EUROGRAPHICS 2012 / P. Cignoni, T. Ertl
(Guest Editors)

Volume 31 (2012), Number 2

Pixel Art with Refracted Light by Rearrangeable Sticks
Yonghao Yue1 , Kei Iwasaki2 , Bing-Yu Chen3 , Yoshinori Dobashi4 and Tomoyuki Nishita1
1 The University of Tokyo 2 Wakayama University 3 National Taiwan University 4 Hokkaido University
1 {yonghao,nis}@nis-lab.is.s.u-tokyo.ac.jp 2 iwasaki@sys.wakayama-u.ac.jp 3 robin@ntu.edu.tw 4 doba@ime.ist.hokudai.ac.jp

(a)

(b)

(c)

(d)

Figure 1: (a) Our fabricated transparent sticks. (b) Arranging the sticks and putting them in a container by a user. (c) Whenthe user puts the arranged sticks between a projector and a screen, a pattern on the screen can be observed due to the refracted
light. (d) Top: the desired pattern (please see Acknowledgments for the details), bottom: the pattern on the screen.
Abstract
Pixel art is a kind of digital art that through per-pixel manipulation enables production of a diverse array ofartistic images. In this paper, we present a new way for people to experience and express pixel art. Our digitalart consists of a set of sticks made of acrylate resin, each of which refracts light from a parallel light source, incertain directions. Artistic users are able to easily rearrange these sticks and view their digital art through therefracted light projection on any planar surface. As we demonstrate in this paper, a user can generate various
artistic images using only a single set of sticks. We additionally envision that our pixel art with rearrangeable
sticks would have great entertainment appeal, e.g., as an art puzzle.
Categories and Subject Descriptors (according to ACM CCS): I.3.8 [Computer Graphics]: Applications—

1. Introduction
Pixel art (a type of digital art) represents game charactersor other general images using a carefully chosen set of pixels, each of which has a finite planar dimension and which
is usually immediately recognizable visually. Pixel art enables rich power of expression, although it usually consistsof only a small number of pixels. Thus, the graphics usedin classic video games or in GUI icons are mostly based on
pixel art [KL11].
The basic concept of pixel art is to tile pieces of ‘pictureelements’ that are the same size. We can find other art formats or toys that share similar concepts, such as 3D pixel art
c 2011 The Author(s)Computer Graphics Forum c 2011 The Eurographics Association and Blackwell Publishing Ltd. Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ,
UK and 350 Main Street, Malden, MA 02148, USA.

(e.g. [QBL,Jea10]), tile art, ‘Post-it’ art (e.g. [Liu09]), jigsaw
puzzles, or Lego building blocks. These art-forms or toys, incommon with pixel art, stimulate human creativity, and people often enjoy creating their desired patterns or shapes bythemselves.
On the other hand, the creation of desirable patterns or
shapes, is itself an interesting research topic in the field ofcomputer graphics. Many methods, possibly utilizing specialist devices or the manufacture of various objects, havebeen proposed for reproducing a number of specialized settings, such as the 6D light fields [FRSL08], the desired
shadows [MP09], shadings [AM10], sub-surface scatter-Y. Yue et al. / Pixel Art with Refracted Light by Rearrangeable Sticks

