EUROGRAPHICS 2010 / H. P. A. Lensch and S. Seipel

Short Paper

A Film Balloon Design System
Integrated with Shell Element Simulation
Yohsuke FURUTA1,2 , Nobuyuki UMETANI1,3 , Jun MITANI1,2 , Takeo IGARASHI1,3 and Yukio FUKUI2
1 JST, ERATO, IGARASHI Design UI Project, Frontier Koishikawa Bldg., 7F 1-28-1, Koishikawa, Bunkyo-ku, Tokyo 112-0002, Japan
2 University of Tsukuba, 1-1-1 Tenno-dai, Tsukuba, Ibaraki 305-0005, Japan
3 The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0003, JapanAbstract
CAD systems that have user-friendly interfaces for assisting ordinary people to design objects is becoming common. Most of these systems combine a sketch interface with physical simulation. In this paper, we propose asystem for designing balloons made of non-stretchy material such as aluminum foil, plastic film and paper. We
implemented the system by using a finite element method that is based on discrete Kirchhoff triangle (DKT) shellelements and a sketch interface that enables users to easily design the realistic shape of an inflated balloon. The
2D pattern for the balloon design is generated automatically by our system. We evaluated our system by a user
study with six elementary school children and their parents. These users designed target objects and responded toa questionnaire.
Categories and Subject Descriptors (according to ACM CCS): I.3.5 [COMPUTER GRAPHICS]: Computational
Geometry and Object Modeling—Physically based modeling

1. Introduction
Three-dimensional computer-aided design (3D CAD) systems are now used widely in product design. In addition,
computer-aided engineering (CAE) systems are becoming
common. As a result, in recent years, the study of user interfaces that target inexperienced users has become popular.
At the same time, the costs for making real 3D objects from3D CAD data are decreasing due to the spread of rapid prototyping systems such as 3D printers. However, it is sometimes
difficult to realize the target shape for objects made of thinmaterials. These materials are used in products such as balloons or stuffed animal toys, which are made by stitching 2D
material. In this case, the designer has to design 2D patterns
for the target 3D shape. Because it is a type of inverse designproblem, much experience and intuition are needed. In addition, it can require trial and error processes that increase thecost due to the extra consumption of materials. Although we
can reduce this cost by using a computer-aided engineering(CAE) system that can analyze the behavior of products, it isstill difficult to introduce the system into the field of casualdesign, such as do-it-yourself (DIY) projects. Most current
CAD and CAE systems operate independently of each other,c The Eurographics Association 2010.
°and it is difficult to make them work together. This meansthat if we design an object with a CAD system, first we haveto design the patterns with CAD and then import the data to
the CAE system. Although we can see the result of balloon
inflation by running a simulation in CAE, we would need toreturn to the CAD system if we are not satisfied with the result. To reduce the time and cost, we propose a system thatenables users to design the 3D shape of a balloon directly.
We believe that a balloon is a reasonable target as one ofcase studies for combining CAD and CAE. The proposedsystem automatically generates the 2D patterns for the 3D
shape by running a physical simulation in the background.
We assume that the target balloon is made of non-stretchy
material such as aluminum, plastic film, or paper because it
is not straightforward to obtain the 2D pattern from the 3D
shape. Furthermore, simulating the inflation of the balloon
requires precise simulation because we assume that the material is non-stretchy. The finite element method (FEM) forthe physical simulation is a feature of this system.
In this paper, we describe the algorithm of the simulation,
the user interface, and present a user study to evaluate oursystem.

Y. FURUTA & N. UMETANI & J. MITANI & T. IGARASHI & Y. FUKUI / Film Balloon Design System

2. Related work
The technology of computer graphics (CG) was first used togenerate images or movies, not to design an actual object
shape. However, it is not unusual to combine a physical simulation with a geometrical modeling system today to generate realistic CG animation. For example, sketch based modeling systems [AD06] and [Ern] include the physical simulation. Popović developed a system in which the user candirectly control the result of a solid body physical simulation [PSE∗ 00]. These systems are intended to assist users in
CG animation, not the design of a physical object.

In our system, the user inputs the projected 2D image ofthe inflated balloon. When the user draws the image, the pattern and the three-dimensional computer graphics (3DCG)
model of the inflated balloon are generated automatically.
The pattern is generated so that the inflated shape matches
the image drawn by the user. Because the balloon is madewith two patterns of the same shape, the system generates only one pattern. Generation of the pattern and inflated
3DCG model is performed every time the user changes theprojected 2D image of the balloon. Consequently, the user
can edit the shape of the balloon interactively by seeing theinflated 3D shape and the 2D pattern.

