SUGISAKAMASANORI

Journal of Robotics, Networking and Artificial Life
Vol. 10(4); March (2024), pp. 308–312
ISSN (Online): 2352-6386; ISSN (Print): 2405-9021
https://alife-robotics.org/jrnal.html

Research Article

CAD Development of Moving Hula Costumes
Satoshi Ikeda1, Taketo Kamasaka1, Kaoru Ohe1, Makoto Sakamoto1, Amane Takei1, Masahiro Yokomichi1, Kenji Aoki1,Tsutomu Ito2, Takao Ito3
Faculty of Engineering, University of Miyazaki, Miyazaki-City, Miyazaki, Japan
National Institute of Technology, Ube College, Ube-City, Yamaguchi, Japan3
Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, Hiroshima, Japan
12ARTICLE INFO
Article History
Received November 25, 2020
Accepted 05 April 2024
Keywords
3DCGCC++CADCollision detection
DirectXHula
Visual studio

1.

ABSTRACTIn recent years, three-dimensional computer graphics (3DCG) technology has been applied invarious fields. One problem with this technique is the problem of contact between clothing andother objects (such as the body). In this paper, we verified simple animations concerning of hulacostumes using three calculation methods, and found that we were able to create simple and stableanimations using the FB Euler method. This paper reports that we were able to create a simple
animation.
© 2022 The Author. Published by Sugisaka Masanori at ALife Robotics Corporation Ltd.
This is an open access article distributed under the CC BY-NC 4.0 license(http://creativecommons.org/licenses/by-nc/4.0/).

2.1. Mass spring model
In the mass spring model, in order to express theanisotropy of the cloth, the shape of the cloth is a springthat connects the mass points arranged in a square gridand the mass points adjacent to each other with thedirection along the warp and weft threads of the cloth as
the axis (See Fig. 1).

Introduction

In recent years, three-dimensional computer graphics(3DCG) technology has been applied to various fields
such as AR/VR technology, movies, games, and virtual
fitting [1]. This research uses a physical model tosimulate fabrics applied to 3DCG animation, focuses onpast research, and creates simple fabrics (for example,skirts) that take into account contact with other objects(the body of a hula dancer). He is working on simulation[2], [3], [4].
2. Simulation method

Fig. 1. Mass spring model

The Modeling methods for expressing cloth can beroughly divided into two types: geometric models andphysical models.
In order to perform dynamic simulation, we will use aphysical model that considers the change process thistime.
Corresponding author E-mail: saka2000@cc.miyazaki-u.ac.jp308

2.2. Mechanical properties of cloth𝒗𝒗𝑖𝑖 (𝑡𝑡 + ∆𝑡𝑡) = 𝒗𝒗𝑖𝑖 (𝑡𝑡) + 𝒂𝒂𝑖𝑖 (𝑡𝑡)∆𝑡𝑡𝒙𝒙𝑖𝑖 (𝑡𝑡 + ∆𝑡𝑡) = 𝒙𝒙𝑖𝑖 (𝑡𝑡) + 𝒂𝒂𝑖𝑖 (𝑡𝑡)∆𝑡𝑡(∆𝑡𝑡: time step)

Of the six mechanical properties of cloth listed by KES,
four are considered when modeling the shape of cloth:tensile properties, shear properties, bending properties,
and weight properties (See Fig. 2.) [5].

(4)2.5.3. Runge-Kutta method
At first glance, the amount of calculation seems to be fourtimes, but since the calculation accuracy is high, the time
step width Δt can be increased, and more stable
simulation is possible.
𝑘𝑘𝒗𝒗𝟏𝟏 = 𝒂𝒂𝟏𝟏 𝛥𝛥𝛥𝛥, 𝑘𝑘𝒙𝒙𝟏𝟏 = 𝒗𝒗(𝑡𝑡)𝛥𝛥𝛥𝛥

