Computer-Aided Design 37 (2005) 609–622 www.elsevier.com/locate/cad
3D virtual apparel design for industrial applications Marzia Fontanaa,*, Caterina Rizzib, Umberto Cuginic a Dipartimento di Ingegneria, Universita` di Parma, 43100 Parma, Italy Dipartimento di Ingegneria, Universita` di Bergamo, 24044 Dalmine (BG), Italy c Dipartimento di Ingegneria Meccanica, Politecnico di Milano, 20156 Milano, Italy b
Accepted 15 September 2004
Abstract The integration of physics-based models within CAD systems for garment design leads to highly accurate cloth shape results for virtual prototyping and quality evaluation tasks. To this aim, we present a physics-based system for virtual cloth design and simulation expressly conceived for design purposes. This environment should allow the designer to validate her/his style and design option through the analysis of garment virtual prototypes and simulation results in order to reduce the number and role of physical prototypes. Garment shapes are accurately predicted by including material properties and external interactions through a particle-based cloth model embedded in constrained Newtonian dynamics with collision management, extended to complex-shaped assembled and finished garments. Our model is incorporated within a 3D graphical environment, and includes operators monitoring the whole design process of apparel, e.g. panel sewing, button/dart insertion, multi-layered fabric composition, garment finishings, etc. Applications and case studies are considered, with analysis of CAD modelling phases and simulation results concerning several male and female garments. q 2004 Elsevier Ltd. All rights reserved. Keywords: Physics-based modelling; Virtual simulation; Cloth design; Newtonian dynamics
1. Introduction Cloth modelling has recently become a topic of large investigation in computer graphics. Laboured garments and drapes, in fact, appear as key visualization elements in animation movies, cartoons, etc. Further, a strong impulse comes from clothing and fabric furniture industries, where CAD tools are increasingly demanded to assist the whole cloth design process. Until now, different systems for virtual cloth modelling have been developed by scientific or commercial communities with different points of view and goals. Fig. 1 portrays a high level classification of some tools used in computer graphics and industrial design. Software products for cloth visualization aim at producing images that look real for computer animation applications, while systems for garment design focus on definition/construction of detailed garment shapes for real manufacture, according to * Corresponding author. Tel.: C39 052 190 5844; fax: C39 052 190 5705. E-mail address:
[email protected] (M. Fontana). 0010-4485//$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.cad.2004.09.004
different 2D/3D modelling tools. In this paper we concentrate our attention on methodologies and applications related to garment design. The skilled-labour dependent nature of apparel and upholstery design did not have encouraged to a large extent of automation and software programs. Although several 2D CAD systems exist on the market for pattern drafting, sizing, nesting, and marker making, together with CAM modules for cutting/sewing, clothing companies complain about the lack of effective garment-oriented CAD packages to design directly in 3D and provide the modellist with tools for shape modelling and cloth behaviour simulation. Regardless of the application domain, however, packages for both animation and design need an underlying cloth model representation. Several geometry- or physicsbased methods for cloth modelling have been proposed since the 1980s (Section 3). Differently from purely geometrical cloth’s descriptions, adequate for computer animation tasks, physics-based models interpret cloth within a physical framework, by considering internal
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Fig. 1. Garment virtual modelling.
mechanical properties and interactions with an external environment. The inclusion of a physical substrate ensures a more accurate shape description, suitable to a new conception of CAD systems targeted to apparel or functional cloth design endowed with simulation capabilities. A current drawback of most of the existing commercial CAD systems is, on the contrary, that they still rely on mere geometrical modelling and do not provide virtual simulation tools (with few exceptions, e.g. the DressingSim module used by Investronica Sistemas [1]). As a contribution to overcome this drawback, a CADoriented physics-based system for virtual cloth design and simulation is here presented. The system is expressly conceived for design purposes, differently from other research prototypes or systems currently available on the market mainly oriented to visualization for movies, or virtual catwalks (e.g. TopixCloth, plug-in for Softimage V3.7 from Topix [2], or MayaCloth, plug-in for Maya from AliasjWaveFront [3]). In the effort of getting closer to cloth manufacturers’ needs, our main target has been the development of a tool to assist the designer/modellist throughout the cloth design process, managing aspects related to the various garments’ structural parts (e.g. shoulder paddings, collars) and to manufacturing processes that influence the final garment shape. This environment should allow the designer to validate his/her style and design options through the analysis of garment virtual prototypes and simulation results and, definitively, reduce the number and role of physical prototypes. As a validation of our approach, we analyse and simulate several female/ male garment models presenting different levels of design complexities (e.g. skirts, dresses, jackets, etc.) whose models have been directly provided by clothing companies.
