabric modelling research began within the textile engineering community in the 1930s with the first fabric model developed by Pierce [1]. In the middle of 1980s the computer graphics community started to study fabric Tekstilec, 2014, letn. 57(4), str. 300–314 DOI: 10.14502/Tekstilec2014.57.300–314 Review of Computer Models for Fabric Simulation modelling and animation techniques. These two groups focused on the same problems from different aspects. The 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 efficiently 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 predefined 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. They must together combine the high computation efficiency, 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]. 2 Basic terms and definitions At the beginning this paper presents the basic terms and definitions commonly used when explaining computer simulations of fabrics and garments. 301 Textile vs. Fabric vs. Cloth: The terms fabric and cloth are used within textile assembly trades (such as tailoring and dressmaking) as synonyms for textile. However, there are subtle differences in these terms during specialised usages. Textile refers to any material made of interlacing fibres. 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 often refers to a finished piece of fabric used for a specific purpose, for example, tablecloth [12]. The 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, flags or curtains etc. [14]. Virtual prototyping of garments: An official definition of virtual prototyping regarding fabrics/garments cannot be found in the literature. In respect of this many definitions for other application areas are presented [15]. The highlights of two of them cover all product types, and they can also be used for virtual fabric/garment prototyping. • Virtual prototyping is a software-based engineering discipline that entails modelling a mechanical system, simulating and visualising its 3D-motion behaviour under real-world operating conditions, and refining/optimising the design through iterative design studies prior to building the first physical prototype [16]. • Virtual prototyping or digital mock-up, is a computer 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. The constructing and testing of virtual prototype models is called virtual prototyping [17]. Tekstilec, 2014, letn. 57(4), str. 300–314 302 Review of Computer Models for Fabric Simulation 3 Computer simulations of fabrics in the air or it is in contact with and interacts with the underlying surface i.e. with the human body [3]. The qualities of computer models for fabric simulation depends on several predefined parameters such as fabric properties, available computer models, schemes for performing mechanical simulation, and fabric surface discretisation [3]. 3.1 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 defined. In the cases of high dynamic situations viscosity parameters should also be precisely defined [3]. Among elasticity parameters are important Young modulus, shear and bending rigidity modulus, and the Poisson coefficient [1, 18−20]. Initially, researchers focused on input parameters for realistic virtual simulations of real fabrics. They studied a material’s behaviour according to its mechanical properties. In the first application of fabric simulations, no measured mechanical and physical properties of fabrics had been used as input parameters. Parameters for different 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 simplified 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. The 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 3.2 Fabric modelling within the textile community In fabric simulation, the main research key factor is to understand the materials’ properties of fabrics. The textile community’s research was concentrated from the beginning on studying the fabric behaviour from the mechanıcal engineering point of view. The research is concentrated on both micro and macro levels when describing the fabric’s behaviour [1]: – micro level: where the fabric’s characteristics are defined 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. The fabric models are presented as geometrical and continuum models. a) Geometrical model of fabric The first fabric model was the geometrıcal yarn-level model developed by Pierce in 1930 [26] and was later modified several times [1]. The 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 defined based on laws of physics and mechanics, Figure 1. Figure 1: Peirce’s geometric fabric model [25] Legend: l – yarn lenght, h1 and h2 – crimp height, φ – weave angle, d – yarn diameter, D – sum of the yarn diameters, p – yarn spacing The 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 Review of Computer Models for Fabric Simulation b) Continuum model of fabric The observations of fabrics’ properties on a continuum level introduced more desirable results. The 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 define the strain energy within the fabric. These methods are classified into two groups as low level structural and high-level continuum models. The 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. The 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. They developed a model based on yarn deformation, and using that model were able to analyse strain energy independent of yarn structure. They 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. Their model was modified by Knoll, Hearle and Shanahan [28−30]. The high-level energy-based method for studying fabric properties was first presented by Amirbayat and Hearle [31, 32]. They proposed an energy-based method for modelling the large-scale deformations of a thin, flexible sheet. The reason arose because the conventional elasticity-based techniques for fabric modelling had many limitations. They state that the thin shell theory is only a collection of specialcase