Fig. 2. Mechanical propeties of cloth𝒂𝒂𝟐𝟐 =𝐹𝐹 �𝒙𝒙(𝑡𝑡) +𝑘𝑘𝒙𝒙𝟏𝟏�
2�𝐹𝐹 �𝒙𝒙(𝑡𝑡) +𝑘𝑘𝒙𝒙𝟐𝟐�
2�

𝐹𝐹 �𝒙𝒙(𝑡𝑡) +𝑘𝑘𝒙𝒙𝟑𝟑�
2�

𝑚𝑚− 𝑐𝑐𝒗𝒗(𝑡𝑡) + 𝒈𝒈

𝑘𝑘𝒗𝒗𝟐𝟐 = 𝒂𝒂𝟐𝟐 𝛥𝛥𝛥𝛥, 𝑘𝑘𝒙𝒙𝟐𝟐 = �𝒗𝒗(𝑡𝑡) +2.3. Power on mass points
The resultant force 𝑭𝑭𝒊𝒊 (𝒕𝒕) of the force applied to theparticle 𝑖𝑖 at time 𝑡𝑡 is as follows from the external force
such as wind force 𝒇𝒇𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘 and gravity 𝒇𝒇𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈 and theforce generated from the internal structure of the clothsuch as the damping force 𝒇𝒇𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅 against the vibrationof the spring and the force 𝒇𝒇𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 by the spring. Can be
expressed in𝑭𝑭𝒊𝒊 (𝑡𝑡) = 𝒇𝒇𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈 + 𝒇𝒇𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅 + 𝒇𝒇𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 + 𝒇𝒇𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘

𝒂𝒂𝟑𝟑 =𝑚𝑚𝑘𝑘𝒗𝒗𝟏𝟏�
2� 𝛥𝛥𝛥𝛥− 𝑐𝑐𝒗𝒗(𝑡𝑡) + 𝒈𝒈

𝑘𝑘𝒗𝒗𝟑𝟑 = 𝒂𝒂𝟑𝟑 𝛥𝛥𝛥𝛥, 𝑘𝑘𝒙𝒙𝟑𝟑 = �𝒗𝒗(𝑡𝑡) +𝑘𝑘𝒗𝒗𝟐𝟐�
2� 𝛥𝛥𝛥𝛥− 𝑐𝑐𝒗𝒗(𝑡𝑡) + 𝒈𝒈
𝑚𝑚
𝑘𝑘𝒗𝒗𝟒𝟒 = 𝒂𝒂𝟒𝟒 𝛥𝛥𝛥𝛥, 𝑘𝑘𝒙𝒙𝟒𝟒 = (𝒗𝒗(𝑡𝑡) + 𝑘𝑘𝒗𝒗𝟑𝟑 )𝛥𝛥𝛥𝛥
11
11𝒗𝒗(𝑡𝑡 + 𝛥𝛥𝛥𝛥) = 𝒗𝒗(𝑡𝑡) + � 𝑘𝑘𝒗𝒗𝟏𝟏 + 𝑘𝑘𝒗𝒗𝟐𝟐 + 𝑘𝑘𝒗𝒗𝟑𝟑 + 𝑘𝑘𝒗𝒗𝟒𝟒 �
63
3
61
1
1
1𝒙𝒙(𝑡𝑡 + 𝛥𝛥𝛥𝛥) = 𝒙𝒙(𝑡𝑡) + � 𝑘𝑘𝒙𝒙𝟏𝟏 + 𝑘𝑘𝒙𝒙𝟐𝟐 + 𝑘𝑘𝒙𝒙𝟑𝟑 + 𝑘𝑘𝒙𝒙𝟒𝟒 � (5)6336𝒂𝒂𝟒𝟒 == 𝑚𝑚𝑖𝑖 𝒈𝒈 + 𝒓𝒓𝒊𝒊 (𝑡𝑡) + 𝒇𝒇𝒊𝒊 (𝑡𝑡) + 𝛼𝛼 cos(𝛽𝛽) sin(𝛾𝛾) + 𝛼𝛼 sin(𝛽𝛽) sin(𝛾𝛾)(1)(∆𝑡𝑡: time step)
The motion of mass points in the virtual world can be
simulated by these equations.

