**Pattern Computation for
Compression and Performance Garment**

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**Principal Investigator: **

Charlie C.L. Wang (Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong)

**Co-investigator(s):**

Kin-Chuen Hui (Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong)

Penelope Watkins (Center of Fashion Science, London College of Fashion, University of the Arts London)

**Funding Resource:**

This project is supported by the Shun Hing Institute of Advanced Engineering (SHIAE) 2008

**Abstract:**

In the clothing industry, compression garments are increasingly being used to mould and confine the malleable shape of the human body. The garment design may require variation in pressure ranging from normal through increased strain in specific areas for the particular application. Therefore compression garments need to be customized because body shapes differ and require different strain distribution. The 3D body shape can be obtained by any popular 3D data-acquisition means (e.g., a human body laser scanner). However, it is the 2D pattern – fabricated into the 3D shape combined with the fabric parameters, which brings about the desired strain distribution – that has to be determined. At present, the 2D pattern design and garment-to-body fit is accomplished through trial-and-error. This subjective procedure is inefficient, inaccurate and costly, as many prototypes have to be produced. Therefore, a computer program is desirable that can automatically generate 2D patterns from an input of the 3D shape that, when fabricated into the final 3D garment, the 2D pattern profiles give the designed strain and pressure on the human body. In this research we propose to develop techniques to compute 2D meshes that can generate a user-defined strain distribution through proper distortion, when folded onto the 3D body.

**Project Objectives:**

1. Develop a new physical/geometric approach that is able to model complicated elastic behaviors of fabrics, and determine the 2D patterns of a given 3D mesh surface satisfying the given strain and/or normal pressure distribution.

2. Investigate numerical schemes to compute optimal 2D patterns efficiently.

3. Develop a test-bed to evaluate the material-related coefficients in the developed physical/geometric model and verify the simulation results according to experimental tests.

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**Background of Research:**

In the clothing industry, compression garment is employed to plastic the shape of a human body so that certain specified strain (or compression) can be obtained at some designated places on the body (see Figure 1-3). The 3D body shape can be obtained by any 3D popular data-acquisition means (e.g., a human body laser scanner, see [1] and [2]). However, no method has been successfully investigated to compute the 2D patterns for compression (or performance) garments by a computer program automatically. This motivates the work proposed in this project.

In computer graphics, the pioneer work of Terzopoulos et al. [3] provided a general physically-based modeling method for elastic objects, which employs the finite-element and the finite-difference methods to solve the dynamic governing equations that simulate the deformation of objects like cloth, rubber, metal, etc. Following that work, much effort has been given to improving the simulation of cloth, either in verisimilitude or efficiency aspects [4-8]. In all of these works, however, the input is a planar pattern (tessellated), and their common purpose is to simulate/predict the three-dimensional shape and motion under some physical theorem. The problem to solve in this research is the inverse – given a 3D shape and certain associated required physical properties (e.g., strain or pressure), how to determine the 2D patterns that can generate such physical properties. No above existing approaches can be directly applied here.

Another sort of research in literature related to our work is mesh parameterization and surface flattening. Similar to our work here, the parameterization of a given 3D mesh surface concerns with finding the corresponding 2D parametric domain via surface flattening. In general, a surface parameterization inevitably introduces distortion in either angle or area. All the known parameterization methods are based on how to minimize the distortions (see [9] for a detailed review). Among the abundant literature of mesh parameterization, only a few schemes (e.g., [10-12]) generate a planar domain with a free boundary so that it can be employed to compute the shape of 2D patterns. However, they never addressed the problem of how to satisfy certain given strain and compression in the 3D shape fabricated from the computed 2D patterns. In the realm of computer-aided design, the surface flattening for pattern design has been studied from various perspectives (cf. [13-15]). Nevertheless, neither mesh parameterization nor mesh flattening approaches provides a solution to the physical/geometric problem posed in this research.

Recently, in [16], a woven-model based geometric approach is proposed for the design of elastic medical braces, where the elastic brace worn by a human body is simulated by a woven model with orthogonal warp and weft threads. In that work, the elastic behavior is simulated by three types of springs: warp, weft and diagonal. An elastic energy is formulated with these springs, and a diffusion process is adopted to minimize the elastic energy that determines the distribution of woven nodes on the given 3D surface, so to obtain the desired 3D-to-2D mapping. There are however serious deficiencies in the approach of [16]:

• Only the elasticity in two directions – warp and weft – is considered; therefore, when in equilibrium, the strain (and stress) on a single weft or warp thread is a constant. The result is that only very simple patterns of strain distribution can be simulated by the woven model.

