Mathematical Progress in Expressive Image Synthesis III by Yoshinori Dobashi & Hiroyuki Ochiai

Author:Yoshinori Dobashi & Hiroyuki Ochiai
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

Another example is shown in Fig. 4. In Fig. 4a, the solid appears to consist of a pole and four horizontal perches that cross at right angles. However, a flat ring hangs in such a way that it passes behind the pole but in front of all four perches. The actual shape of the solid is shown in Fig. 4b; the four perches are all behind the pole [9].

Fig. 4 Impossible motion “Four Perches and a Ring”: a a ring hangs from the perches in a strange way; b another view of the same solid

A solid that generates an impossible motion illusion can be constructed in the following way. First, we generate a description of an ordinary three-dimensional object; this can be done using a solid modeling system. Next, we select a viewpoint and an image plane, and we generate the projected picture of the object; this can be done using computer graphics techniques. Finally, we generate and solve the associated system of Eq. (3). Due to the degrees of freedom specified by Eq. (4), there are infinitely many solutions, among which we can choose an object that can create a motion that appears to be impossible.

One interesting observation is that the impossible motion is perceived even if the observer is told the true shape of the object. This implies that the impossible motion illusion cannot be removed, even if we know the truth.

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