analyses derived for specific, 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 effect of tensile and shear forces. This model’s limitation regarding fabric representation is in its specific 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] firstly presented the application of an 303 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. This 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 finite element approach to modelling the draping behaviour of fabric. They 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 finite 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 defined as a two layer lamina, Figure 2. Layer 1 – Fabric 1 2 Bond Layer 2 – Interlining Figure 2: Fused penal of fabric and fusible interlining two layer lamina [19] Each layers (fabric and interlining) were described with its properties i.e.: specific density, fabric thickness and rheological parameters such as Young’s and shear modulus in warp and weft directions, and Tekstilec, 2014, letn. 57(4), str. 300–314 304 Review of Computer Models for Fabric Simulation the Poisson ratio. The 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]. 3.3 Fabric modelling within the computer graphic community Figure 3: Weil`s geometrical model (a) and simulated fabric (b) [37, 38] 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 efficiency [1]. Fabric modelling techniques within the computer graphic community are classified into three categories: geometrical, physical, and hybrid. 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]. The first attempt at automation of garment manufacturing using the geometrical model for simulating a garment’s parts was done by Hints et al. [41]. They constructed the first garment shape adapted to the body by interpolating a user-defined set of points. Agui et al. presented the next attempt at computer modelling the sleeve on a bent arm [39]. They constructed the fabric as a hollow cylinder consisting of a series of circular rings. The configurations of the folds on the sleeve were constructed as a consequence of the differences in curvatures between the inner and outer parts of the bent sleeve. The researchers Ng et al. [33] used a geometrical approach for developing an animation tool for the quick reproductions of fabric images. They presented the fabric as two layers that consisted of a series of sections with identical numbers of vertices on each layer, Figure 4. a) Geometrical-based models Geometrical models were the first techniques to be used in computer graphics for fabric simulation. The models were simple geometrical formulations of fabric without the fabrics’ physics of dynamic and mechanıcal properties such as wrinkle formulations on local surfaces. These models were unsuitable for complex reproducible fabric simulation. They focused on appearance, particularly folds and creases, which were represented by geometrical equations. The geometrical models’ characteristics were of high controllability and predictable animation sequences. However, these models were also insufficient for responding to situations for exhibiting high variability. Weil presented the first 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. The 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. Vertices Cloth layer Skin layer Cross section Skeleton layer Figure 4: Structure of cloth (fabric), skin and skeleton [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]. That model was purely geometrical and did not involve stiffness coefficients or elastic modulus regarding problem formulation. It was able to simulate for example the wrinkles, only theoretically. The obtained simulation for a skirt in Figure 5 was achieved for 100% non-extensible fabric [22]. The mentioned method has many conservative solutions; therefore their simulations are very artificial. Initial shape Different postures and skirts’ shapes Figure 5: Skirt model deformation: the initial shape and the deformation shapes because of different postures [22] All the mentioned models haven’t included any mechanical properties but by definition the points and their interpolations simulated the imitations of real fabric behaviour. The folds’ deformations were generated along the lines of a fabric’s surface, and the folds could be either automatically determined or manually edited [22]. The main interest of the used geometrical models for fabric simulation application is to have a computationally efficient and highly controllable model which can perform the simulation well within certain predefined 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. The points have defined finite masses at the intersections. The numbers of points are defined according to the used problems and techniques. The continuum models for computer simulation can find solutions as fabric models based on simple geometry 305 and also for more complex formulations of fabric structure presentation such as models based on energy and elasticity. The 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-defined mechanical constraints and relatively stable mechanical contexts. The continuous models are independent of geometrical representation therefore with them it is possible to solve complex numerical problems by integrating various constraints. The complex computation requirements are the reason for their slow performances. The Lagrange or finite methods are used for fabric behaviour calculations. The more common models for interpreting the interactions amongst defined points are energy-based models, models based on the theory of elasticity, particle-based and finite 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 defined points. The finite element method and Lagrange equations are mainly used for the problem solving of fabric behaviour. Next, very often 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. The 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 306 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]. The way the springs are connecting the particles (the topology of the object) and the differences in strength of each spring influence the behaviour of the object as a whole. A simple particle model for fabric simulation [1‒3] is shown in Figure 6. The first 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. approach for the production of a garment by manufacturing. This 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 Thalaman`s system. Breen et al.