In the Proceedings of Computer Animation 2001, Seoul, Korea, November 2001.

Real-time Cloth Simulation with Sparse Particles and Curved Faces
Masaki Oshita Akifumi Makinouchi
Department of Intelligent Systems, Graduate School of Information Science and Electrical Engineering,
Kyushu University, Japanmoshita@db.is.kyushu-u.ac.jp
Abstract
In this paper, we present a novel technique for real-time
cloth simulation. The method combines dynamic simulationand geometric techniques. Only a small number of particles (afew hundred at maximum) are controlled using dynamic
simulation to simulate global cloth behaviors such as waving
and bending. The cloth surface is then smoothed based on theelastic forces applied to each particle and the distance between
each pair of adjacent particles. Using this geometricsmoothing, local cloth behaviors such as twists and wrinkles
are efficiently simulated. The proposed method is very simple,
and is easy to implement and integrate with existing
particle-based systems. We also describe a particle-based
simulation system for efficient simulation with sparse particles.
The proposed method has animated a skirt with rich details in
real-time.

1. Introduction
Physically based cloth simulation is an important current
topic in computer animation. At present the most efficient andcommonly used approach is particle-based cloth simulation. In
particle systems, clothes are modeled as mass-distributed
particles that are grouped into a fixed topology. In addition,
forces that work on the particles, such as the fabric, gravity, andair forces are also modeled. Then, by solving a differential
equation based on Newton’s law, particle motions arecomputed. Currently this method is mainly used in off-line
processes, such as for making motion pictures and real-time
simulation is still difficult. One major problem is the large
number of particles required for accurate simulation. Typically,
from a few hundred to a hundred thousand particles are
required to simulate a garment. Such a large number ofparticles needs a lot of computational time per step of the

(a)

(b)

Figure 1. An example of the proposed approach. (a)A small number of particles (66 particles in this case)are controlled using dynamic simulation. (b) The
cloth surface is then smoothed using geometrical
techniques (1,944 faces were rendered).
dynamic simulation and requires small time steps to avoid
numerical instability. Although many techniques have beendeveloped for fast and robust simulation, dynamic simulation
requires too much computational time to animate clothes inreal-time.
In this paper, a novel technique for real-time cloth
simulation is presented. The method combines dynamic
simulation and geometric techniques. Only a small number ofparticles (a few hundred at maximum) are controlled using
dynamic simulation to simulate global cloth behaviors such as
waving and bending. The cloth surface is then smoothed basedon the elastic forces applied to each particle and the distance
between each pair of adjacent particles. Using this geometricsmoothing, local cloth behaviors such as twists and wrinkles
are efficiently simulated (Figure 1).
The proposed method assumes that the motion of a cloth iscomputed using a coarse mesh. Therefore, the application of
the proposed method to waving cloths, such as skirts or jackets,is appropriate because tight garments, such as sleeves or tightpants, need a fine mesh for dynamic simulation. In this paper,
animation of a skirt is presented as an example. The proposed
approach that has potential uses in computer games, real-timeanimation, virtual environments, and virtual fashion shows.
This balance of this paper is organized as follows; section 2
describes a geometrical smoothing method for generating afine cloth mesh from a small number of particles. In section 3,
a particle-based dynamic simulation system is described.
Finally, an experimental result is presented and discussed.

2. Related Works
Smoothing of surfaces is a common technique in computer
graphics. Many methods have been developed for modelingand compressing meshes, such as subdivision faces, parametricsurfaces, and so on. These methods generate curved surfaces
from a coarse mesh. However, just smoothing is not enoughfor generating a realistic cloth surface. For this, a kind ofgeometric method specifically for cloth surfaces is required.
Some researchers have developed heuristic models forcomputing a static cloth shape. These methods combine
dynamics and geometric techniques. Taillefer [15] proposed a
computational model for modeling the folds of a hanging cloth.
Dhande et al. [4] modeled a wept surface. Kunii et al. [8]developed a formulation and deformation method for wrinkles.
However, the deformation of wrinkles does not consider
physical interactions with the underlying body. In these hybrid
methods, an appropriate geometric cloth model is used tocompute a specific and static cloth shape. Therefore, it isdifficult to integrate them with an existing dynamic simulation
system and animate them interacting with the changing
environment. In this paper, we present a geometrical techniquethat is generically designed and easily integrated with standard
particle-based cloth simulation systems.
Recently, Volino et al. [18] proposed a method forgenerating wrinkles using height maps. The method was
expanded by Hadap et al. [7]. Using good looking wrinkle
patterns provided by the designer as height maps, varying
wrinkles are produced by modulating the height maps based on
the compression of the cloth face similar to our method and themulti-layering of the height maps. Although this method
generates realistic wrinkles, the pattern is basically designed
for a specific posture. Therefore, it may produce a unnatural
result under unexpected conditions, such as nonstandard
posture of the underlying body, a strong wind, other external