2. Apparel as a design process Apparel appears in a large variety of shapes, textile materials, as the result of several design, manufacturing and finishing operations. We started our collaborations with Italian and European clothing companies1 (Section 7), by examining the apparel life cycle from earlier conceptual design up to finished products ready for purchase. 2D CAD systems and automated cutting/sewing devices are used in most cases; nevertheless, human factors such as creativity of stylists and technical skills of dressmakers for made-tomeasure clothing still continue to play a fundamental role, making difficult a complete automation of the whole apparel design process. Such a difficulty is reinforced by several levels of design complexities that have to be faced while defining shape, assembly rules and aesthetic/functional details of real tailored garments. A classical man jacket, for instance, is a significant example of a particularly complex and laboured garment (Fig. 2). It originates from a large number of 2D panels corresponding to front, back and side parts, sleeves, collar, lapel, etc. with complex-shaped borders connected with each other by means of various darts and single/multiple seams. Sewings needs to be carefully applied with different degrees of tightness/looseness, depending on position, function and shape curvature effects (e.g. roller), by considering possible differences in the length and shape of borders that have to be joint together, with definition of markers and constraint points. Besides, 1 F.lli Corneliani, garment manufacturer, team coordinator of the italian TA2000 Consortium, and Confecciones Mayoral (ES), GFT Donna (IT), garment manufacturers cooperating in the framework of the Brite-Euram MASCOT project [4].
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Fig. 2. A man’s jacket: 2D patterns with specification of fabric layers, seams, darts and pleats.
the peculiar volume and shape consistency characterizing male jackets is also the result of a multi-layered fabric composition, following well-defined rules, with fabric layers varying in number among the several jacket’s structural parts and made of different heavier or lighter materials (cotton, canvas, linen, horsehair, etc.). Internal smooth linings, reducing friction against the body, give stability to jacket’s shape, together with reinforcements and tassels. Fig. 2 shows the multi-layered structures of jacket’s front part and sleeve as well as types of sewing lines. Stuffings for shoulders are placed to strategically correct shape proportions along horizontal directions, emphasizing larger shoulder-torso parts typical of male clothing. Small aesthetic and functional features enrich the structure of the jacket, e.g. buttons, hooks, external and internal pockets and other finishings. Last but not least, the different sculptured or smooth volume effect can be controlled/forced by starching, pleating, ironing, and other several mechanical/ chemical actions inducing permanent or semi-permanent deformations on jacket’s fabrics. Is it possible to reconstruct such a complexity in a fully computerized way? This is, evidently, a very cumbersome and ambitious task. In spite of garments’ variety in shape,
material, function, and differentiation of each functional garment template (jacket, skirt, shirt, etc.) due to different human body sizes, aesthetic factors and fashion trends, there exist, nevertheless, design/manufacturing stages generally valid in all cases. Stylists’ and manufacturers’ way of working can be, in fact, analysed as a 3D-to-2D-to-3D process. Typically, the process starts with stylists’ creative ideas originating essentially from a 3D shape (a 3D conceptual idea in mind or a completed garment already existing) from which 2D information are extracted, such as 2D patterns with corresponding fabric layers (3D-to-2D stage). 2D fabric panels are then assembled and sewn together to get a 3D garment shape as close as possible to the original stylist’ idea (2D-to-3D stage). Procedurally, of course, a more detailed sequence of design/manufacturing steps has to be considered, involving aspects such as: † definition of a reference 3D shape; † 2D patterns definition/extraction (2D models); † definition of assembly rules (seams, darts, overlapped layers, buttons, etc.); † definition of materials;
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† cut of 2D fabrics (single layers); † assembly of fabrics by layer overlapping; † assembly of one- or multi-layered fabrics along border parts (seams, darts, etc.); † mechanical/chemical post-treatment of textiles by shape deformation (pleats, ironing, etc.); † 3D configuration/placement over supports or external objects (e.g. mannequins); † analysis of the final garment’s shape and behaviour in the 3D physical space. These common aspects help us in defining a computerassisted garment design methodology (Section 4). Our most significant contribution, in particular, is the definition of a design and simulation approach that takes into account the following key-issues of cloth’s tri(bo)logy: † Shape and structure, i.e. geometrical description of garments and relation among parts (e.g. 2D profiles of basic patterns and multi-layered parts); † Material, i.e. mechanical/physical properties (e.g. KES or FAST measurements of fabric types); † Process, i.e. design and manufacturing processes (e.g. ironing, starching). Our approach leads to the definition of a complete physics-based model for real apparel that incorporates the above-mentioned aspects, aiming at reaching accurate simulation of garments’ shape and behaviour for virtual prototyping tasks.
3. Cloth models As already mentioned, a key issue is the choice of a model for cloth, capable of accurately reproducing/simulating its behaviour. Theoretical studies about fabrics and fibers started about 60 years ago, mainly funded by the textile industry, from Peirce’s precursor work in 1937 [5] up to De Jong et al.’s model in the 1970s [6]. We focus here on computable cloth models proposed in computer graphics literature since the mid 1980s. Among the so-called geometry-based approaches, the well-known model from Weil in 1986 [7] describes drapes through nets of suspended catenary curves. Agui et al. in 1990 [8] model the effect of a bended elbow, while Hinds et al. [9] in 1990–1992 realize one of the first cloth-oriented CAD prototypes, based on surface modelling. More accurate than geometrical representations, physicsbased approaches analyse cloth’s behaviour through laws derived from discrete dynamics, structural mechanics, elasticity theories, fluid dynamics, or other physical contexts. Cloth is dealt as a dynamic system with material properties, subjected to internal interactions, and interacting with an external environment through external forces/ stresses and response to collisions with obstacles.
