Image-Based OA-Style Paper Pop-Up Design via Mixed-Integer Programming

Origami architecture (OA) is a fascinating papercraft that involves only a piece of paper with cuts and folds. Interesting geometric structures 'pop up' when the paper is opened. However, manually designing such a physically valid 2D paper pop-up plan is challenging since fold lines must jointly satisfy hard spatial constraints. Existing works on automatic OA-style paper pop-up design all focused on how to generate a pop-up structure that approximates a given target 3D model. This article presents the first OA-style paper pop-up design framework that takes 2D images instead of 3D models as input. Our work is inspired by the fact that artists often use 2D profiles to guide the design process, thus benefited from the high availability of 2D image resources. Due to the lack of 3D geometry information, we perform novel theoretic analysis to ensure the foldability and stability of the resultant design. Based on a novel graph representation of the paper pop-up plan, we further propose a practical optimization algorithm via mixed-integer programming that jointly optimizes the topology and geometry of the 2D plan. We also allow the user to interactively explore the design space by specifying constraints on fold lines. Finally, we evaluate our framework on various images with interesting 2D shapes. Experiments and comparisons exhibit both the efficacy and efficiency of our framework.