forces, constraints and so on. The method proposed in thispaper produces a curved cloth surface based on the condition,is generically designed, and does not need extra data such as
wrinkle patterns.

3. Geometric Smoothing for Cloth Surfaces
In this section, a geometric smoothing method is described.
The smoothing method generates a fine cloth mesh based on acoarse cloth mesh that consists of a small number (typically a
few hundred) of particles that are grouped into triangular faces.
In smoothing a cloth surface, this method simulates the cloth’s
local behaviors within each original triangular area rather thanjust smoothing angular faces.
The proposed smoothing method consists of two stages;
surface generation and deformation. Surface deformation
involves particle normal control and edge length control. For
surface generation, an existing method is used. Therefore, theoriginal part of the smoothing method is the surface
deformation method. In each simulation step, a cloth surface isrendered by the following steps;
1. The positions of all particles of the coarse cloth mesh arecomputed using dynamic simulation.
2. Surface generation. A cloth surface is generated bysmoothing the triangular faces of the coarse cloth mesh.
3. Particle normal control. The generated surface isdeformed so that its shape reflects the elastic forces
applied to the particles.
4. Edge length control. The generated surface is deformed sothat it keeps its original dimension by maintaining thelength of each edge.
5. Triangular tessellation. The cloth surface is rendered as anumber of small triangular faces.

3.1. Smoothing Triangular Faces
In the proposed method, PN triangles [16] are used tosmooth triangular faces in a coarse cloth mesh. PN triangles
substitute a three-sided cubic Bézier patch for each triangularface facilitating control of the smoothing mesh using thenormal of the vertices (Figure 2). In addition, PN triangles
ensure that the generated surface matches the original mesh oneach vertex. These features are suitable for the control of the
shape of clothes. Using PN triangles, the ten control points forrepresenting a three-side cubic Bézier patch are computed fromthree positions, and from the normals of the vertices of the3.2. Particle normal control

triangular face as illustrated by Figure 2.
(a)

n3

(b)
p3

b003

n2

b102

p2

b201

b012
b021

b111

b030
b120

n1
b210
p1

b300

Figure 2. PN triangles replace a triangular face by athree-sided cubic Bezier patch computed from thethree positions and normals. The cubic Bezier pathc
is represented by coefficients or control points (Bijk).
Many smoothing techniques have been proposed formodeling and compressing geometrical meshes. However,most smoothing techniques such as subdivision surfaces (e.g.
Catmull-Clark [5]) and parametric surfaces (e.g. NURBS)
generate a smoothed mesh from the topology of a coarse meshand the positions of the vertices without considering theirnormals. Moreover, the generated surfaces are so smooth thatthey are away from the original vertices. These features makeit difficult to control the shape of the produced surface. This is
why we choose the PN triangles.
DeRose et al. [5] applied Catmull-Clark subdivision surfaces
to cloth simulation. However, the subdivision surfaces wereused for modeling clothes and the fine cloth meshes areproduced for dynamic simulation. They discussed the problem
regarding computing the continuous fabric parameters in a
subdivision surface. Biermann et al. [3] proposed a subdivision
surface technique with normal control. Although the shape ofthe generated surface can be controlled by the normal of its
vertices, the generated surface is still too smooth and difficult
to control. Volino et al. proposed SPHERIGON [17] thatgenerates curved polygons based on the position and normal ofthe vertices of an original flat polygon in a similar way to PN
triangles. SPHERIGON provides us the same facilities as do
PN triangles that control the shape of a curved surface with
their normal and ensure a curved face match on vertex
positions. Therefore, SPHERIGON can also be used with theproposed surface deformation method. We have chosen PN
triangles for first implementation since it just seems to be fasterthan SPHERIGON which involves a normalization process incomputing a point on a curved polygon, and hardware
accelerations for PN triangles [16] are expected. A more
explicit comparison of the two methods in both visual results
and computational time is a future topic.