ing properties [DWP∗ 10, HFM∗ 10], and hologram patterns(e.g. [RRMG10]). Additionally, the redirection of light togenerate desired patterns is a powerful approach that enables
rich power of expression. Such approaches include methods of computing reflective or refractive surfaces for producing caustics [WPMR09, FDL10, PJJ∗ 11], and a method for ahigh contrast projector using light reallocation [HSHF10].
In this paper, we bring the expressive power of pixel art
and the light redirection approach together, and present a
new approach to producing creative and enjoyable pixel art,as shown in Figure 1. Our method consists of a set of transparent sticks made of acrylate resin (refractive index: 1.49),
each of which refracts light in a certain direction. By arranging these sticks and placing them appropriately between
a parallel light source (e.g. sun-light or a projector) and a
viewing-surface (screen), one can observe the resulting pixel
art on the screen.
By bringing pixel art and the light refraction together, people can enjoy the surprise in that they cannot tell what happens by just taking a look at the sticks because the resulting pattern is only visible when the sticks are appropriately
placed between the light source and the screen. In this sense,
our art can be used as a tool for steganography.
In our system, the number and types of the sticks are fixedin advance. A user first inputs an image of the desired pixel
art. Then, our system solves an optimization problem to determine the layout of the sticks so that the light redirectedby the sticks forms the pixel art on the screen. According
to the layout, the user arranges the sticks manually and inserts them into a container. Finally, the user can enjoy the
pixel art by actually placing the container between the lightsource and the screen.
Using only a single set of sticks, the user can produce various patterns of pixel art by rearranging the sticks. This concept is similar to that of Lego building blocks, and it helps
to stimulate imagination and creativity. We believe that thework that is needed to arrange the sticks is not a burden to theuser’s creativity, since the amount of effort is small thanks to
the nature of pixel art: a small number of pixels is sufficient
to enable rich power of expression.
Our method can be closely related to the method presented by Papas et al. [PJJ∗ 11]. In their method, they useda NC (Numerical Controlled) machine to fabricate a plate
made of acrylate resin, whose surface has micro-facets. With
this plate, one can produce smooth caustics that are highly
detailed, but the user needs to create individual plates for individual caustics patterns. Our method has some advantages
in the terms of the entertainment aspect and the cost for production can be reduced, since the user can produce various
patterns using only a single set of sticks.

Figure 2: An illustration of the problem settings. We arrange
the sticks like a grid.

2. Our Approach
2.1. Problem Settings
As shown in Figure 2, we use a set of two integer 2D orthogonal coordinates to describe the locations of the sticks (px ,py ) and the screen pixels (qx , qy ). We assume that the desired pixel art consists of a set of square pixels, and that theirsizes are all the same. As shown in Figure 3, the shape of a
stick differs slightly from a parallelepiped. The difference isthat one of its faces is slightly tilted in order to redirect light
via refraction. The redirected (refracted) light will point to a
pixel on the screen (Figure 4). Unless otherwise stated, we
let the light that is incident onto the sticks all contribute toone of the pixels in the pixel art. It is also possible to letsome of the light refract toward the outside of the resulting
pattern. The base size of the stick is the same as the size of a
pixel, which could be e.g. 5mm × 5mm or 10mm × 10mm.
The height of a stick is sufficiently large (e.g., 10mm) for theuser to handle it easily.
Because the base shape of a stick is square, if we rotate thestick along its height axis by 90◦ , 180◦ or 270◦ , the refracted
light will point to different pixels. Therefore, allowing forthe rotation, a single stick can potentially redirect the lightto 4 locations. As shown in Figure 4, if the shift or translation in the locations sx and sy satisfy sx ≥ 1 and sy ≥ 0 (i.e.,
the redirected location is in the gray region), we state thatthe stick is in its basic orientation. When two sticks in theirbasic orientations and at the same location redirect the lightto different locations, we state that their types are ‘different’.
We basically assume that the number of pixels in the desired pattern is the same as the number of arranged sticks.
Additionally, we also assume that the pixel resolution, measured as the number of pixels, is square in shape, though, ourmethod can handle more general settings beyond these two
assumptions.
On one hand, it is possible to provide the user a large numc 2011 The Author(s)c 2011 The Eurographics Association and Blackwell Publishing Ltd.