However, in recent years some researchers have been developing systems that can design actual objects easily by using the technologies of computer graphics and user interfaces. Mitani developed a system for generating patterns forpapercraft by approximating a given triangular mesh modelwith a set of triangle strips [MS04]. A system that automatically generates the relief from a 3D model was developedby Weyrich [WDB∗ 07]. Mori developed a system that generates patterns for stuffed animal toys [MI06]. These systems have the same purpose, which is to enable inexperienced users to design actual objects with a computer. Mori’s
study is especially similar to ours in that experimental subjects design a shape made with thin materials and then thesystem generates 2D patterns automatically from the userdesigned 3D shape. The difference is that Mori’s system usesa spring-mass simulation but our system uses FEM analysis with discrete Kirchhoff triangle (DKT) shell elements,
which are used in industrial CAE systems to simulate thinand non-stretchy materials, which require precise calculations. The effectiveness of the simulation using DKT shellelements for various lamina elements was shown by Batoz
in numeric experiments [BBH80].

To generate the pattern, the system uses the outline of theimage drawn by the user as the initial pattern. Because theinflated shape from the initial pattern often differs from theuser’s intended shape, the pattern can be modified so that theinflated (simulated) shape more closely resembles the drawn
image (details are described in Sec 3.4). The flow of the design process with our system is as follows:

3. Overview of the proposed system

1. A user draws a projected image of the inflated balloon on
the screen by using a mouse or pen tablet.
2. A closed loop of the silhouette is extracted from thedrawn image. The system triangulates it with Delaunay
triangulation.
3. The system generates the inflated 3D shape from the pattern by FEM analysis with DKT shell elements .
4. The silhouette of the inflated 3D shape and the drawn image are compared. Then the pattern is modified according
to the difference between them.
5. Return to (3.).
6. When the final pattern is generated, a representation of
the air intake is added.

First, we describe the target object of our system. The object
is a balloon made with aluminum foil, a thin film material
with little retractility; that is, material that is more rigid thanrubber. To simplify our example, we make a balloon by gluing the border of two same-shaped patterns together (Fig.
1). Even though the structure of the balloon is very simple,
it is not easy to predict the inflated shape from the pattern.
The inverse is also true: it is difficult to estimate the shape ofpatterns from the inflated 3D shape.

(2)

(1)

(4)

(3)

(5)

(6)

Figure 2: Flow of our system.

3.1. Simulation

Figure 1: An example of the balloon targeted with this system.

We implemented the FEM analysis with the DKT shell elements (Kirchhoff hypothesis conducts that a continuous condition is necessity for thin shell, but entirely C1 condition isvery complex. Dhatt [Dha69] proposed an element that hasc The Eurographics Association 2010.
°Y. FURUTA & N. UMETANI & J. MITANI & T. IGARASHI & Y. FUKUI / Film Balloon Design System

C1 condition on discrete point in the element. It is called discrete kirchhoff triangle (DKT) element). The strain energy Uof a linear thin material is described as follows:

U=12a clockwise direction to find Pi+1 (Fig. 3(2)). Finally, weobtain the closed loop by repeating the previous operationuntil |Pi − P1 | < n (Fig. 3(3)). In our implementation, we set
n = 10 pixels.

ZΩκDb κdΩ(1)

P0nP1

P1

where E is Young’s modulus, v is Poisson’s ratio, and t is
the thickness of the board. Db is calculated as follows:Db =
Et 3

212(1 − v ) (1)

1


1
1(2)

(1 − v)/2We analyze only one side of the balloon, under the condition that the outline of the pattern does not move in thevertical direction for the simulation because of its symmetry property. Pressure is added in the direction normal to atriangular element. We used an implicit method for the analysis because of its stability, and the Newmark-β algorithm
for temporal integration. To solve the simultaneous linear
equations, the conjugate gradient method is used for preprocessing the imperfect ILU resolution with ordering by theminimum degree method.
3.2. Mesh reuse for FEM
Our system uses the Delaunay triangulation algorithm togenerate the mesh for FEM simulation. In theory, the meshis regenerated according to the changes of the target shape.
However, because this mesh generation consumes muchcomputational time, we can omit the remeshing operations
and reuse the previous mesh as long as none of the following conditions are true:• The topology (connectivity) of the mesh needs to bechanged according to the Delaunay triangulation algorithm.
• One or more triangles is reversed.
• When R × 15 < L, where R is the radius of the inscribedcircle of a triangle, and L is the length of the longest edgeof the triangle.
With this simplification, we realize a fast simulation.
3.3. Paint interface and extraction of outline
The painted texture and outline are extracted from the shapedrawn by the user. To extract the outline, which is a closed
loop with no self intersections, we trace the boundary of theshape. The algorithm of this tracing is as follows. First, wedefine an initial position (P1 ) of the boundary by scanninghorizontally from the upper left to the lower right (Fig. 3(1)).
We set P0 = (P1x , P1y + n). Then we trace the boundary byscanning pixels on a circle with radius n and center Pi inc The Eurographics Association 2010.
°P2
P3

