> 1. Will it be correct to say that there is a whole category 3D polyhedral > surfaces, and it can appreciate different unique methods: Tachi's method, > Chit's method and others. If it is so, what name would you give this whole > category? I really liked those criterions, with them Matthew described the > Tachi's method. Is it possible to define the criteria for the whole > category? > > > > 2. Or other statement is correct. Tachi's method is a separate part in the > system. In future, it has the potential to expand and one day may become a > whole category, on level with Origami Tessellations, Origami Corrugations > and others. If it is so, how is Tachi's method related to 3D polyhedral > surfaces. And where is the place of Chit's method in the system? > > I think that Tachi's origami should belong in a category together with a lot of algorithmic origami design techniques; this category is characterized by (1) choosing a subject, (2) breaking the surface of the subject into polygons, (3) arranging the polygons on the paper, (4) fitting creases into the gaps between the polygons, and (5) folding the creases to close the gaps and bring the polygons back together into the target surface. In this sense, Tachi's origami is not as unique as it seems, for this approach is an intuitive way to fold a sheet of paper into a surface. Examples of other designers who use this method include:
(i) Jun Mitani (http://cadanda.homestead.com/CAD_6_1__69-79.pdf) (ii) myself (Fig. 7 from http://www.sciencedirect.com/science/article/pii/S0010448511003058) (iii) from a less algorithmic perspective, John Montroll's "Origami Polyhedral Design" (a bit of theory at http://www.origami-resource-center.com/origami-polyhedra-design.html) (iv) several origami tessellation also have such a feel (e.g. the coat on Beth Johnson's sheep, and http://static.neatorama.com/images/2008-02/tessellation-fractured-flower.jpg ) (v) to give a more surprising example, compress this model ( http://cristinaleau.files.wordpress.com/2011/11/20111120_13.jpg) lengthwise so that the twists fully close. However, with regards to step (2), examples (i)-(iii) depend on the net of the surface, while Tachi's origami and examples (iv)-(v) use a more fragmented arrangement of polygons. There should also be another "dual" category that uses creases to define surfaces instead of polygons, containing models like the hyperbolic parabloid, a great variaty of "curved-crease sculpture" ( http://erikdemaine.org/curved/history/), Tachi's variations on the Miura Map Fold (Fig. 6 from http://www.tsg.ne.jp/TT/cg/RigidFoldableQuadMeshOrigami_tachi_IASS2009.pdf), and some of Cheng Chit's work ( http://www.flickr.com/photos/chengchit/4143769758/in/photostream) Regards, Herng Yi
