Folding a 3D Euclidean space
| Autor: | Lucero, Jorge C. |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | R. J. Lang, M. Bolitho and Z. You, editors. Origami7 - Proceedings from the 7th International Meeting on Origami in Science, Mathematics and Education, Volume 2: Mathematics (Tarquin, St Albans, UK), pp. 331-346, 2018 |
| Druh dokumentu: | Working Paper |
| Popis: | This paper considers an extension of origami geometry to the case of "folding" a three dimensional (3D) space along a plane. First, all possible incidence constraints between given points, lines and planes are analyzed by using the geometry of reflections. Next, a set of 3D elementary fold operations is defined, which satisfy specific combinations of constraints with a finite number of solutions. The set consists of 47 valid fold operations, and solutions to some of them are explored to determine their number and conditions of existence. Comment: 22 pages, 18 figures. Expanded explanation in Section 4.1 and minor corrections. This is an expanded version of the paper published in Origami7 |
| Databáze: | arXiv |
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