In particle-based systems, particles usually have no
orientation. Only the position and velocity of particles are usedin dynamic simulation. When the cloth faces are renderedusing Gouraud shading, the particle normal is simply
computed by taking an average of the normals of the adjacentfaces.
Szeliski and Tonnesen [14] introduced oriented particles fora particle-based surface modeling system. They used oriented
particles to keep the shape of surfaces in dynamic simulation.
However, this approach makes the dynamic simulation more
complex, and it is difficult to integrate with existing
particle-based simulation systems. In our method, particles
have no explicit orientation in dynamic simulation, and theparticle normal is computed in the surface deformation step.
The proposed method computes particle normal so that the
curved patch reflects the in-plane forces that are applied toeach particle. Many force models such as elastic, bending,shearing, and twisting forces have been proposed[11]. Of these,
elastic forces are the strongest and are responsible for thein-plane deformation of the clothes. Therefore, only elastic
forces are considered in our implementation. Elastic forces areusually defined as a spring model in which a spring force
works along each edge as follows.
f ij = k elasticpi − p j
Lij(p − p − L )
i

j

ij

(1)

where i, j is a pair of adjacent particles, pi and pj are the current
positions of the two particles, Lij is the distance between pi andpj in their rest positions,, and kelastic is the spring coefficient. The
elastic force is computed for each edge and it works to makethe distance between the two side particles close to the original
distance.
Normal control is based on the principle of energy
minimization, as illustrated in Figure 3. When the position of aparticle is fixed, the normal on the particle is computed so as tominimize the energy on the particle (Figure 3(a)). When aparticle receives an elastic force from an adjacent face, it canbe assumed that the energy on the particle is proportional to theinner product between the elastic force and the normal vector
on the particle (Figure 3(b)).
jj

Ei = ni ⋅ f i .

(2)

The more parallel the normal vector is to the elastic force, themore the energy on the particle from the elastic force.

(a)

f1

(b)

n

f1

f2
tangent
face 2

face 1

(c)

(d)

n'

n1
tangent

Figure 3. Normal control in section view. (a) The
curved surface is computed based on the original
normal using PN triangles. The elastic forces f1 andf2 are applied to p from face1 and face2 respectively.
(b) The energy on p from f1 is assumed to be
proportional to inner product between f1 and n. (c) f1
makes the tangent proportional to f1, and n
proportional n1 which is the normal of f1. (d) The
normal n’ is computed by taking a weighted average.
Consequently, an elastic force on a particle works to make thetangent on the particle parallel to the elastic force (Figure 3(c)).
Because a particle usually receives some elastic forces from all
adjacent faces, to minimize the energy on the particle, theparticle normal is computed by taking a weighted average ofthe normals of all adjacent faces with the magnitude of theelastic forces applied from each face (Figure 3(d)) as follows.
fikNi = ∑nj
j =1

k

j

∑ fi

j

, ni =

Ni
Ni

(3)

j =1

where k is the number of adjacent faces, nj is the normal on thejth face, fi j is the elastic force that applied to the ith particle
from the jth adjacent face, and fi j is computed by taking the
average of the two elastic force on the two edges on the jthface.
j

f i = f ia + f ib

(4)where i, a, b are three particles in the jth triangle, and fia and fib
are computed by equation (1).