2.4. Equation of motion

Based on the equation of motion, the acceleration 𝒂𝒂𝒊𝒊 (𝑡𝑡)is expressed by the following equation.
(2)
𝒂𝒂𝒊𝒊 (𝑡𝑡) = 𝑭𝑭𝑖𝑖 (𝑡𝑡)⁄𝑚𝑚𝑖𝑖

2.6. Collision with other objectsIn this study, we consider the collision between the clothand the body. Since a large number of mass points andthe body must be judged, a penalty method that takes asimple calculation is used. This time, the mass point isregarded as a point and the bone is regarded as a capsule,and collision judgment is performed.

2.5. Numerical calculation method

In this study, Euler method, FB Euler method, andRunge-Kutta method were used from the explicit
formulas [6].
2.5.1. Euler method

2.6.1. Expression of the body

Assuming that the mass point moves linearly withconstant acceleration between time 𝑡𝑡 and time 𝑡𝑡 + ∆𝑡𝑡 thevelocity 𝒗𝒗𝒊𝒊 and the coodinates 𝒙𝒙𝑖𝑖 can be calculated by thefollowing equations using the force acting on the particles
calculated in Section 2.2.
𝒗𝒗𝑖𝑖 (𝑡𝑡 + ∆𝑡𝑡) = 𝒗𝒗𝑖𝑖 (𝑡𝑡) + 𝒂𝒂𝑖𝑖 (𝑡𝑡)∆𝑡𝑡(3)𝒙𝒙𝑖𝑖 (𝑡𝑡 + ∆𝑡𝑡) = 𝒙𝒙𝑖𝑖 (𝑡𝑡) + 𝒂𝒂𝑖𝑖 (𝑡𝑡)∆𝑡𝑡(∆𝑡𝑡: time step)

A capsule is a cylinder with hemispheres attached to bothends, defined by a line segment and radius 𝑟𝑟, and is thepart within the distance and radius 𝑟𝑟 from this line
segment.
Calculating the position of the capsule with the back, hips,thighs, and shin bones as the axis of the cylinder did not
perform collision detection correctly (see Fig.3).
Therefore, this time, in order to increase the number ofcapsules and improve the accuracy of collision detection,
the back and shin bones are divided into two, and thethigh bones are divided into three.

2.5.2. FB Euler method

It is a numerical calculation method that uses both theEuler method and the backward Euler method at the sametime. Velocity applies the Euler method for current
acceleration, and position applies the backward Euler
method for future speed.
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2.6.2. Penalty method

3. Simulation environment

The penalty method is one of the rigid body simulation

This program was created using the DirectX SDK, which
is a standard CG library, in a program development
environment using the C / C ++ language. Microsoft
Visual Studio Community 2019 was used to create theprogram this time. It ran on Intel Core i7 (Windows 10Pro).
4. Simulation result
The FB Euler method is used as the numerical calculationmethod. The simulation results are shown in the figure
below (See Fig. 4).

