Modeling methods of cylindrical and axisymmetric waterbomb origami based on multi-objective optimization

The basic principle of origami is to use two-dimensional flat materials to obtain various three-dimensional target shapes by folding crease patterns. Among them, the study of waterbomb tessellations inspires the design and functionality implementation of engineering structures. However, there are some optimization spaces when building three-dimensional structures based on waterbomb origami. In this paper, we propose modeling methods to construct cylindrical and axisymmetric three-dimensional waterbomb tessellations with multi-objective optimization. Our methods aim to solve two optimization problems: (I) Constructing waterbomb tessellations to approximate the target surface more accurately. (II) Unifying waterbomb units to construct flat-foldable three-dimensional waterbomb tessellations. In addition, we present waterbomb approximations, the performance of optimization, rigid folding sequences, comparison of crease patterns, and physical origami fabrications to demonstrate the validity of our methods. Our work can expand the exploration of cylindrical and axisymmetric origami-inspired structures, such as foldable roofs, tubular materials, etc.