Continuous physics-based models interpret cloth in the framework of continuum mechanics, by means of PDE problems generally solved by finite element or finite difference methods. In the classical model by Terzopoulos et al. proposed in 1986–1988 [10], cloth’s surface deformation is described by continuous Lagrange equations, as set of displacements from equilibrium positions. In 1996, Eischen et al. [11] provide a non-linear shell description for cloth. In 1990, Aono [12] simulates the effect of wrinkle and drape propagation, considering the elasticity theory and D’Alembert principle, from a modified wave equation propagating in a continuous elastic medium. In 1993–1996, Li et al. [13] describe cloth immersed in a quasi-stationary viscous fluid by combining Navier-Stokes equations and Terzopoulos’ model. In discrete physics-based approaches, cloth objects are modelled as systems composed of a finite number of mechanical constitutive elements subjected to certain static/dynamic laws. In the so-called particle-based model, constitutive elements are particles with mass, subjected to internal and external forces, subjected to Newtonian dynamics (force-based formulation), or assuming certain potential energies, e.g. Lagrangian formulations (or other energy-based approaches). Compared to continuous formulations based on deformable thin shells or plate beams, particle-based cloth models tend to represent more efficiently the highly flexible behaviour of cloth and its characteristic ‘discrete’ structure as a woven or knitted (or, in some cases, unorganized) plot of interlaced threads (Fig. 3). Feynman in 1986 [14] introduces the first discrete model representing woven patterns by structured rectangular grids defined from orthogonal weft and warp directions (Fig. 4). Breen and House since early 1990s [15] have been investigating in detail textiles as particle-based ‘mechanisms’ having certain internal stretching/repelling, bending and trellising energies. In the period 1995–1997, Provot [16] proposes a Newtonian mass-spring model in which the elastic forces act not only along the weft and warp directions, but also along the two diagonal directions of each cell in the textile grid. At MiraLab laboratory in Geneve, since the early 1990s, Magnenat-Thalmann and Volino have been working intensively on virtual clothing [17,18]. Initially influenced by the continuous Terzopoulos’
Fig. 3. Thread patterns: (A) knitted; (B) woven.
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Fig. 4. Particle-based model of a woven fabric.
approach, successively they have worked mainly on particle-based systems, more efficient for non-linear deformations in dynamic cases, using non-structured triangular meshes with continuum mechanics applied inside each element. Various techniques for collision detection and response have been also investigated, to face constrained cloth motion in complex scenes including obstacles and self-collisions [17]. Since the mid 1990s, work on structured thin deformable bodies, e.g. fabrics and other objects, has been carried out at IMAG institute in Grenoble, by Desbrun, Cani and others [19]. Recently, a great interest has been addressed to efficient time discretization techniques for ODE systems generated by cloth’s particle-based grids. Explicit low-order methods (e.g. explicit Euler) used in the past are progressively substituted by implicit and semi-implicit schemes (e.g. modified backward Euler’s, multi-step BDF techniques), as indicated by Baraff and Witkin in 1998 [20], Kang et al. in 2000 [21], Etzmuss et al. in 2001 [22,23], and Choi and Ko in 2002 [24]. Hybrid models, with mixed geometric and physical representations in cloth sub-regions, have been also investigated. Earlier examples come from Rudomin [25] and Kuni et al. [26] in 1990, Taillefeur [27] and Tsopelas [28] in 1991, and Dhande et al. [29] in 1993. Among the most recent results, in 2001 Oshita et al. [30] and Kang et al. [31] propose coarse particle-based models coupled with smoothing and interpolation techniques, and in 2002 Rudomin et al.’s consider [32] mesh particles moving accordingly to sets of ellipsoids defining mannequins. For a detailed overview on physics-based modelling, see [33,34]. What emerges from the above-mentioned cloth models, is that they describe cloth either as a geometrical
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entity or a mechanical system, and in some cases with significantly accurate results [18,24], but very rarely cloth is interpreted in its ‘construction process’, from single fabric pieces up to complex-shaped assembled and finished textile configurations, such as garments. This is a key issue: although advanced virtual reality environments have been proposed [18–22], these are not intended for design applications, i.e. are not capable to drive the garment design and manufacturing process as it is conceived for real production tasks. Our intention is rather focusing on this integration between particle-based modelling and CAD for clothing production, as shown in the following sections.
