Scissor-Based 3D Deployable Contours

Abstract

Because of its property of saving space, scissor structure, which can transform from a compact state to an expanded state, is widely applied in various fields. In this paper, we solve a challenging problem: designing scissor structures that can expand from a 3D contour to another 3D contour. Given two different 3D shapes specified by users, a non-uniform concentration is required, which makes the problem non-trivial. We propose a three-step algorithm to construct a 3D scissor structure. Firstly we generate scissor segments that are composed of a sequence of planar scissor units based on the shape correspondence. Secondly, we compute the scissor unit parameters of each segment in a suggestive manner. Finally, we introduce ball-shaped joints with parameterized guide slit to realize the deployment in 3D space. The results demonstrate that our algorithm is able to generate scissor structures for a wide range of 3D contours.