P4 P5 P6(2)(3)

Figure 3: Extracting the closed outline loop. (1) Defining theinitial position. (2) Repeated tracing of the next positions.
(3) The traced positions forming the final image.

3.4. Modification of the pattern
The goal of our system is to generate patterns of a balloon
conforming to the shape drawn by the user. If we simply inflate the initial patterns (the same shape as the drawn image),
the result will not be suitable; in particular, the result tends
to be small. Hence, we have to modify the initial patterns sothat the inflated shape matches the drawn image. To realizethis, our system modifies the patterns according to the difference between the shape drawn by the user and the inflated(simulated) shape. The flow of this operation is as follows:
1. Extract the outline from the image drawn by the user.
This is used as the initial shape of the pattern.
2. Triangulate the closed region with Delaunay triangulation and run the FEM simulation to produce the inflated
shape.
3. Translate the coordinates L0 of the silhouette of the inflated shape so that the barycenter matches the barycenter of the coordinates L of the outline extracted from thedrawn image.
4. Apply the least squares method to rotate L0 so that thedifference from L becomes the smallest.
5. Obtain the difference vector vi , which is Li − Li0 .
6. Shorten vi if the length exceeds the threshold (we set 3mm).
7. Add −vi to the previous coordinate of each vertex of thepattern.
8. Apply the Laplace smoothing operation to the outline ofthe pattern to smooth the pattern.
9. Return to (3.)(6.) and (8.) are applied for easier simulation convergence.
3.5. Creation of actual balloon
The balloon, our target object, inflates by applying pressure
from inside to outside, so an air intake is required. We developed our system to add the air intake to the pattern automatically. The site is a thin rectangle which has a 10 mm

Y. FURUTA & N. UMETANI & J. MITANI & T. IGARASHI & Y. FUKUI / Film Balloon Design System

inner width. The direction of the rectangle is set so that itmatches the direction from the center of the pattern to thefarthest coordinate on the outline.
After printing the pattern on the real material, the user
glues the two patterns at the specified lines together manually, and inserts a straw into the air-intake spot. Then user
blows through the straw to inflate the balloon.
4. User study

Figure 5: Examples created in the workshop. Left col.: created objects, Center col.: images designed by the subjects,
Right col.: patterns generated by our system.

Figure 4: Photo of the workshop.
We held a workshop as a user study to evaluate our system. The subjects were 6 pairs of schoolchildren and theirparents. Figure 4 shows the user study. The objects shownin Fig. 5 are the balloons created by the subjects. We used
sheets of tracing paper as the material.
We distributed questionnaires after the workshop. Most of
the answers for the question “Was the system easy to use?”
were Yes, and we received comments such as “Viewing thesimulated shape is fun,” “The 3DCG looks real and it is goodfor viewing the shape from different angles,” and “I could
see the possibilities using computers.” Moreover, almost allof the schoolchildren gave the highest score for the question “Could you draw the picture that you imaged?” In theworkshop we prepared tablet PCs, so it seems that even thechildren could easily carry out the drawing operation.
The comment “I wanted advices or software support toshow the shapes that would be inflated well” was given for
the result that the shape did not inflate well in the simulation
when the shape was long and included a thin section.
5. Conclusions and future work
We developed a system for designing the shape of a balloon
made with thin and non-stretchy material. By using FEM
analysis with TDK elements, the inflated shape can be simulated. We evaluated the usability of our system by organizing
a workshop. As future work, a comparison of the results withand without using our system will be conducted. We will
also evaluate the computing time. This will help ascertain
the most appropriate mesh for the simulation. In addition,
we want to develop this system so that it can process more

complicated balloons made with multiple pieces of patterns.
Moreover, many materials, such as other aluminum foils andpolyvinyl, will be input as the thin film material for the balloon. Finally, we want to enable the use of various materials
so that the user can easily specify the physical properties thatare best suited to the object.
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