4. The proposed garment physics-based model 4.1. Particle-based characterization of fabrics We start by analysing single fabric pieces, as basic garment model’s components. Woven textiles are considered, the most frequently used for apparel, with threads interlaced according to orthogonal warp and weft directions. Fabric’s flattened pieces, assumed to have a negligible thickness, are defined as open connected and bounded figures F 4R2 with piecewise regular boundary vF (e.g. a closed loop of linear or curved edges). Similarly to Breen’s and Provot’s models [15,16], we associate a particle-based model to each fabric panel by defining a structured 2D grid with coordinate lines along warp and weft directions. Interior particles correspond to grid nodes, located at warp/weft thread intersections, while boundary particles are defined from intersection of grid lines with the fabric border. Triangular elements are derived from the original rectangular grid cells by adding diagonals (Fig. 5). Differently from Breen’s energy-based method, we here use a Newtonian force-based approach, as it can include more general dynamic problems where parts can be in motion (e.g. walking virtual humans, etc). Taking into account the woven structure of threads, we consider (Fig. 5): stretching/repelling forces, acting to keep particles at rest distance (modelled as Kelvin visco-elastic springs directed along weft and warp);
Fig. 5. Particle grid associated to fabric panels with internal force characterization.
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bending forces, acting out-of-plane to keep objects flat (derived by torsional moments normal to their support surface); trellising (or shear) forces, acting to contrast any possible deformation of the rectangular cells (modelled again through torsional moments normal to the cells). Internal force values are estimated from global mechanical data for textiles, measured by the Kawabata Evaluation System (KES), a well-known system for ‘hand evaluation’, based on experimental stress and deformation tests performed on rectangular fabric samples with fixed dimensions [35]. KES data are provided for a large list of textiles typically used for clothing, and quantitatively measure properties about geometry and mass (fabric thickness and mass density); tension (elongation percentage, tensile deformation energy and tensile resilience); compression (shortening percentage, compression deformation energy and resilience); bending (bending rigidity and corresponding hysteresis); shear (shear stiffness and corresponding hysteresis); superficial behaviour (averaged friction coefficient, standard deviation and rugosity). Panel’s grid topology characterizes the internal discrete force distribution, computed as linear or torsional springs connecting neighbouring particles. Extracting from KES data’s list the elongation ratio 3 under tension, the bending rigidity B[N$m] and the shear stiffness T [N/(m$deg)] for a certain fabric, easy computations provide kS Z
fS hy ; 3 hx
kT Z Thx hy cos wm ;
kB Z
Bp 180
(1)
as estimates of constants for spring forces, torsional moments for trellising and bending, respectively [36]. In Eq. (1), fS is the magnitude of a known imposed force causing fabric’s tension or compression, wm is the (known) angle of bending, while hx and hy are grid cell sizes along weft and warp. 4.2. From fabrics to a assembled garments A garment is the complex-shaped result of assembled components. Thus, geometrical abstraction helps us in defining a full garment shape as a non-manifold entity GZ
g iZ1;.;nF
Fi0 g
g iZ1;.;nA
Ai ;
(2)
where Fi0 are fabric layers in a spatial configuration (2D manifolds in R3) deformed from original flat panels Fi 4R2 , for iZ 1; 2; .; nF , and Ai 4R3 are geometries of rigid or soft accessories, for iZ 1; 2; .; nA . When existing, the latter are generally few small entities, such as buttons, hooks, zips, paddings, etc. Fabric layers are sewn with each other along portions of their boundary, or can be partially or totally attached in interior sub-regions with other layers (as it occurs in multi-layered parts as shown in Fig. 2).
Under these premises, after particle grid discretization of single fabric layers, we consider further steps to generate a complete physics-based model for garment simulation. On this regard, we define proper algorithms that locally modify/upgrade the geometry and topology of cloth’s particle meshes, with corresponding physical discrete parameters (e.g. particle masses and internal force distribution) with the purpose of emulating the following design steps: (a) sewing of fabric panels; (b) insertion of darts; (c) fabric layer overlapping; (d) insertion of buttons and hooks; (e) placement of the full garment model in a 3D space configuration (e.g. on a mannequin). 4.2.1. Sewing of fabric panels For sake of simplicity, we interpret sewings as unary or binary relationships, i.e. involving one or two fabric components at a time, and locally preserving the ‘manifold’ behaviour. These constitute the basic ‘single’ seams considered in garment manufacturing. In our future analysis, however, we will consider also multiple sewings, involving more than two components at a time. The counterpart of a sewing process from the point of view of the particle-based model is essentially a mesh assembly operation accompanied with local modification of the internal force distribution. We implemented a new algorithm in which panels’ particle grids to be connected pairwise can present a different number of particles at the border segments (we say that the two grids can be locally non-conformal), as it occurs in case of particle resolution different between one panel and the other, or in case of complex-shaped borders. Fig. 6 shows a sewing process between two particle grids of fabric panels. Suppose a panel A has to be sewn with a panel B: geometrically, this corresponds to know a one-to-one mapping between a given sequence of consecutive oriented border segments of panel A with another given sequence of oriented border segments of panel B. The sewing algorithm is then a grid assembly procedure progressively merging each sewing segment pair of the mapping. For each segment pair, in fact, let n be the number of original particles of the segment in A (in the following denoted by A-segment) and m the number of original particles of the corresponding segment in B (B-segment). If the number of particles is different, say n!m, then mKn particles will be added to the A-segment in proper intermediate positions to define a ‘local’ one-to-one mapping also between particle pairs. Such positions are derived as follows. First, one by one, we progressively search for n ordered original particles of the B-segment having relative line abscissa values in the segment that are as close as possible to the relative line abscissa values of the n particles of the A-segment. Practically, this corresponds to finding out the particles in the more-refined segment that have a relative distribution in the segment as similar as possible to the particle distribution in the less-refined segment: this is the local particle-to-particle mapping within the segment pair.