Fig. 3. Execution result by

FB Euler method

methods. When objects collide with each other and aslight sunk occurs, a force (penalty force) proportional to
the sunk value can be applied to obtain the behavior after
the collision (See Fig. 3).
From this, it is possible to push back the lattice points
colliding with the cloth to the outside of the body by theforce of the spring so as not to be sunk into the body.
2.6.3. Collision detection with capsule pointThe reason why capsules are used for collision detectionis that the judgment only needs to be replaced. The
collision between the capsule and the point is divided intoa columnar part and a hemispherical part at both ends. Let
the point 𝑥𝑥 for collision determination be the intersectionof the perpendicular and the line segment drawn from thepoint 𝑥𝑥 to the line segment: the point 𝑦𝑦 is obtained. At
this time, the coordinates 𝑎𝑎 and 𝑏𝑏 at both ends of the line
segment are set, and since the point 𝑦𝑦 is on the line
passing through the coordinates 𝑎𝑎 and 𝑏𝑏, it is expressedby the following equation.
𝒚𝒚 = 𝒂𝒂 + 𝑠𝑠(𝒃𝒃 − 𝒂𝒂)(6)(𝒂𝒂, 𝒃𝒃, 𝒚𝒚: 3D vector, 𝑠𝑠: Scalar)
Since the perpendicular line is orthogonal to this line, itis necessary to satisfy the following equation.
(𝒚𝒚 − 𝒙𝒙) ∙ (𝒃𝒃 − 𝒂𝒂) = 0(7)(𝒙𝒙: 3D vector)
The only unknown is 𝑠𝑠, and when 𝑠𝑠 is found, the point 𝑦𝑦
is found, and it is possible to determine the collision
between the cylinder and the foot. At this time, if thepoint 𝑦𝑦 exists on the line segment and the distance 𝑟𝑟 ′between the point 𝑥𝑥 and the point 𝑦𝑦 is smaller than 𝑟𝑟, it
can be seen that the point 𝑦𝑦 collides with the cylinder.
Since 𝑟𝑟 − 𝑟𝑟 ′ is the distance from the surface of thecylinder to the point 𝑥𝑥, this value is calculated using thepenalty method.
If it is found that the cylinder does not collide, then thecollision between the point and the sphere is determined.
The collision between a point and a sphere can bedetermined by examining whether the distance between
the points 𝑎𝑎 and 𝑏𝑏 and the point 𝑥𝑥 is within 𝑟𝑟. Collisiondetermination between a capsule and a sphere (radius 𝑟𝑟 " )is based on the same principle, and the above 𝑟𝑟 is
replaced with 𝑟𝑟 + 𝑟𝑟 " for calculation and determination.

Fig. 4 Execution result by FB Euler method
using the proposed method
Simulations were performed using the Euler method andthe Runge-Kutta method. The Euler method resulted in
the cloth moving violently and moving away from thebody (See Fig. 5). In the Runge-Kutta method, themovement of the animation became heavy, and the result
was that the contact between the foot and the skirt caused
the animation to dig in (See Fig. 6).
In addition, all the calculation methods resulted in theanimation moving being heavier than the execution result
when the bones were not divided.

Fig. 5. Execution result byEuler method using theproposed method

Fig. 6. Execution result by
Runge-Kutta method using
the proposed method

5. Consideration
As a result of the simulation, as mentioned in theexecution results in Chapter 4, the collision detection
considering the contact between the skirt and the bodyusing the FB Euler method was stable, and a simpleanimation could be executed. However, there are thefollowing problems.

310
Parameters must be changed manually.
Examination of implicit numerical calculation
methods and contact force calculation methods.
Consideration of texture mapping method for skirt.
Consideration of methods that require lesscalculation.

Authors Introduction
Dr. Satoshi Ikeda
He received PhD degree from Hiroshima
University. He is an associate professor
in the Faculty of Engineering, Universityof Miyazaki. His research interest
includes graph theory, probabilistic
algorithm, fractal geometry and measuretheory.

6. Conclusion
The purpose of this research was to refer to past researchand experiment with simple animations that dynamically
express fabrics and take into account the contact between
the body and the skirt. The animation completed in thisresearch was a simple animation with a small number ofquality points, and there were many parts that could not
be implemented, such as texture mapping and cloth
texture expression. It is still difficult to perform realistic
clothing simulations. Additionally, you need to pay
attention to how to dress 3D characters, how to represent
differences in cloth materials, how to determine
collisions with higher accuracy, and how to reduce
calculations. In addition, we would like to conduct
practical research, including the above-mentioned
improvement measures, by simulating various
movements such as hula dance and dress design, andworking on CAD production that can express more
realistic fabrics.

r. Taketo Kamasaka
He received a master's degree from
Department of Computer Science andSystem Engineering, University ofMiyazaki. His current research interests
are computer graphics, entertainment
computing, and so on.
Dr. Kaoru Ohe

She received her Ph.D. degrees fromUniversity of Miyazaki, Japan, in 2014.
Currently she is an associate professor ofthe Center for Science and Engineering
Education, Faculty of Engineering. Her
research is separation engineering
especially adsorption hazardous heavy
metals and oxyanions.