[1] simulated fabric behaviour using the particle-based model. This method treats the crossing points of the warp and weft threads as particles. The Breen et al. simulation was in two stages. In the first, 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 fine detail in the shape of the fabric. Deforming body Warp Weft Undeformed body a b Figure 8: Particle representation (b) of plain weave (a) fabric [1] Figure 7: Terzopoulos model for deformable subjects [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: E(Pij) = ksEelast ij + kbEbend ij + kgEgrav ij Zhang and Yuen [46] presented a fast fabric simulation method using multilevel meshes based on the Provot model [47]. The 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. The multilevel method provided very good results especially for fabric draping simulation, Figure 9 [46]. (1) where Pij is energy at point, ks , kb, kg are elasticity, bending, density constants, Eelast ij is elasticity energy, Ebend ij is bending energy and Egrav ij is gravitational energy. Terzopoulos’s model was later extended by Thalaman et. al [3, 43]. Thalaman’s research team has dealt with the visualisation problems using an analogous a b Figure 9: Draping simulation of a piece of fabric hanging over a disc plate with multilevel meshes: initial position (a), final position after simulation phase (b) [46] Tekstilec, 2014, letn. 57(4), str. 300–314 Review of Computer Models for Fabric Simulation d) Particle-based approach This particle-based approach to fabric modelling was first 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. The various inter-crossing strain energies are represented by energy functions parameterised by simple geometrical relationships amongst particles. These 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. The model does not consider twisting strain, however. The strain energy for crossing particle i is given by equation [2]: Ei = Erepel i + Estretch i + Ebend i + Etrellis i garment manufacturing processes. Li et a1. [50] simulated fabric immersed within an airflow, Gröller et al. [51] modelled the microstructure of the knitted fabrics. They also built a rendering method for the simulation of knitted fabrics (fabric modelling and animation). The classic mass-spring model shown in Figure 11 was used by Provot [47]. Flexion Springs Structural Springs Shear Springs (2) where Ei is strain energy for crossing article, Erepel i is artificial energy of repulsion that effectively keeps, is Estretch i energies of tensile strain between each particle and its four-connected neighbours, is Ebend i energy due to yarns bending out of the local plane of the fabric and Etrellis i is energy due to bending around a yarn crossing in the plane. Collision and Stretching 307 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. Bending Trellising Figure 10: Fabric model’s energy function [2] Figure 12: Baraff ’s and Witkin’s simulation using continuum mechanics [52] 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 final 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 e) Finite element method The finite 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 finite elements. This method is also being developed today as a special scientific discipline within the textile area. Tekstilec, 2014, letn. 57(4), str. 300–314 308 Review of Computer Models for Fabric Simulation The 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 significant for a fabric. R. Collier et al. were the first to use the finite element method for modelling fabric drape [18]. The 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. The calculated drape coefficient was analysed by experimental measurement using a Cusik drape metre. Drapability over the square table was analysed by Govindaray using the finite element method [20]. He studied the draping behaviour of fabrics by using a non-linear finite element method based on a classical non-linear plate theory. J. Hu et al. [53] used a geometrically nonlinear finite-volume method for the numerical simulation and analysis of fabric drape. An initially flat circular fabric sheet is first subdivided into a number of structured finite 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 stiffness matrix iterative method was used to reduce simulation time. The 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 coefficient matrix during iteration. was the fusible interlining, therefore the mechanical model of a fused panel was based on the laminate theory. The author also simulated the extension and shear properties according to a measuring process using KES methodology for fabric and fusible interning [19, 36]. 3.4 Hybrid model The hybrid techniques combine the physical and geometrical methods. The advantages of combining the physical and geometrical methods were first 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. The 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. This process focuses on regions where folds are most likely to appear, that is those regions with large curvatures. These 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 13: Drape simulations of fused paned using finite elements [36] S. Jevšnik [36] used the finite elements method for modelling and simulating fused panel drape, Figure 13. The fused panel was treated as a two layer laminate; one lamina was fabric and the other lamina Figure 14: Simulation of horizontal and vertical types of folds [40] The bending properties are one of the most influential 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 significantly improves the realism of garment simulations. The efficient physically-based bending model using hysteresis in fabric simulation was developed also by Wong et al [59]. They compared the bending model with previous methods and plasticity models [1, 17, 44]. The 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]. 