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Fig. 6. Sewing process between two fabric panels: (1) seam definition as mapping 1 to 1 between vertices of panel borders; (2) detail of the sewing process over a single segment pair.
Then, the particle grid in the A-segment is refined (in one or more parts, depending on the local mapping) along each original grid edge having as a vertex a particle excluded from the local mapping, for a total of mKn new border grid edges, with corresponding local re-triangulation around the sewing segment pair at the side of the A-segment. Thus, when definitively A-segment and B-segment have the same number of particles, say again nZm for simplicity, each ith particle of A is merged with the corresponding ith particle of B, for iZ 1; 2; .; n; by moving particle pairs to an intermediate position. n particles belonging to one of the two border segments are then removed from one side. Correspondingly, the mesh topology (grid particles, edges, triangles) around that side is updated similarly to any standard mesh assembly algorithm now involving conformal meshes. Internal force values are re-computed around the sewn edges with particle mass summation and value increment of the constants of bending forces for all sewn edges. Note that dart insertion is again a sewing operation, as darts can be regarded as special seams along a fixed sequence of edges, in which panel B coincides with panel A. In other words, one (or more) vertice(s) is (are) sewn with another (other) vertice(s) belonging to boundary loops of the same panel. 4.2.2. Other construction processes As regards the successive construction steps, an algorithm for layer overlapping is considered to update the original cloth particle-based grid in order to model the presence of possible fabric layers placed on top of each other, as in case of paddings, linings, etc (e.g. to strengthen jackets). To this aim, we change physics-based properties (masses, springs, bending and trellising forces) corresponding to particles and edges inside specified subregions of the main panels, substituting them with proper values measuring all effects of single added layers, with their specified materials, through the effect of a unique equivalent material (e.g. mass summation, equivalent constants in parallel spring networks, etc.) Insertion of button and hooks is also considered. The effect of buttons and hooks intervenes when two panels to be
connected are sufficiently close to each other. Each virtual button is simulated by connecting the two grid points closest to the required button position, imposing significantly hard spring force effects and mass increment. Once the garment particle-based model is assembled with all its components, the corresponding garment’s placement in 3D has to be defined. 3D particles’ configuration is arranged by considering the presence of external rigid objects in the scene (e.g. mannequins or rigid supports) and according to mapping laws from 2D onto 3D, respecting local isometries in grid triangles/edges. Note that the 3D placement of the garment onto the rigid support can be chosen with a certain (relatively small) offset distance from rigid supports. The final accurate 3D placement of the garment model onto the support will be scope for the physical simulation phase.
5. Dynamic simulation 5.1. Newtonian constrained dynamics The complete particle-based model of a garment is defined by a system SZ fPi : iZ 1; .; Ng of N particles, having masses mi, positions ri and velocities vi Z r_t , for iZ 1; 2; .; N. The configuration of particles is assigned at an initial time t0, by known positions {ri0} and velocities {vi0}, iZ 1; .; N. The dynamic behaviour of the system is thus governed by Newton’s problem 8 ci Z 1; 2; .; N > > < (3) mi r€ i Z FðintÞ C FðextÞ i i > > : ri ðt0 Þ Z ri0 ; vi ðt0 Þ Z vi0 _ tÞ and FðextÞ _ tÞ are, respectively, where FðintÞ ðr; r; ðr; r; i i the total internal and external resultant forces acting on particles i, being rZ ðr1 ; .; rN Þ the system configuration at time t. Eq. (3) is a Cauchy problem for a system of 3N second order ordinary differential equations, equivalent to a system of 6N first order equations. Solutions are trajectories {r i(t)}, with corresponding velocities {vi(t)}, for iZ 1; 2; .; N, t 2½t0 ; T, uniquely determined under
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hypotheses of sufficiently regular data Fi, satisfied in our linear force estimation method [37]. In Eq. (3), the total internal force FðintÞ is computed by summing up the resultant i stretching, repelling, bending and trellising forces FðstretchÞ , i Fi , FðbendÞ and F acting on particle i, while the total external i i force FðextÞ is computed by summing up FðaÞ i i , resultant active external force on i, with FiðrÞ , reactive force associated to possible constraints imposed on i. Among the several methods for constraint management (e.g. penalty method, rate-controlled constraints, Lagrange multipliers and dynamic constraints [38–40]), the dynamic constraint method has been here considered, with reactive forces FðrÞ i computed from Lagrange multipliers by solution of a linear system, since it permits to apply multiple constraints to the same particle and ensures the respect of all the constraints at each time step of the simulation. Several types of bilateral constraints have been considered, such as fixed positions, constant distances between points or particles, area or volume conservation, as well as assigned trajectories for points or particles. The solution of Eq. (3) can be numerically estimated by using proper time discretization schemes on a discrete sequence t0 ; t1 ; .; tn of time steps. In our case, an improved two-steps Euler scheme has been utilized [16], stabler than explicit Euler’s and still computationally cheap, with particles’ positions at kth time step derived from velocities updated at kth time step and corrected with post-collision response. To increase the convergence speed and manage stiff equations, implicit or semiimplicit integration schemes are currently under implementation, according to [20–22,24].