Y. Yue et al. / Pixel Art with Refracted Light by Rearrangeable Sticks

Figure 3: A stick is shown on the left, while a 2D diagram ofthe stick is shown in the center. We call the blue square facethe ‘base’ of the stick. On the right we show a 2D illustrationof the light transfer (orange arrows) related to a stick (shownas the solid black lines). The light is assumed to enter the
stick perpendicularly from the base and transmit through the
stick. Then, the light gets refracted at the tilted face. As thelight refracts in the ‘opposite’ direction to the normal (boldblack arrow) of the tilted face, it will usually not be blocked
by the neighboring sticks (shown as the dashed black lines),or else the amount of blocked light is negligible.

ber of sticks in advance, and then let the user arrange thesticks using only a small subset of them. On the other hand,from an entertainment point of view, it is interesting if there
are no superfluous sticks after the user arranges the sticks.
Therefore, we basically consider that the number of sticks
the user has in advance is equal to the number of arranged
sticks, and thus is also equal to the number of pixels in thedesired pattern. By keeping the number of sticks smaller, it
is easier for the user to find the necessary sticks during thearrangement. The user can, of course, use additional sets ofsticks (e.g. colored sticks) for extending power of expression.
2.2. Constraints
For simplicity, we first consider only the intensity of lightand ignore the color. We formulate the problem as an optimization problem as follows. We use the binary variables
γi j,k = 0 or 1,(1)

to denote all of the possible ways of placement of the sticks.
The integer subscript i = 1, ..., NT denotes the type of the
stick, and NT is the number of types. The integer subscript
j = 1, 2, 3, 4 indicates the basic orientation (i.e., 0◦ ) and the90◦ , 180◦ and 270◦ rotated orientations, respectively. The
integer subscript k = 1, ..., NP denotes the location of the
sticks, and NP is the number of pixels. γi j,k = 1 means thatat the location k, we place a stick whose type is i and its
orientation is according to j.
For later use, we also introduce alternative representations
for the subscripts i and k. For the type of a stick, we alternatively represent it by the shift of the stick i.e., sx and sy
c 2011 The Author(s)c 2011 The Eurographics Association and Blackwell Publishing Ltd.

Figure 4: The relation between a stick (shown above) andthe screen location of the redirected light (shown as orange).
The blue region shows the base of the stick. If the light is not
redirected, it will reach the red pixel on the screen. We define
the difference (sx , sy ) between the red pixel and the orange
pixel as the shift, or translation, of the stick.

(Figure 4). For the location of a stick, we alternatively represent it using the integer coordinates px and py (Figure 2).
When we place a single stick at a location, we have thefollowing constraint,NT4∑ ∑ γi j,k = 1.

(2)i=1 j=1

For each stick type i, the number of the sticks is limited toMi . Thus, we have4NP

∑ ∑ γi j,k ≤ Mi .

(3)

j=1 k=1

The constraint for making the resulting desired pattern canbe formulated as follows. Let us use sx and sy as describedabove instead of i, and px and py instead of k. Then, if we denote the desired pattern at the screen pixel (qx , qy ) as c(qx ,qy ) ,we have∑sx, j +px =qx
sy, j +py =qyγ(sx ,sy ) j,(px ,py ) = c(qx ,qy ) ,(4)

where sx, j and sy, j represent the shift after considering therotation, i.e.,(sx , sy )
j=0



(−sy , sx )
j=1
.
(5)
(sx, j , sy, j ) =(−sx , −sy ) j = 2(sy , −sx )j=3
However we cannot always reproduce the desired patternexactly. This can be caused by an unachievable desired pattern, e.g., the total intensity of the desired pattern exceeds thetotal available incident light, or it requires a setting for which
the number and types of sticks are limited. We believe that,in practice, the introduction of a small amount of modification to the desired pattern is acceptable. Thus, we represent
the amount of modification using variables ε(qx ,qy ) , and use

Y. Yue et al. / Pixel Art with Refracted Light by Rearrangeable Sticks(a)Figure 5: Left: the input pattern (we prepared the patternaccording to the Eurographics logo). Center and right: theresulting patterns using the objective functions shown asEq.(8) and Eq.(9), respectively. Note that by using Eq.(9),the black regions and the smoothness of the pattern is better
preserved. The computation time is set to 1 minute.

∑(6)

γ(sx ,sy ) j,(px ,py ) = c(qx ,qy ) + ε(qx ,qy ) .