3.3. Edge Length Control
In particle-based dynamic simulation, the length of an edge
on a cloth mesh sometimes varies from its original length in a

resting state because of the movements of particles and theconstraints on the particles. When using a coarse cloth mesh,the variation of each edge length has a large influence on theentire cloth dimension because the initial edge length is longer
than when using a fine cloth mesh. Therefore, each edge length
is controlled to keep its original edge length.
When the length of a cubic Bézier curve is shorter than its
original length (Figure 5(b)), the shape of the curve isdeformed to make it longer while keeping the positions of thetwo terminal particles. To control a curve length, we firstdivide the curved patch into four curved patches (Figure 4).
This divides each curve into two curves. The position of the
midpoint p on the curve is then moved in the normal direction
n. The position p and the normal n on the midpoint is obtained
from the original curved patch (Figure 5(c)).
p ′ = p + hn

(h > 0)(5)

In equation (5), h is computed so that the curve length isclose to the original edge length. The divided four patches arealso computed from the three corner particles and the three
midpoints by again using PN triangles (Figure 5(d)).

Figure 4. A cubic Bézier patch (Figure 2(b)) divided
into 4 cubic Bézier patches. The 3 midpoints are
obtained from the original PN triangle.
Unfortunately, the length of a cubic Bézier curve cannot becomputed in a closed form. Therefore, the length should becomputed numerically. By subdividing a Bézier curve into a
number of segments and summing the length of all segments,
we can approximate the curve length. Similarly, the edge
length is controlled numerically and incrementally. Using arecursive bisection method [12], h in equation (5) is computed.
We found the following equation to be a good approximationof the control distance as an initial guess.

(h0 = k Lij − pi − p j)(6)where Lij is the initial edge length and k is an empiricallydetermined parameter.
However, when a curve length is longer than its originaledge length, it is difficult to make it shorter by using this(a)normal(b)shortened edge

control point

(d)

(c)
n

pi

midpoint

p

p'

pj

Figure 5. Edge length control in section view. (a)Original edges in the at rest length. (b) When anedge is shortened, (c) the midpoint of the shorter
curve is controlled (d) so that the curve length isclose to the original edge length.
approach. Therefore, in our system, instead of curve
deformation in geometric smoothing, spatial constraints areapplied in a dynamic simulation to avoid such elongated edges.

implementation. Recently, implicit methods are widely used inmany systems [1] [19], because they ensure stability which is
the most important issue in interactive systems, and allow large
steps instead of losing some accuracy. However, they havedifficulties handling non-continuous constraints in dynamic
simulation. On the other hand, explicit methods are a classic
but accurate integral method. Each step of an explicit method
is faster than an implicit method. Moreover, they are easily
integrated with non-continuous constraints. However, a larger
number of particles is used, so an explicit method requires
smaller time steps. Therefore, as Baraff described [2], whenmany particles are used, explicit methods are slower than
implicit methods and they become unstable.
However, when, only a few hundred particles are used, as
here, an explicit method works faster than an implicit method.
In addition, an explicit method is easily integrated with spatialconstraints on penetrating particles and elongated edges thatare introduced in our dynamic simulation. Therefore, an
explicit numerical integral method, technically 4th-order
Runge-Kutta, is currently used in our system. Further
discussions about numerical integration are to be found in theliterature [12][1].

4. Dynamic Simulation with Sparse Particles
4.2. Cloth Model
The smoothing method presented in the previous section isvery simple, and is easy to integrate with an existing
particle-based system because only particle positions are
required for generating a smoothed surface. Many methods forparticle-based simulation have been developed[11][20], butdeveloping a successful particle-based system is still difficult.
In developing a particle-based system, it is necessary to choose
an appropriate method from many alternative methods for the
purpose, trading-off between accuracy, speed and stability [2].
This section describes the chosen methods in our system andhow they were modified to work efficiently with a small
number of particles and the proposed smoothing method.

4.1. Numerical Integral method
Numerical integration is the essence of particle-based
simulation and is the most important factor in the design of aparticle-based simulation system. Using numerical integration,a partial differential equation is solved to compute thetime-varying state of the particles.
There are two major methods for numerical integration:
explicit and implicit. An explicit method was chosen for our

For modeling a cloth surface, triangular faces are used in our
proposed method to apply the proposed smoothing method as
explained in section 2. Elastic and bending force are introduced
as internal cloth forces. The elastic force is described in section
3.2. The bending force is computed for each edge, andprevents bending between the two adjacent faces. In addition
to the fabric forces, additional forces such as gravity, airvelocity and damping forces [2] are also introduced. In someparticle-based systems, square faces are used for representing acloth instead of triangular faces. Here, diagonal forces such as
shearing and twisting forces are used to prevent skews [11].
However, these are not introduced in our system because
elastic and bending forces in triangular faces are considered tohave similar affects on cloth surfaces.

