Simulation of Rigid Origami

Simulation of Rigid Origami
Tomohiro Tachi
The University of Tokyo
tachi.tomohiro@gmail.com
This paper presents a system for computer based interactive simulation of rigid origami. The system shows the continuous process of folding a piece of
paper into a folded shape by calculating the configuration from a crease pattern. This helps users to understand the structure of the model and to fold the
model from a crease pattern. The system can also simulate the folding process from a folded shape to another represented by different crease patterns.
We can control the overall folding process by a sequence of multiple crease patterns. Thus the system can be used for publishing the way of folding
without drawing a diagram.
Global constraint matrix for rigid origami simulation is calculated from necessary conditions for single vertex rigid origami shown by Belcastro and
Hull[1]. We calculate the deformation mode by solving the pseudo-inverse of the constraint matrix. The system uses ORIPA[2] file as a crease pattern
input. Mountain/valley attribute of each crease line gives the moment around it. This results in avoiding irreversible self-intersection for multiple cases
without any collision detection algorithm.
Many origami models with vertices of valency 4 are not rigidly foldable. By adding crease lines on polygons with more than 3 vertices, we can often
make the model rigidly foldable. We investigate the efficient direction of the crease lines to be added.
The folding process from a folded shape to another is simulated by using the folded configuration for the old crease pattern as the initial configuration for
the new. We use interpolated vertex positions for the recalculation of the new crease lines to make the change in the configuration small.
Fig. Rigid Origami Simulation Program (simulation of the folding process of a model “5x5 checker pattern”)
[1] Sarah-marie Belcastro and Thomas C. Hull, "A Mathematical Model for Non-Flat Origami", Proceedings of the 3rd International
Meeting of Origami Mathematics, Science, and Education, 2002.
[2] Jun Mitani, “ORIPA; Origami Pattern Editor”, http://mitani.cs.tsukuba.ac.jp/pukiwiki-oripa/