Collision detection plays a significant part in the total computational time of simulations, as proximity queries and checks for possible collisions need to be done between pairs of elementary object entities (points or particles, edges, triangles). Among several techniques for collision detection, e.g. voxel subdivision, octree subdivision, bounding box hierarchy, proximity tracking, and curvature-based methods [16–18], aligned axis bounding box (AABB) hierarchies with region subdivision have been here adopted, as a good compromise between simplicity and efficiency. In the collision response phase, the velocities of particles belonging to colliding entities are modified due to elastic/ anelastic bouncing off. The corresponding velocity variations due to collisions are computed as solution of a linear system, by handling collisions as unsatisfied scalar unilateral constraints di ðr1 ; r2 ; .; rN ; tÞ! 0, for iZ 1; 2; .; s, where s is the number of collisions at a certain time, and using again the dynamic constraint approach [38,40].
5.2. Collision management
† 2D/3D modeller, creating the physics-based model associated to the 3D configuration of the garment. It generates the particle-based grid of all 2D panels, sewing and assembling them over the mannequin, to create the initial 3D configuration for garment simulation (Section 4). † 3D simulator, generating garment’s simulated frames at discrete time steps t0 ; t1 ; ::; tn , with simulation based on constrained Newtonian dynamics with collision management (Section 5).
To complete the analysis of the interactions with the surrounding environment, also possible collisions are taken into account. These occur, for instance, when parts of flexible objects (e.g. garments) hit some rigid objects (e.g. mannequins) or penetrate towards each other (self-collisions). In Fig. 7, for instance, collision effects were dominant in simulating cloth positioning on a table or a sphere, or cloth fall on the floor.
6. SoftWorld system The particle-based model described in Sections 4 and 5 has been implemented in a system named SoftWorld2.0, running on Windows, Unix/Linux, SGI-IRIX platforms. SoftWorld is composed of several executable modules, with functions for data conversion, geometric modelling, physics-based modelling, dynamic simulation, provided with a graphical user interface. Grouping together the several modules by purpose, two fundamental systems are singled out:
Fig. 7. Simulation of fabrics on rigid objects: (1) tablecloth on a table; (2) carpet on a sphere; (3) tablecloth falling on the floor; (4) ribbon falling on the floor.
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Fig. 8. Basic SoftWorld’s architecture.
The system is provided with a Graphical User Interface to create a unique environment from which both the Modeller and the Simulator are executed. Fig. 8 displays the overall SoftWorld architecture. Table 1 displays input and output data of the 2D/3D Modeller, while Table 2 describes the main algorithm in the 3D Simulator.
7. Case studies Several tests were done to evaluate our computer assisted design methodology and simulation results using SoftWorld2.0. Fig. 7 already showed earlier SoftWorld’s simulation results such as fabrics falling over rigid objects such as a table, a sphere, or the floor—classical reference test cases in the literature of cloth modelling. Actually, for our design intents, these examples are not so significant because they deal with simple-shaped onelayered fabric without any of those design complexities (seams, complex borders, layers, different materials, etc.) encountered in real cloth manufacture. As we were interested in real complex-shaped apparel, analysis and simulation of garment examples were carried out starting from initial geometrical 2D and 3D models directly provided by clothing companies. The next sections present the adopted methodology and some simulation results, with case studies for both male and female clothing. Results were obtained within the framework of Brite-Euram MASCOT [41] and Italian TA2000 [42] research projects, in cooperation with industrial partners from the clothing industry (see note1), and CAD/CAM developers2. Although based on the same modelling and simulation algorithms, the two ways of proceeding while defining male and female clothes were quite different.