• The computation of re-distributing the woven nodes on the surface is based on the knowledge of a strain distribution. However, computing such strain distribution in general is not straightforward. And thus again, the woven-model based approach in [16] can only mimic very simple and limited patterns of strain distribution.

• The strains on the springs around a point with a user specified normal pressure is calculated by fitting a quadratic polynomial. Such an approximation is not accurate enough.

• The boundary of the woven model takes a zigzag-like shape, which brings great difficulty in modeling the physical interactions between the 2D pieces that will have to be sewed together.

• There is no guarantee that all the threads will be in the tensile state, which though is strongly required by a compression garment.

*Figure 1*. Computing optimal strain values on 3D
garment pieces whose 2D patterns satisfy certain compression requirements. The color
map shows the strain distribution on the human body with the suit fabricated
from the 2D patterns in the right.

*Figure 2*. Application in the geometric design of a
customized assistive medical brace: (a) the 3D mesh surface of the brace is
acquired from a scanned human model, and the initial planar pattern is obtained
by a parameterization algorithm [11]; (b) different planar patterns are
computed – different colors on the 3D brace represent different strain levels.
The places pointed by arrows are with large normal pressures
specified. Figure 3. The
geometric design for a wrist brace: (a) the 3D mesh surface of the wrist, the
initial woven fitting of the wrist, and the corresponding strain distribution
of the brace; (b) the fitting result without normal pressure constraints; (c)
the fitting result with normal pressure constraints.

*Figure 3*. The geometric design for a wrist brace: (a)
the 3D mesh surface of the wrist, the initial woven fitting of the wrist, and
the corresponding strain distribution of the brace; (b) the fitting result
without normal pressure constraints; (c) the fitting result with normal
pressure constraints.

**References:**

[1] Cyberware Web site, 2005. At: http://www.cyberware.com

[2] TC2 Web site, 2005. At: http://www.tc2.com

[3] Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K., “Elastically deformable models”. ACM SIGGRAPH 87, pp.205-214, 1987.

[4] Volino, P., Courchesne, M., and Magnenat-Thalmann, N. “Versatile and efficient techniques for simulating cloth and other deformable objects”. In Proceedings of ACM SIGGRAPH 95, pp.137-144, 1995.

[5] Baraff, D., and Witkin, A., “Large steps in cloth simulation”. ACM SIGGRAPH 98, pp. 43-54, 1998.

[6] Choi, K.-J., and Ko, H.-S. “Stable but responsive cloth”. ACM Trans. Graphics, 21(3), pp.604-611, 2002.

[7] Etzmuss, O., Gross, J., and Strasser, W. “Deriving a particle system from continuum mechanics for the animation of deformable objects”. IEEE Transactions on Visualization and Computer Graphics, 9(4), pp.538-550, 2003.

[8] Goldenthal, R., Harmon, D., Fattal, R., Bercovier, M., and Grinspun, E. “Efficient simulation of inextensible cloth”. ACM Trans. Graphics, 26(3), 2007.

[9] Hormann, K., Sheffer, A., Levy, B., Desbrun, M., and Zhou, K. Mesh Parameterization: Theory and Practice (SIGGRAPH 2007 Course Notes), ACM, 2007.

[10] Desbrun, M., Meyer, M., and Alliez, P. “Intrinsic parameterizations of surface meshes”. Computer Graphics Forum, 21(3), pp.209-218, 2002.

[11] Levy, B., Petitjean, S., Ray, N., and Maillot, J. “Least squares conformal maps for automatic texture atlas generation”. ACM Trans. Graphics, 21(3), pp.362–371, 2002.

[12] Sheffer, A., Levy, B., Mogilnitsky, M., and Bogomjakov, A. “ABF++: fast and robust angle based flattening”. ACM Trans. Graphics, 24(2), pp.311-330, 2005.

[13] Aono, M., Breen, D., and Wozny, M. “Modeling methods for the design of 3d broadcloth composite parts”. Computer-Aided Design, 33, pp.989-1007, 2001.

[14] McCartney, J., Hinds, B., and Seow, B. “The flattening of triangulated surfaces incorporating darts and gussets”. Computer-Aided Design, 31, pp.249–260, 1999.

[15] Wang, C., Smith, S., and Yuen, M. “Surface flattening based on energy model”. Computer-Aided Design, 34(11), pp.823-833, 2002.

[16] Wang, C., and Tang, K. “Woven model based geometric design of elastic medical braces”. Computer-Aided Design, 39(1), pp.69-79, 2007.

[17] Fung, Y.C. Foundations of Solid Mechanics. Englewood Cliffs, N.J.: Prentice-Hall, 1965.