A Mathematica module for Conformal Geometric Algebra and Origami Folding

13 pages•Published: March 27, 2016

Mitsuhiro Kondo, Takuya Matsuo, Yoshihiro Mizoguchi and Hiroyuki Ochiai

Abstract

We implemented a Mathematica module of CGA which includes functions to denote CGA elements and compute several operations in CGA. We can draw the figure in 3D space which is corresponding to a CGA element. Our draw function is using Gr\"{o}bner Basis for simplifying equations of figures. It can be used for any dimensional figures. One of our motivations is to realize 3D origami system using our own CGA Library. We follow the 2D computational origami system E-Origami-System developed by Ida et.al. and formulated simple fold operations in 3D by using CGA points and motions. Then, we proved some geometric theorems about origami properties by computing CGA equation formulas.

Keyphrases: computational origami, conformal geometric algebra, mathematica

In: James H. Davenport and Fadoua Ghourabi (editors). SCSS 2016. 7th International Symposium on Symbolic Computation in Software Science, vol 39, pages 68-80.

Links:	https://easychair.org/publications/paper/8jDf
	https://doi.org/10.29007/6fc5

BibTeX entry

@inproceedings{SCSS2016:Mathematica_module_Conformal_Geometric,
  author    = {Mitsuhiro Kondo and Takuya Matsuo and Yoshihiro Mizoguchi and Hiroyuki Ochiai},
  title     = {A Mathematica module for Conformal Geometric Algebra and Origami Folding},
  booktitle = {SCSS 2016. 7th International Symposium on  Symbolic Computation in Software Science},
  editor    = {James H. Davenport and Fadoua Ghourabi},
  series    = {EPiC Series in Computing},
  volume    = {39},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/8jDf},
  doi       = {10.29007/6fc5},
  pages     = {68-80},
  year      = {2016}}

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