Finalist

Capricious Hearts
Kokichi Sugihara

Kokichi Sugihara “Capricious Hearts” 2017, Material: RGD720, Size: 249.6W x 74.4D x 127.2H (mm)The object appears to be four hearts in a line when we see it directly, but the reflection in a vertical mirror behind the object appears
to be the set of all four suits of the trump, i.e., diamond, club, heart and spade. We know that the shape of an object and its mirror
image are mirror symmetric to each other, and hence heart cannot change to diamond, etc., in a mirror; the behavior of this object
seems impossible. However, this is possible because our perception is subject to optical illusion.

22Finalist

Keywords: ambiguous cylinder, impossible object, optical illusion

1 Behavior of the Object
From a special viewpoint it appears to be four hearts in a

apt to interpret 2D images as 3D objects with as manyline, but if we rotate it around the vertical axis by 180

rectangles as possible [3]. Hence, if we present cylindricaldegrees, it appears to be the set of all four suits of the trump,shape with a constant height, we usually interpret the edge

i.e., diamond, club, heart and spade. These two appearances

curve of the cylinder as a plane curve perpendicular to thewill be enjoyed at the same time if we place a vertical mirror

axis of the cylinder, even if it is a space curve.

behind the object and look at the object and its mirror image

Combining these two observations, we can constructsimultaneously.

ambiguous cylinders. This is the basic idea for ambiguous

We know that the shape of an object and its mirror image arecylinders. I applied this method to four pairs of shapes, onemirror symmetric to each other, and hence heart cannot

is heart and the other is one of the four suits of the trump,change to diamond, for example, in a mirror; the behavior ofand thus generated four ambiguous cylinders. Finally I

this object seems impossible. However, this is possible

joined them to the present object

because our perception is subject to optical illusion.

3 Software & System

2 Production Process

With my original program written in Fortran, I computed theI found a systematic method for creating a new class ofshape of four objects corresponding to the four suits, andimpossible objects, which I named “ambiguous cylinders.”

then generated their STL data. Finally, using theThis class of objects generates optical illusion in the sensecommercialized modeling tools Rhinoceros version 5.0, I

that their appearances change drastically in a mirror [1]. The

merged them into one final object.

ambiguous cylinders are based on two observations, one is
physical and the other is psychological.

References

Physically, a single image of a 3D object does not have[1] Sugihara, K., Ambiguous cylinders: A new class of im-information about depth, and consequently there are infinitely

possible objects. Computer Aided Drafting, Design andmany possible 3D objects that yield the same 2D image [2].

Manufacturing, Vol.25, No.3, pp.19-25, 2015.

Hence, we can generate a 3D object that has two desired 2D[2] Sugihara, K., Machine Interpretation of Line Drawings.

appearances when seen from two special viewpoints, if theMIT Press, Cambridge, Massachusetts, 1986.

pair of appearances satisfies a certain condition.

[3] Perkins, D. N., Visual discrimination between rectangu-

Psychologically, on the other hand, our vision systems have alar and nonrectangular parallelopipeds. Perception andstrong preference for rectangularity in the sense that we are

Psychophysics, Vol.12, pp.293–331, 1972.

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