Because the intensity of the pixels on the screen should not
be negative, we have the following constraint,c(qx ,qy ) + ε(qx ,qy ) ≥ 0.

(7)

2.3. Objective Function
The objective of the optimization routine is to make the modification smooth and small enough to retain the desired pattern. To measure the amount of modification, we consider
the quadratic norm of the modification ∑ ε2(qx ,qy ) and that of

the gradient of the modification ∑ |∇ε(qx ,qy ) |2 . By making∑ ε2(qx ,qy ) and ∑ |∇ε(qx ,qy ) |2 small, the modification would besmall and smooth.
Although we could use the following simple objectivefunction,argmin(wa ∑ ε2(qx ,qy ) + wb ∑ |∇ε(qx ,qy ) |2 ),{γi j,k },{ε(qx ,qy ) }qx ,qy(8)

qx ,qywhere wa and wb are ‘weights’, we found it more useful toallow the weights for each pixel to change as follows;argmin∑ (wa,(q ,q ) ε2(q ,q ) + wb,(q ,q ) |∇ε(q ,q ) |2 ).

{γi j,k },{ε(qx ,qy ) } qx ,qy

x

y

x

(c)

Figure 6: (a) The refraction pattern of the stick. We can seethat the face is slightly distorted near the edges. (b) The resulting pattern on the screen. The light leaks to the neighbor pixels. (c) In our prototype, we attach to the container
a transparent filter with a black grating pattern to avoid theleak of light.

2.4. Solving the Optimization Problem

the following constraint instead,sx, j +px =qx
sy, j +py =qy

(b)

y

x

y

x

y

(9)

For the default values of these weights, we usewa,(qx ,qy ) = 1.0/(c2(qx ,qy ) + δ),(10)

where δ = 0.001 is a constant, andwb,(qx ,qy ) = 1.0/(|∇c(qx ,qy ) |2 + δ).

(11)

Using these default weights, the intensity and/or gradient of
the desired pattern will be better preserved if their values
are lower. This property is important, as the ‘black’ regionsand ‘smooth’ regions will be well preserved (see Figure 5).
The user can increase or decrease the weights for stronger or
weaker preservation if needed.

In summary, we minimize Eq.(9) subject to the constraints
shown as Eqs.(1), (2), (3), (6), and (7). Due to the constraint
shown as Eq.(1), our optimization problem becomes a classof mixed integer programming problem, which is NP-hard.
We have found that an approximated solution will usually
give a good result. In our prototype, we used the IBM ILOG
CPLEX Optimizer [CPL]. The user can set the time allowed
for solving the problem (e.g., a few minutes to 10 minutes),then the solver utilizes a branch-and-bound algorithm andprogressively refines the solution during the allocated time.
2.5. Fabricating the Sticks
We calculate the normals of the tilted faces from the shifts ofthe sticks according to Snell’s law. The main considerations
in fabricating the sticks are; 1) how to manufacture flat surfaces for the base and the tilted face; 2) how to make thesesurfaces face the desired orientation; and 3) how to make thedeviation in the sizes of the bases small. The first and second considerations are important for accurate redirection oflight, while the third consideration is important for arranging
the sticks as a grid.
In our prototype, we created a single mold that can produce 10 different types of sticks, with base sizes of 5mm
× 5mm. The number 10 comes from the following reason.
When we cast the hot acrylate resin into the mold, it willflow following the path created in the mold, and it will reacheach of the cavities for the sticks sequentially. Since we do
not want the hot acrylate resin to cool too much before it
reaches all the required areas, there is a limit to the numberof sticks that can be cast in a mold at any one time.
As the accuracy of production in our prototype is not very
high, there are slight distortions near the edges of the sticks
as shown in Figure 6(a). As a result, the redirected lightwill leak to the neighbor pixels (Figure 6(b)). To avoid thisproblem, we attach to the container a filter as shown in Figure 6(c). We believe that we can improve the production process of the mold and the casting process of the acrylate resin
to avoid this problem in the future.
c 2011 The Author(s)c 2011 The Eurographics Association and Blackwell Publishing Ltd.

