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MIRALab Copyright © Information 1998
Developing Simulation Techniques for an Interactive Clothing System
Pascal Volino and Nadia Magnenat Thalmann MIRALab, University of Geneva Abstract In this contribution towards creating interactive environments for garment design and simulation, we present a powerful mechanically based cloth simulation system. It is based on an optimized way to compute elastic forces between vertices of an irregular triangle mesh, which combines the precision of elasticity

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MIRALab Copyright © Information 1998
Developing Simulation Techniques for anInteractive Clothing System
Pascal Volino and Nadia Magnenat Thalmann
MIRALab, University of Geneva
Abstract
In this contribution towards creating interactive environments for garment design and simulation, we present a powerful mechanically based cloth simulation system. It is based on anoptimized way to compute elastic forces between vertices of an irregular triangle mesh, whichcombines the precision of elasticity modelisation with the speed of a simple spring-mass particlesystem. Efficient numerical integration error management keeps computation speed efficient byallowing high computation timesteps and also maintains very good stability, suitable for interactive applications. Constraints, such as collisions or elastics , are integrated in a unified way that preserves robustness and computation speed. We illustrate the potentialities of our newsystem through examples showing its efficiency and interactivity.
Keywords :
cloth animation, mechanical simulation, particle systems, collision response,constraints, stability, interaction, garment design tools
1. Introduction
In a step towards unifying cloth simulation to the wonderful universe of Virtual Reality anddreaming about a world where virtual humans could manipulate cloth in real time and in a waythat seems so natural for us, real humans, we present a contribution for a fast and robust clothmodel suited for interactive virtual cloth design and simulation system.Literature now brings us several techniques for cloth simulation. Many of them presentphysically based models for simulating in a realistic way fabric pieces based on elasticdeformation and collision response. The first of them used simple mechanically-based models,such as relaxation schemes, for simulating objects such as flags or curtains ([WEI 86], [HAU88]). More general elastic models were developed for simulating a wide range of deformableobjects, including cloth ([TER 87], [TER 88]). Recently, several particle system based modelsattempted to simulate simple cloth object realistically using experimental fabric deformation data([BRE 94], [EBE 96]). These models claim to be fast and flexible, as opposed to finite elementmodels ([COL 91], [KAN 95], [EIS 96]), which are very accurate, but slow and complex to usein situations where behavior models are complicated and where collisions create non-linearitiesand complex boundary conditions, thus not suited for interactive applications.Dressing a virtual body is a complex application for these models. It involves the ability todesign complex garment shapes, as well as a complex simulation system able to detect and to
handle multiple collisions generated between the cloth and the body. Our work contributed to thedevelopment and evolution of this topic through several contributions ([LAF 91], [THA 91],[YAN 91], [CAR 92], [YAN 93]). More recently, we studied how to consider cloth as being anobject that could be considered independently from the body which wears it, involving the issuesof folding, wrinkling and crumpling, with all the associated problems related to collisiondetection and response ([VOL 95]). Our work was materialized by several garment design anddressing systems for animated virtual actors ([WER 93], [THA 96]).On the other hand, new V.R. technologies and efficient hardware open a very attractiveperspective for developing interactive systems where virtual actors would interact autonomouslywith mechanically animated objects, such as the garment they themselves wear. In a nearer goal,we could take advantage of these new tools for interactively designing garments and dressingvirtual actors in ways that are much more natural and close to the real way of manipulatingfabric.With this article, we provide simulation tools to take a step towards the requirements definedabove. Of course, the main problems for interactive or real time mechanical simulation arerelated to computation speed issues. We should not however trade away design flexibility andmechanical modelisation accuracy that would lead to unrealistic cloth simulation. Thus, wedescribe here a mechanical model that allows to modelise elastic behavior of cloth surfacesdiscretized into irregular triangle meshes, and which is not much more complicated to a simplespring-mass modelisation. This approach combines the flexibility obtained in [VOL 95] withsimulation speeds aimed in [EBE 96] and [HUT 96] which are restricted to regular meshes.Furthermore, a suited integration method has been associated to this model to maximizesimulation timesteps and computation speeds without trading away mechanical stability, which isensured in a very robust way, compatible with all the inaccuracies resulting from most trackingdevices used in 3D positioning and V.R. devices.Beside this, a new approach for handling geometrical and kinematical constraints (such ascollision effects or elastics ), generalization of the collision response process described in [VOL95], ensures collision response as well as integration of different manipulation tools in a robustway that does not alter simulation efficiency and thus makes this system efficient for interactivepurposes.We illustrate the achievements brought by these techniques with the help of examplesconcerning cloth manipulation, dressing and realtime interactive manipulation.