2 Lectra Systemes (FR), Investronica Sistemas (ES), and TELMAT (FR), in the framework of MASCOT project.
7.1. Design of women’s garments The activity on female garment design was carried out within MASCOT project [41]. The main goal was to develop a 3D graphic environment for industrial applications in clothing industry to permit the design of woman base garment in 3D, the evaluation of the style by comparing different types of fabric, and the automatic generation of the 2D panels starting from the 3D representation. SoftWorld was integrated with a geometric 3D garment modeller, based on NURBS representation and developed by the University of Valenciennes [43]. Regarding the modelling phases, we started from 3D garment models, directly chosen from a library of template cloth shapes (skirt, blouse, etc.) that were modified by 3D surface modelling tools acting on characteristic lines. Seams, pences, and other textile characterizations were defined on the 3D model, from which 2D panels were extracted with all information (e.g. sewing lines) necessary to the simulator for their correct location on virtual mannequins. Once generated the 2D panels from the geometric 3D modeller, our 2D/3D Modeller (Table 1) could define the particle-based grid of each 2D panel associating proper KES Table 1 Input and output data of the 2D/3D Modeller 2D/3D modeller Input data (a) Material properties (e.g. KES data for fabrics) (b) Rigid bodies (e.g. mannequins, frames) (c) Geometry of 2D panels (for extended version with full 3D soft modelling tools: geometry of 3D soft shapes) (d) Rules for 2D/3D mapping (e) Model construction constraints (e.g. textile operations: seams, darts, fabric layers, buttons) (f) (If any) dynamic constraints (kinematics of rigid parts) Output data (a) Physics-based information about soft objects (particle 3D positions, masses, associated grid, internal/external forces, geometric and kinematic constraints) (b) Physics-based information about rigid parts (3D point positions, the associated grid, geometric and kinematic constraints)
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Table 2 Main algorithm of the 3D simulator 3D simulator Known configuration {ri(t0), vi(t0)}, for iZ 1; 2; .; N For step kZ 1; 2; .; n: (1) It computes the active forces FiðaÞ ðtk Þ (from internal and external contributions) on each particle i; (2) Estimates the effect of bilateral constraints by computing equivalent reactive forces FðrÞ i ðtk Þ for each i; (3) Computes the new velocities vi(tk) from numerical solution of Newton’s law (ODE solver, first part); (4) Detects the colliding particles; (5) Updates velocities vi(tk) with vi(tk)CDvi for the colliding particles, from velocity variation of collision response algorithm (linear system solution), with DviZ0 for uncolliding particles; (6) Computes the new particle positions ri(tk) from ODE solver, second part
data of the chosen fabric material. By using information provided by the geometric modeller, 2D panels were sewn and located properly on the mannequin for the final simulation of its behaviour in static conditions. To generate the physics-based model, we started from the following basic assumptions: † use of a simplified model representing the fabric as composed of a single equivalent layer; † generation of a final configuration in 3D depending on the 2D geometry of patterns but also on intrinsic mechanical properties due to the considered type of fabric (e.g. cotton, linen, silk, etc.); † choice of KES measurements to characterize fabric’s mechanical behaviour; † use of geometric information at several levels, e.g. to define 2D patterns profiles, and functional/aesthetic
Fig. 9. Particle-based models of women’s garments placed on mannequins before simulation.
Fig. 10. Simulation of women’s garments: dress, tunic and trousers.
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Fig. 11. System architecture in the design of men’s garments.
details such as the location of seams, darts, buttons and other constraints. In Fig. 9, we display the particle-based models of a skirt, a top and a woman’s dress before simulation, showing the different 2D panels sewn along the sewing lines and darts. Fig. 10 presents the accurate simulation results of a dress, a linen tunic and a pair of trousers. Validation and assessment procedures were defined and the environment was experimented by the end-users participating to the project. As concerns the simulation phase, we selected a set of different garments (Figs. 9 and 10), whose physical prototypes were realized by the end-users
allowing a comparation with the simulation results, in most cases considered satisfactory. At this stage, however, comparisons have only been made at a qualitative level. 7.2. Design of men’s garments Tasks for men’s garment design were developed in the framework of TA2000 [42]. Differently from female fashion, the production of men’s garments follows more standardized shapes (jackets, trousers, shirts, etc.) that only slightly differ from one season and the other. Here, therefore, we chose to work by modification of existing apparel articles. Together
Fig. 12. Virtual design of male garments. Main steps: (1) Selection of base jacket. (2) Modification module—definition of a new garment style. (3) Generation of 2D patterns. (4) Particle-based model of each panel. (5) Panel assembly with final particle-based model ready for 3D simulation. (6) Simulation results.
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Fig. 13. Right front 2D panel and related regions.