Y. Yue et al. / Pixel Art with Refracted Light by Rearrangeable Sticks

indicate the basic orientation (i.e., 0◦ ) and 90◦ , 180◦ and270◦ rotated orientations, respectively.
We show the layout of the stick by using a map which wecall layout map (see, e.g., Figure 10). In the map, the typeof the stick for each location is shown using the number.
According to the color of the number, we align the stick sothat the number with the color will face upward.
2.8. Using Color Sticks

Figure 7: We show the types of the sticks by the locations of
the redirected light. A stick is assumed to be located at thecenter of each gray circle, which shows the range in consideration. The orange pixels show the locations of the redirected light when the sticks are in their basic orientations.
The black pixels show the locations of the redirected lightwhen the sticks are rotated by 90◦ , 180◦ or 270◦ . (a) to (f)show 6 different configurations of types.

2.6. Choosing the Types of Sticks
Focusing now on the creation of a mold, we should consider
the case where the number of types of sticks is 10. In our prototype, we choose 10 different shifts within the range where
the distance of a shift is no larger than 8 times of the widthof the stick, as shown in Figure 7.
There are many possibilities in choosing the types of stick.
We first chose 10 types of stick with the smallest different
shifts (in pixels), as shown as Figure 7(b). We found that thisselection is not ideal if the desired patterns contain a wide
black region. This is because the redirected light cannot diverge far from the incident light, and thus cannot avoid theblack region. On the other hand, by choosing the 10 typesof sticks that give the largest shifts (Figure 7(c)) we cancreate various desired patterns fairly easily. One disadvantage is that when the shifts are larger, the shape of the redirected light becomes much more distorted. Thus, we thentested others configurations of stick-types, this time including both sticks that produced a large shift along with sticks
that caused a small shift in different distributions, as shownin Figures 7(a), (d), (e) and (f). The ability of these different
bundles to create the desired patterns seemed to be similar.
We chose the set shown as Figure 7(a), with the intention of
making the distortion small.
2.7. The Layout Map
To identify the type of a stick, we first align the stick in its
basic orientation and its tilted face in the near side. Then,we draw a number with different colors on the faces of the
stick for better identification of the type and the orientationof the stick. Black, red, green and blue colors are used toc 2011 The Author(s)c 2011 The Eurographics Association and Blackwell Publishing Ltd.

Our method can be extended to handle colors. We can createa ‘colored’ stick by simply painting the color onto the tilted
face or by pasting a color filter onto the tilted face using
instant glue (cemedine). Note that by using the cemedine,
the transparency and the refraction index is then retained
pretty well, since the dominant component of the cemedine
is cyanoacrylate. In our prototype, instead of actually creating colored sticks, we attach to the container a color filter created by printing the color pattern onto a transparency
sheet using a standard ink-jet printer.
To work with colored sticks, we can extend Eq.(6) as follows.

(r)
(r)
(r)

∑sx, j +px =qx T(px ,py ) γ(sx ,sy ) j,(px ,py ) = c(qx ,qy ) + ε(qx ,qy )



s
+p
=q
y, j
y
y


(g)
(g)
(g)
∑sx, j +px =qx T(px ,py ) γ(sx ,sy ) j,(px ,py ) = c(qx ,qy ) + ε(qx ,qy ) ,
s
+p
=q

y, j
y
y


(b)
(b)
(b)


 ∑sx, j +px =qx T(px ,py ) γ(sx ,sy ) j,(px ,py ) = c(qx ,qy ) + ε(qx ,qy )sy, j +py =qy(12)where the superscripts (r), (g) and (b) indicate the red, green
and blue components, respectively, and T indicates the transmittance of the filter (the color and the intensity of the lightsource can be included as well, if needed). Although we canmix different colors to produce new colors, multiple sticks
are needed for representing a single mixed color pixel, possibly resulting in a reduced power of expression. As an alternative, we can use a few set of sticks with basic colors.
To obtain the layout, we first solve the optimization problem
for the intensities, then the colors of the sticks are chosen to
be the corresponding pixel colors.
3. Results

