Designing deployable 3D scissor structures with ball-and-socket joints

摘要

Scissor structures, which transform from a compact state to an expanded state, are widely used in various fields, ranging from architectural design to aerospace applications. We focus on a challenging problem that breaks through the restriction of planarity: to design scissor structures that expand from one given 3D shape to another 3D shape. To achieve this purpose, we propose a three-step algorithm to construct a 3D scissor structure that realizes non-uniform concentration between two different 3D curves. First, the input shapes are divided into scissor segments, which are composed of a sequence of planar scissor units based on the shape correspondence. Secondly, we compute the scissor unit geometry of each segment in a suggestive manner. Finally, the ball-and-socket joints with parameterized guide slits are integrated in order to connect the scissor segments, thereby completing the 3D deployment. Judging from a series of simulation and fabrication results, we demonstrate that our approach generates deployable structures for a wide range of 3D shape pairs.