4 Accuracy of fabric computer simulations The 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 (flags, 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. The 309 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 differential 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. The 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]. The mechanical computer models of fabrics have to provide the simulation of fabric properties rapidly and realistically. The 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] Tekstilec, 2014, letn. 57(4), str. 300–314 310 Review of Computer Models for Fabric Simulation the simulated fabric. Volino and Magnenat-Thalmann in their book pointed out four parameters having a significant influence 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. The speed is validated by offline computation systems, interactive applications, and real-time applications. for modelling fabric models because of reasonable computation time and quite good realistic presentations of virtual fabric behaviour. The 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. 5 Comparisons between used methods Table 1 collates and presents some of the used models and techniques for fabric simulation. The 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. The 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. The advantage of this is that the computation time is faster than by other modelling techniques. Physical techniques are the most commonly used 6 Conclusions Visualisation of a garment within a virtual environment is an exciting branch for textiles as well as for computer graphics engineers. The correct selection of a fabric model for virtual simulation is a very important issue during the designing of an efficient fabric simulation system. Nowadays developed fabric models for obtaining realistic fabric behaviour are still insufficient 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 significant solutions of models for fabric simulations have not been forthcoming. The development of fabric models for computer simulation was mostly focused on physically-based models or their hybrids. Their main advantage is good realistic presentations of simulated fabrics. The 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 modifications of existing methods. The reasons are probably in the necessity of developing highly efficient computer performances that can simulate fabric on the micro level with the least possible limitations regarding fabric characteristics. Table 1: Comparison of used techniques and parameters for defining fabric models regarding simulations Geometrical models Models Authors Used techniques Parameters for defining the model Weil [38] Curve fitting, subdivision, relaxation Position of constraint points Agui et al. [39] Polygonization, relaxation, Bending angle, thresholds Hinds et al. [41] 3D interaction, interpolation Geometrically offset from the object Ng et al. [39] Mapping Various functions Ming Chen and Kai Tang [22] Algorithm for interpolation Thresholds, Position of constraint points Tekstilec, 2014, letn. 57(4), str. 300–314 Review of Computer Models for Fabric Simulation Hybrid models Physical models Models Authors Used techniques 311 Parameters for defining the model Feynman [42] Energy minimization, Multigrid method Elasticity, bending, gravity Terzopoulos et al. [21] Elasticity theory, Lagrange`s theory Density, damping curvature tensor, Aono [39] Elasticity theory, D`Alemberts`s principle, finite difference Stress, strain, Young's rigidity, Poisson`s ratio, density, damping, constantly lame Sakaguchi et. al. [39] Newtonian dynamics, the deformable model Density, elasticity, viscosity, plasticity Thalmann et al. [43] Deformable model, Newtonian dynamics Deformable model`s parameters Volino et al. [44] Newtonian dynamics, elasticity theory Stress, strain, Young's modulus, rigidity, Poisson's f »efficient, density, thickness Breen et al. [1] Energy minimization, Newtonian dynamics Repulsion, stretching, bending, trellis, gravity Ocabe et al. [49] Energy minimization, elasticity theory Elongation, shearing, bending, twisting, density Li et al. [50] Simplified Navier-Stokes equation, Bernoulli's equation, deformable model Air velocity, deformable model's parameters Provot et al. [47] Newtonian dynamics, Euler integration Mass, stiffness, damping, viscosity Ng et al. [39] Energy minimization, multigrid method Elasticity, bending, gravity Jevšnik [36 ] Newton-Raphsonova method, shell/plate theory Laminate theory Shear, bending modulus, Young`s and Poisson’ modulus, mass Zhang et. al. [46] Newtonian dynamics, Euler integration, Multi mesh Bending force, mass, constraint points Wong et. al. [59] Triangle mesh Bending hysteresis Forces for bending and unbending, Bending hysteresis loop, Residual curvature Pabst et. al [58] Bending element consisting of two adjacent triangles Bending stiffness Rudomin [ 55] Convex hull, the deformable model Shape of the object, deformable model's parameters Kunii et al. [56] Energy minimization, singularity Theory, curve fitting Mass, stiffness, positions of characteristic points Tailleler [39] Curve fitting, relaxation Positions of hanging points, stretching, bending, weight, self-repulsion Tsopelas [57] Thin-wall deformation, elastic, NURBS fitting Thickness, diameter, rigidity Dhande et.al. 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