In this section, all of the results are generated by rearranging a single set of sticks. The types are introduced in Section 2.6. The number of sticks of each type is 25 or 26, andthe total number of the sticks is 256. The resolutions of the
input patterns are all in 16 × 16. For computation, we used anotebook PC with an Intel(R) Core(TM)2 Duo U9600 CPU(1.6GHz) and 4GB main memory, and set 10 minutes forsolving the optimization problem. The default weights areused for all the tests. We let users arrange the sticks, and thetimes they took for arranging them varied between 12 and23 minutes.
We show the results of simulation and the results createdY. Yue et al. / Pixel Art with Refracted Light by Rearrangeable Sticks

(a)

(b)

(c)

Figure 8: The input pattern is the same as the one used for
Figure 10(c). Using the layout map as shown in (a), we canredirect the light toward the outside of the resulting pattern
as shown in (b). Then, the intensities of the pixels in the 16
× 16 region (c) match that of the input pattern perfectly. If
we do not allow the light redirection toward the outside of
the resulting pattern, the result will be Figure 10(c).

by the sticks fabricated by using a mold. We show the results of monochromatic patterns in Figures 10(a) to (c), andcolored patterns in Figures 10(d) to (g). In Figure 10(c), we
projected yellow color from the projector. In the colored examples shown in Figures 10(d) to (g), we attached color filters to the container instead of actually coloring the sticks. In
Figures 10(a) to (d), the total intensities of the input patterns
are smaller than the total intensity of the incident light. As aresult, some pixels in the simulated results become brighter.
Conversely, in Figure 10(g), the total intensity of the input
pattern is larger than that of the incident light. As a result,some pixels in the simulated results become darker. Nevertheless, we believe that these results still look good. In Figures 10(e) and (f), the total intensities of the input patterns
are the same as the total intensity of the incident light, andwe were able to obtain the results that perfectly match the
input patterns.
We can replace some of the transparent sticks with opaque
sticks. Additionally, we can fix the locations of these opaque
sticks so that we can observe a pattern on the arranged sticks,
as shown in Figure 9. By calculating the layout for the restof the sticks, we can also make this set produce a (different)
hidden pattern on the screen. This usage of our art-form canbe regarded as a kind of steganography. To realize this artform, we simply set γi j,k = 0 for the locations k where wewant to place the opaque sticks, and delete the corresponding
constraints shown as Eq.(2).
As mentioned before, we may consider the option to redirect the light toward the outside of the resulting pattern. By
considering this option, the modification can be reduced if
the total intensity of the desired pattern is less than that of
the incident light (Figure 8). On the other hand, it is moreconstrained and interesting if we discard this option, sincein this case all of the incident light is used. Thus, we did not
use this option other than the example shown in Figure 8. We
can easily disable this option by omitting some of the vari-

Figure 9: (a) The input pattern. (b) The layout map. (c) The
simulated result. (d) Opaque (black) sticks are introduced
so that we can observe the pattern ‘A’ directly from the arranged set of sticks, while (e) transparent sticks produce a
different pattern on the screen.

ables γi j,k that redirect light toward the outside of the desired
pattern.

4. Limitations
We show three typical failure cases in Figure 11. Figure 11(a) shows a toy example where the input pattern contains a large black region. Due to the capability in redirecting
light, it is not possible to redirect all the light to the lowerright corner using the set of the sticks. To handle input patterns like this example, we need to use the sticks that canredirect light to farther locations. We would like to note thatan input pattern usually does not contain such a large black
region.
For general input patterns, a failure case happens more
likely when the difference between the total intensity of the
input pattern and that of the incident light is larger. This isbecause we need to apply much modification to the pattern
to adjust the total intensity. As a result, some specific region
cannot be represented well. For example, in Figure 11(b),the total intensity of the input pattern greatly exceeds thatof the incident light. Thus, we need to suppress the intensity
variation to reduce the total intensity. As a result, we cannot represent the gradation pattern well. We show anotherfailure case in Figure 11(c). This example is created by increasing the intensity of the hair of the character shown in
Figure 10(e). Thus, the intensities of some of the pixels in
the resulting pattern need to be reduced for the conservationof light. Although our method tries to make the modification
as smooth as possible, since the regions of the hair are separated by the hair accessory, the resulting intensities becomec 2011 The Author(s)c 2011 The Eurographics Association and Blackwell Publishing Ltd.