with the technical staff of F.lli Corneliani company (manufacturer of male garments) we selected a jacket as a significant test-case (Section 2), to properly validate the physics-based modeller and simulator for real complexshaped clothing. Fig. 11 shows the overall architecture of the software environment developed for men’s cloth design, including SoftWorld (here named 3D Simulator) to physically model and simulate men’s garments. The design process currently followed by clothing companies was first analysed to extrapolate useful functionalities for the geometric modelling phase. Typically, the designer defines a new style by modifying the shape of a physical prototype, e.g. changing the length of the sleeves or tightening the waist, according to fashion trends and stylist’s sketches. To do this, the designer uses some reference elements such as sewing lines or significant and structural elements (e.g. waist or shoulders, etc.). A modelling system should permit the designer to operate in the same way, using a digital prototype instead of a physical one. Therefore, an editor module was implemented by using and combining MAYA Deformers [44], to enable the user to change the shape of a geometric model. From the analysis of modellist’s modus operandi, we identified and implemented a set of shape modifiers emulating traditional modifications on garment’s parts. Some examples were: shorten/lengthen sleeves, tighten/enlarge shoulders, tighten/enlarge waist, shorten/lengthen jacket. An export module could
automatically generate a file, containing information about the modified 3D geometric model, to be used as input for 2D panel extraction. The generation of 2D panels was done by means of a commercial CAD package used at Corneliani site. The 3D simulator could generate the particle-based grids of the panels, which were then assembled together and placed on a virtual mannequin thanks to the 2D/3D mapping rules stored by the 2D/3D modeller. Once the complete particle-based model was created in 3D, simulation could be performed. Fig. 12 displays the main steps of the jacket’s design procedure. It is important to point out that some assumptions made for the physics-based model of female apparel are not adequate for men’s jackets. These can have, in fact, a very complex structure, whose volume/shape is obtained by overlapping different types of material layers and by resorting to particular manufacturing processes inducing permanent local deformation (e.g. by ironing, starching, and special tight-loose sewings). Therefore, as described in Section 2, it is necessary to generate a model that takes into account not only data related to fabric properties but also information on structural multi-layered parts (shoulder-paddings, collars, etc.) and the effects of additional manufacturing processes. Garment’s physical model was thus enriched according to the following ideas: 2D panels were subdivided into regions, each corresponding to a structural part of the jacket, e.g. shoulder, facing, collar, etc. Each region was characterized by different physical parameters, to integrate the abovementioned manufacturing effects. Further parameters were introduced in order to amplify/reduce the effect of permanent material deformations (e.g. lapel pleat) obtained by means of manufacturing processes, such as ironing. Fig. 13 shows the 2D panel corresponding to the right front of the jacket and related sub-regions: (A) shoulder,
Fig. 14. Some views of a simulated jacket.
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(B) pleating line of the lapel, (C) facing, and (D) bottom of the jacket. Fig. 14 shows several points of view of the simulated effect of the jacket leaned on the bust of a mannequin in static conditions. The results of tests carried out with the end-users are encouraging and prove the validity of our approach. We envisage the need to execute further KES measurements on specimens of jacket’s structural parts, e.g. fabricClining, in order to get results that are more precise. Moreover, the man’s jacket example was computationally more expensive than woman’s models such as skirts and dresses. This was due to a fine particle discretization, necessary for accuracy requirements, for a complex model composed of 12 panels, designed with multi-layered fabrics, different materials, seams, darts and buttons. Details about the jacket model, simulation results, and computational aspects can be read in [43]. At present, to decrease the computational time, we are working on the implementation of implicit methods as suggested by [22,24], and on optimized collision detection techniques.
designer of the 2D patterns in Fig. 2, and all colleagues that participated to the research projects on non-rigid materials modelling and simulation.
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8. Conclusions and future work Physics-based models show their potential in realistically simulating cloth shapes, as the geometrical substrate is enriched with information derived from structural fabric properties and dynamic laws. In this work, the physicsbased cloth shape simulation is derived from a discrete particle-based model, embedded in constrained Newtonian dynamics, provided with collision management. The system includes specific algorithms for textile operations such as sewing, button and dart insertion, etc. and has been integrated within CAD environments for cloth design. Applications and examples on simulated test cases for the design of men’s and women’s garments, directly provided by clothing companies, were shown. Work is currently in progress to extend system’s CAD functionalities in functional and aesthetic cloth design details, e.g. parametric sewing algorithms (puffed sleeves, close-fitting sewings, jacket rollers, etc.), multi-layered fabric modelling (linings, paddings, etc.), and virtual emulation of manufacturing processes inducing fabric deformations (e.g. by ironing, etc.). To increase the efficiency of computations, we are currently implementing implicit ODE’s time discretization methods, as suggested by [22,24]. Further, we are implementing a parallel version of the system.
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Ms Marzia Fontana is a PhD candidate at the Department of Industrial Engineering, University of Parma, Italy. She received her MSc Degree in Mathematics at the same university and was awarded with grants for research programs at the Institute of Applied Mathematics, CNR, Genoa, Italy, and at Chalmers University of Technology, Goteborg, Sweden. She is author and co-author of several publications in the area of mathematical physics, finite element methods, surface modelling and physics-based modelling.
Dr Caterina Rizzi is full-time Professor at the Faculty of Engineering, University of Bergamo, Italy. Previously, she was Professor at the Universities of Neaples and Parma, Italy. She participated at several national and international projects in the area of modelling, simulation and CAD applications. She is author and co-author of more than 80 publications in the fields of CAD, physics-based modelling and simulation, knowledge-based modelling, virtual prototyping, cloth modelling.
Dr Umberto Cugini is full-time Professor at the Department of Mechanics, Polytechnic of Milan, Italy. Previously, he was Researcher at CNR, Milan and, successively, Professor at the University of Cagliari and Parma, Italy. He participated at several national and international projects in the area of modelling and simulation, and directed several national projects and consortia in the area of design and robotics. He is author and co-author of more than 150 publications in the fields of CAD, industrial design, modelling and simulation, knowledge-based modelling, virtual prototyping and robotics.