4.3. Elastic Forces and Constraints
Clothes strongly resist stretching but allow bending, sharing
or twisting. To realize such stiffness, the spring coefficientkelastic in equation (1) should be of a large value. Otherwise, thecloth changes length and acts like a rubber or spring. Such alarge coefficient value causes instability in numericalintegration and requires very small time steps in dynamic
simulation making the simulation slower. However, our systemallows a comparatively small value of kelastic because the edge
length is maintained at its original length and large elastic
forces are not required. Therefore, our system allows large time
steps in dynamic simulation making the simulation faster.
In our system, two different methods are applied forhandling shortened and elongated edges. As explained in
section 3.3, when an edge length is shortened, the edge curve isdeformed to keep the original edge length in geometricsmoothing. However, this method cannot handle elongatededges. Therefore, when an edge length is elongated, spatialconstraints are applied on the elongated edges in dynamic
simulation in a way similar to that proposed by Provot [13]. If
a curve length is longer than its original edge length, thepositions of the two end-points of the elongated edge are
directly altered to close the distance between the two particles.

4.4. Collision Detection and Constraints
Collision detection and response are also important issues inparticle-based systems. To prevent a cloth penetrating theunderling body contacts between the cloth and the body object
should be detected and resolved. In our system, a simple statecorrection approach is used as explicit methods work well withthis approach, while implicit methods require some extra
techniques [2][19] to maintain stability.
If a fine cloth mesh with a large number of particles is used,the collisions between the cloth and any solid object can behandled by keeping the particles out of the solid object [2][6].
However, when using a coarse cloth mesh, as in our case, acloth face may intersect with a solid object although the cornerparticles of the cloth face are kept away from the solid object.
Therefore, in our system, we need to handle both vertex
penetration and face intersection. Even though this needs extra
computational time, using a coarse mesh makes collision
detection and the related response faster.
For collision detection, a proximity query package (PQP) [9]a collision detection library is used in our system. PQP reports
an intersection between a cloth face and a solid face. When anintersection is reported, an initial determination is madewhether a vertex of the cloth face penetrates into the solid(Figure 6(a)) or the cloth face intersects with the solid but its
vertices do not penetrate (Figure 6(b). When a cloth particle
penetrates inside the solid, the position of the particle iscorrected to the nearest point on the solid face (Figure 6(c)).
When a cloth face intersects the object, the cloth face including
its vertices is moved to the farthest point on the solid face
(Figure 6(d)). When a particle contacts a solid face, theacceleration of the particle is directly constrained in dynamic
simulation so that the relative velocity between the particle andthe contacting face maintains the normal direction of thecontacting face.
(b)

(a)
cloth

cloth
solid

solid

(c)

(d)

Figure 6. Collision detection and penetration
avoidance. (a) Cloth vertex and solid penetration. (b)Cloth face and solid intersection. (c) Cloth particle or(d) cloth face position is corrected and constrained.
Collision detection and penetration avoidance is performed
based on the original flat triangles. Therefore, the curved faces
may penetrate into a solid object or the cloth itself. In terms ofcloth-solid collisions, it is not a large matter because any
generated surface basically matches the original mesh. To
handle cloth-cloth collisions, collision detection between
curved faces is required. Although a penalty-force approach
could be a solution, this would involve large computationalcosts, and so a cloth-cloth collision detection method is yet to
be introduced in our system.