References
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Zorah Lahnar, Daniel Cremers and Tony Tung
DeepWrinkles: Accurate and Realistic Clothing Modeling,
15th European Conference on Computer Vision, 2018, pp.
1-18.
Makoto Sakamoto and Ayumi Taniue, Attempt of Cloth
Animation by OpenGL, Memoirs of the Faculty ofEngineering, University of Miyazaki, in Japanese, Vol. 37,
2008, pp. 299-304．
Makoto Sakamoto, Seira Nagatomo, and Ayumi Taniue,
Attempt of Cloth Animation by OpenGL Ⅱ, Memoirs ofthe Faculty of Engineering, University of Miyazaki, inJapanese, Vol. 39, 2010, pp. 327-332．
Makoto Sakamoto and Minaho Sakumoto, Attempt ofCloth Animation by Considering the Collision with theObject, Memoirs of the Faculty of Engineering,
University of Miyazaki, in Japanese, Vol. 40, 2011, 223227.
Mari Inoue, Research on the Mechanics of Fibrous
Materials, SEN’I GAKKAISHI(Textiles and industry). ,in Japanese, Vol. 64. No.8, 2008, pp.246-251.
Norimasa Yoshida, Mikihiro Sato, and Yasuo Yamashita,
Interactive Visual Simulation of Cloth and Its Stability
Test, Report of the Research Institute of Industrial
Technology, Nihon University, No. 86, 2006, pp.1-14．

Prof. Makoto Sakamoto
He is a professor in the Faculty ofEngineering, University of Miyazaki. His
first interests lay in hydrodynamics andtime series analysis, especially thedirectional wave spectrum. He is atheoretical computer scientist, and his
current main research interests areautomata theory, languages, and computation. He is alsointerested in digital image processing, CG, VR, AR, MR,AI, complex systems, and so on.
Prof. Amane Takei
He is working as a professor for
Department of Electrical and systems
Engineering, University of Miyazaki,
Japan. His research interest includes highperformancecomputingfor
computational
electromagnetism,
iterative methods for the solution ofsparselinearsystems,
domaindecomposition methods for large-scale
problems. Prof. Takei is a member of IEEE, an expert
advisor of IEICE, a delegate of IEEJ, a director of JSST.

311

Dr. Masahiro Yokomichi
He is an associate professor of Facultyof Engineering at University ofMiyazaki, Japan. He received his D.
Eng. degree in Precision Engineeringfrom Hokkaido University in 1995. His
research interest is Robotics andComputer Vision.
Dr. Kenji Aoki

He received Ph.D. of Engineering fromKagoshima University in 2010. He iscurrently working in Information
Technology Center at University ofMiyazaki as an associate professor, since2010. His research interests include bioinformatics,evolutionarycomputation, information system andIntelligent systems. He is a member of IPSJ and JSET.
Dr. Tsutomu Ito

He is an associate professor of theDepartment of Business Administration
at National Institute of Technology, Ube
College, Japan. His current researchinterests include internet of things (IoT),mechanicalengineering,artificial
intelligence (AI), automata theory,
quantitative analysis of Japanese
Keiretsu. He earned his doctor degree of Engineering from
Hiroshima University, Japan in 2018.
Prof. Takao Ito

He is a professor of Management ofTechnology (MOT) in Graduate Schoolof Engineering at Hiroshima University.
His current research interests include
automata theory, artificial intelligence,and systems control, quantitative
analysis of interfirm relationships usinggraph theory, and engineering approachof organizational structures using complex systems theory.

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