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

Area of Science:

• Computational geometry
• Computer graphics
• Origami engineering

Background:

• Origami architecture (OA) designs physically valid pop-up structures from folded paper.
• Manual design of OA is complex due to spatial constraints.
• Previous automated methods focused on 3D models, limiting use of readily available 2D resources.

Purpose of the Study:

• To present the first framework for automated origami architecture design using 2D images as input.
• To address the challenge of designing physically valid pop-up plans from 2D profiles.
• To enable efficient and interactive exploration of the design space for paper pop-up structures.

Main Methods:

• Developed a novel theoretical analysis to ensure foldability and stability from 2D input.
• Introduced a new graph representation for paper pop-up plans.
• Proposed a mixed-integer programming optimization algorithm for joint topology and geometry optimization.
• Enabled interactive user control over fold line constraints.

Main Results:

• The framework successfully generates origami architecture designs from various 2D images.
• The proposed methods ensure the foldability and stability of the designed pop-up structures.
• Experimental results demonstrate the framework's efficacy and efficiency compared to existing approaches.

Conclusions:

• The presented framework is the first to enable origami architecture design from 2D images.
• The novel theoretical analysis and optimization algorithm effectively address design challenges.
• This approach broadens the applicability of automated OA design by leveraging 2D image resources.