Y. Yue et al. / Pixel Art with Refracted Light by Rearrangeable Sticks

Figure 10: Results of monochromatic patterns ((a) to (c)) and colored patterns ((d) to (g)). (a), (b), (c), (d) and (f): we prepared
the input images according to the Stanford bunny, the Utah teapot, the Eurographics logo, the landscape and the national flagof Italy, and an image of a killer whale, respectively. Please see Acknowledgments for the details about the input image (e). The
input image (g) is copyrighted by Nintendo Co., Ltd. The captured results show the images captured from the screen.

c 2011 The Author(s)c 2011 The Eurographics Association and Blackwell Publishing Ltd.

Y. Yue et al. / Pixel Art with Refracted Light by Rearrangeable Sticks

derivative work of the character "Hatsune Miku", originallycopyrighted by Crypton Future Media, INC. A modification of the character is permitted under Piapro Character
License (http://piapro.jp/license/pcl) by Crypton Future Media, INC.
References[AM10] A LEXA M., M ATUSIK W.: Reliefs as images. ACM
Transactions on Graphics (Proc. of SIGGRAPH 2010) 29, 4(2010), 60:1–60:7. 1[CPL] IBM
ILOG
CPLEX
Optimizer.
http://www01.ibm.com/software/integration/optimization/cplex-optimizer/.
4

Figure 11: Typical failure cases. The input image (b) is
copyrighted by Nintendo Co., Ltd. Please see Acknowledgments for the details about the input image (c).

different among these regions. The user could modify thesepatterns to obtain better results, though.
5. Conclusions and Future Work
We have presented a new type of creative and enjoyable pixel
art. By rearranging a set of sticks made from acrylate resin,and by positioning this set appropriately between a parallel light source (e.g. sun-light or a projector) and a viewingsurface (screen), one can observe the resulting pixel art on
the screen. According to the user specified pattern, our system solves an optimization problem to find the layout of the
sticks so that the resulting pattern on the screen represents
the specified pattern. We have shown that the user can produce various patterns by rearranging the sticks, using onlya single set of sticks. Another interesting aspect of our art
is that the resulting pattern is only visible when the sticks
are appropriately inserted between the light source and thescreen. Thus, our art can also be used as a tool for steganography.
For future work, we would like to create sticks with otherbase shapes, such as triangles or hexagons. Furthermore,
we would like to increase the pixel resolution by creatinga jigsaw-puzzle like version, where some of the sticks are
glued together to form basic blocks. Instead of using the individual sticks, it would then be easier for the user to rearrange these blocks.
Acknowledgments
We gratefully acknowledge helpful comments and thoughtful suggestions from the anonymous reviewers. We also
thank Prof. Chandrajit Bajaj for his useful discussions andproofreading. This work was supported by JSPS Grantin-Aid for Research Activity Start-up (23800011). The input images shown in Figures 1 (d), 10 (e) and 11 (c) are[DWP∗ 10] D ONG Y., WANG J., P ELLACINI F., T ONG X., G UO
B.: Fabricating spatially-varying subsurface scattering. ACM
Transactions on Graphics (Proc. of SIGGRAPH 2010) 29, 4(2010), 62:1–62:10. 2[FDL10] F INCKH M., DAMMERTZ H., L ENSCH H. P. A.: Geometry construction from caustic images. In Proceedings of the
11th European Conference on Computer Vision: Part V (2010),
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c 2011 The Author(s)c 2011 The Eurographics Association and Blackwell Publishing Ltd.