Reflexively-Fused Cylinders
The present paper introduces a method for designing 3D objects that are initially incomplete, but become complete when they are augmented by their mirror reflections. Physically, the mirror image is plane-symmetric with respect to the original object, but the perceived shape is not necessarily symme...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-07-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | http://www.mdpi.com/2073-8994/10/7/275 |
| _version_ | 1811302218199990272 |
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| author | Kokichi Sugihara Masaki Moriguchi |
| author_facet | Kokichi Sugihara Masaki Moriguchi |
| author_sort | Kokichi Sugihara |
| collection | DOAJ |
| description | The present paper introduces a method for designing 3D objects that are initially incomplete, but become complete when they are augmented by their mirror reflections. Physically, the mirror image is plane-symmetric with respect to the original object, but the perceived shape is not necessarily symmetric because of optical illusion. In the proposed method, a 2D shape that is not necessarily symmetric is divided into two halves, one of which is used to construct a solid object. When we place the solid object on a plane mirror, the other half is generated by the mirror, and thus, a whole shape is realized. In the present study, the design algorithm and examples are shown, and the condition for constructability is also presented. |
| first_indexed | 2024-04-13T07:24:08Z |
| format | Article |
| id | doaj.art-d995eb3e88d14e47b87412b0c858d04f |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T07:24:08Z |
| publishDate | 2018-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-d995eb3e88d14e47b87412b0c858d04f2022-12-22T02:56:32ZengMDPI AGSymmetry2073-89942018-07-0110727510.3390/sym10070275sym10070275Reflexively-Fused CylindersKokichi Sugihara0Masaki Moriguchi1Meiji Institute for Advanced Study of Mathematical Sciences; Tokyo 164-8525, JapanMeiji Institute for Advanced Study of Mathematical Sciences; Tokyo 164-8525, JapanThe present paper introduces a method for designing 3D objects that are initially incomplete, but become complete when they are augmented by their mirror reflections. Physically, the mirror image is plane-symmetric with respect to the original object, but the perceived shape is not necessarily symmetric because of optical illusion. In the proposed method, a 2D shape that is not necessarily symmetric is divided into two halves, one of which is used to construct a solid object. When we place the solid object on a plane mirror, the other half is generated by the mirror, and thus, a whole shape is realized. In the present study, the design algorithm and examples are shown, and the condition for constructability is also presented.http://www.mdpi.com/2073-8994/10/7/275mirroroptical illusionambiguous cylinderimpossible objectanomalous symmetry |
| spellingShingle | Kokichi Sugihara Masaki Moriguchi Reflexively-Fused Cylinders Symmetry mirror optical illusion ambiguous cylinder impossible object anomalous symmetry |
| title | Reflexively-Fused Cylinders |
| title_full | Reflexively-Fused Cylinders |
| title_fullStr | Reflexively-Fused Cylinders |
| title_full_unstemmed | Reflexively-Fused Cylinders |
| title_short | Reflexively-Fused Cylinders |
| title_sort | reflexively fused cylinders |
| topic | mirror optical illusion ambiguous cylinder impossible object anomalous symmetry |
| url | http://www.mdpi.com/2073-8994/10/7/275 |
| work_keys_str_mv | AT kokichisugihara reflexivelyfusedcylinders AT masakimoriguchi reflexivelyfusedcylinders |