2. A mechanical model suited for interaction
The mechanical simulation system is the core of a physically based cloth animation system, andalso the most time consuming part. Our main contribution has been to improve the speed androbustness of the associated computation, first on the mechanical model itself (2.1), then on theintegration algorithm and the associated numerical error managements (2.2), and finally on theconstraint management, including collision response (2.3).
2.1. A fast and robust, yet realistic elastic model
The first problem of particle-system based models is to compute accurately the forces derivingfrom internal elasticity applied on each vertex.
2.1.1. What has been done until now
The simplest, and fastest method is to consider the surface as being a mesh of vertices, each onelinked to its neighbors by a damped spring, forming a structure usually called mass-spring structure. Such models have already extensively been used for simple and fast cloth simulation([PRO 95], [HUT 96]).Most of these models rely on a regular grid. In [BRE 94] and [EBE 96], a square grid is used tocompute tension, shear and bending. Internal forces are then computed using precise modelsresulting from experimental data. Mesh regularity is extensively used to keep geometricalproperties easily computed in an accurate way. In [PRO 95] and [HUT 96], bending and sheareffects are simply modeled by extra diagonal springs. However, our goals require non regularmeshes as a basis for cloth structure. We need to be able to model complicated cloth shapes thatmay contain high curvature with as few elements as possible, and our interactive design process(cutting, seaming, local topology or size modifications) highly relies on a very general and multi-purpose triangular mesh structure.In [VOL 95] and [THA 96], we have proposed a model derived from particle system modelswhich computes the mechanical deformation state in each triangle elements of such an irregularmesh. By computing contributions from the edge elongations, compression and shear strains of the triangle material are found in local coordinates by solving a linear system, in a way similar toa stress rosette computation [TIM 82]. This model allowed a precise modelisation of an elasticmaterial, taking into account the Young modulus and the Poisson coefficient, along with otherparameters concerning viscosity and plasticity. However, this computation was quite expensive,as it required complex geometrical evaluations with the construction of local coordinates in eachtriangle element. At the opposite, the simplest spring and mass system, in which the forcesapplied on each vertex directly derives from the elongation of each edge connected to it, is verysimple to compute, but would merely modelise more than a simple elastic material with aPoisson coefficient unrealistically high, unsuitable for any realistic cloth deformation.Thus, our contribution is to define a new way to compute the forces applied on the vertices,comparably simple to the basic spring-mass system, but which allows precise modelisation of theYoung modulus and the Poisson coefficient, which are the basic parameters of an elasticmaterial.
2.1.2. The proposed elastic model
Let's consider a triangle
(P
a
, P
b
, P
c
)
in which deformations have elongated its edges from restlength
(L
a
, L
b
, L
c
)
to the current length
(l
a
, l
b
, l
c
)
(Fig. 1). In a simple elastic spring-mass model,each edge would attract its vertices to reach its rest length, and impose a displacement along itsmain direction, proportionally to the amount of elongation from the rest length. Please refer tothe Annex for detailed formulas.
Fig. 1:
Deforming a triangle element.Quite easy to compute, this model does not however reflect the actual forces when a fullmaterial triangle gets deformed. Each deformed edge will produce a force component along itsdirection, which is usually not the deformation direction, as in the example shown in Fig. 2. Theresulting effect is an extra orthogonal deformation similar to the one produced by the Poissoncoefficient, but which produces unrealistic effects especially when the triangles are notequilateral (irregular meshes or high deformations).
Fig. 2 :
Vertical compression stretches the triangle horizontally.The main idea of our new model is to recompute the individual elongation contribution of eachedge of the triangle by taking into account the interdependence of the displacements that wouldbe generated by each of them in their respective directions. Thus, the combined effect of the edgeforces based on these corrected displacements will produce a more accurate constraint situation.In the situation shown in Fig. 3, if we suppose that the length of the edge
J
varies an amount of
d
j
, its extremity points
P
i
and
P
k
will be displaced in its direction by a amount proportional to
d
j
,weighted in function of the values
M
i
and
M
k
, the
inverse
mass of
P
i
and
P
k
. The elongationcontribution on edge
I
is then the displacement of the point
P
k
multiplied by the cosine of theangle between the two edges,
c
k
. We linearize the problem by supposing that the edge angles donot vary significantly.
(i, j, k)
are all the permutations of
(a, b, c)
.As we would like the final length variation of the edge
I
to be the value
l
i
-L
i
, we equal this to thesum of the elongation contributions of the three edges
I
,
J
and
K
individually would elongate atan amount of
d
i
,
d
j
and
d
k
. Doing this on the three edges simultaneously yields a linear system of three equations with three unknowns
(d
a
, d
b
, d
c
)
, shown in Annex B (4).

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