5. Results
In this section an experimental result generated using the
proposed method is presented and discussed. For the first test,
we chose a skirt. Figure 7 shows the images from a generated
animation of the skirt. The original skirt mesh used for the
dynamic simulation consists of 66 particles grouped into 108
triangles. For the smoothed surface, each triangular face isrendered as 4 cubic Bézier patches using 18 small flat triangles.
Consequently, 1,944 faces are tessellated using PN triangles
and rendered. The skirt model is generated procedurally andFigure 7. Images from an animation of a skirt.
(a)

(b)

(c)

(d)

Figure 8. Smoothing surface in a frame of the animation. (a) Original mesh. (b) Smoothed surface using only PN
triangles. (c) Smoothed surface using our proposed method. (d) Visualization of the surface deformation.
the figure animated in the motion-captured sequence ofkicking.
Efficiency of the proposed method. Figure 8 showssmoothing stages in a frame of the animation. Figure 8(b) is thesmoothed surface using only PN triangles and Figure 8(c) is
the smoothed surface using our proposed method. Figure 8(d)shows the particle normal and edge length control used in
Figure 8(c). Sticks in yellow and orange from the particles
show the original and modified normals, respectively, andpurple sticks show the edge length control. Although it isdifficult to judge the visual results, it is found that the smoothedsurface using our proposed method has rich details such as
folds and twists around the left thigh in Figure 8(c), leading we
believe to improved results. It is also found that the particle
normal and edge length control are applied mainly on the left
leg and on other shortened parts. When a cloth is relaxed andhanging naturally, the difference between the generated surface
using only PN triangles and that using our proposed method issmall. Our proposed method works more effectively when apart of the cloth is exposed to external constraints or isshortened.

Computational time and its optimizations. In theexperiments, the duration between each simulation step was
1/30 seconds fixed. Each frame was divided into three steps inan explicit Eular integration. As a result, a 30 Hz animation
was generated in real-time on a PC (PentiumIII 800MHz CPU+ GeForce2MX video card). The computational time is shownin Table 1. For the proposed smoothing method, 2.4 extra
milli-seconds were used compared to when using only PN
triangles. This means that, by allowing a few extra
Used method

Computational time (ms / frame)
Integration Collision Smoothing Total

Speed
(fps)

Proposed method

3.5

14.7

6.4

23.7

29.8

PN triangles

3.6

14.6

4.0

21.9

32.1

Teble 1. Maximum computational time per frame in
the animation of skirt when our proposed method or
only PN triangles were used. The computationaltime for cloth simulation (numerical integration,
collision handling, and smoothing surface) was
about 60% of the entire computational time.

mill-seconds per a hundred faces in addition to that allowed for
the PN triangles, more realistically deformed cloth surfaces areachieved. Although the triangular tessellation is currently
computed in the CPU and the tessellated triangles are stored inmemory, hardware supports for PN triangles [16] could
accelerate the smoothing method. Since the program used inour experiments has not been optimized yet, the computationaltime in table 1 could become faster after optimization for both
numerical computation and rendering.

Acknowledgements

6. Conclusion and Future Work

[2]

The work was partially supported by the Grant-in-Aid for
Scientific Research (10308012) from the Ministry of
Education, Culture, Sports, Science and Technology of Japan.

References
[1]

[3]

The smoothing method presented in this paper is very
simple and efficiently adds rich details on a coarse cloth mesh.
However, the generated surfaces are slightly limited. The edge
length control adds at most one fold on the center of ashortened edge and the direction of the fold is determined fromjust the normal of the two end points. To generate more
realistic surfaces, the number, position, and direction of thefolds should be controlled. This we think might be possible bytaking into account bending forces and compression speed. For
more subtle and more wrinkles, wrinkle patterns provided by adesigner [7] or pre-computed using dynamic simulation [10],could be appropriate and could be integrated with our proposed
method. However, such wrinkle patterns require extra
modeling processing or pre-computation time, and cannot
produce appropriate wrinkles under unexpected conditions.
The goal of our research has been to provide a geometricmethod that is easily usable and generates cloth surfaces under
any conditions using heuristic methods that capture thecharacteristics of clothes rather than using static and expensive
wrinkle patterns.
We intend to apply our proposed method to garments suchas jackets, shirts and pants in which the interaction with theunderlying body is more complex and critical. To simulate adifficult interaction, such as the figure putting on a garment or
picking up a cloth, while keeping a fast and robust simulation,an adaptive technique that inserts and removes appropriate
particles into the cloth mesh would be required.
Currently only coarse cloth meshes achieve real-time
performance. Many on-line applications such as computer
games require real-time cloth simulation at a small
computational cost. We believe that our proposed methods thatadd detail on a physically simulated coarse cloth mesh are aneffective and reasonable approach.

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