Origami and Polyhedra Folding

The MASC Origami and Polyhedra Folding is a project by the Motion and Shape Computing Group to solve foldability issues for rigid origami and polyhedral nets which could assistant their designs. This website describes the approaches we proposed and software and tools we developed.

Principal Investigator: Jyh-Ming Lien
Students: Yue Hao and Zhonghua Xi

Polyhera Folding and Unfolding


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Compacting Voxelized Polyhedra via Tree Stacking (2018 Spring)
  • An extension of our Compact Folding of Thick Origami via Stacking project to overcome the structural drawbacks.
  • A completely new heuristic based pipeline to find the optimal stacking in a search space whose dimension is exponential to the complexity of input polyhedron.
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Computational Laser Forming Origami of Convex Surfaces (2019 Spring)
  • We develop the first known computational method to fabricate convex 3D metal surfaces using laser forming.
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    Super Compaction and Transformation (2018 Spring)
  • We found a universal method to compact 3D shapes via stacking while allowing transformation between different shapes.
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    Creating Foldable Polyhedral Net (2018 Spring)
    • A Study of the Foldability of Polyhedral Nets
    • Combine Topological and Geometric Features to Obtain Easily Foldable Nets
    • A Learning Strategy to Optimize Genetic-based Unfolder
    • Use Transfer Learning to Handle Complex Models
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    Disjoint Convex Shell and its Applications in Mesh Unfolding (2017 Spring)
    • Preventing convex objects from overlapping
    • Faster and robust collision response and more realistic fracturing simulation.
    • Without disjointness constraint, a physical realization of the approximation becomes impossible.
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    Polyhedra Fabrication Through Mesh Convexification (2017 Spring)
    • A Study of Foldability of Nearly Convex Shapes
    • Remove local concavity via inflation
    • Remove global concavity via segmentation
    • Paper IDETC/CIE 2017
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    Compact Folding of Thick Origami via Stacking (2017 Spring)
    • Find the compactest state of a given mesh and fold it to that state via stacking.
    • Tech Report GMU-CS-2017-6
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    Learning to Segment and Unfold Polyhedral Mesh from Failures (2016 Spring)
    • Simultaneously segment and unfold a non-convex mesh
    • Paper SMI 2016
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    Continuous Unfolding of Polyhedra (2015 Spring)
    • We developed a general framework for continuously unfolding polyhedra
    • Sampling in discrete domain
    • Path segments are linearly connected
    • Provide more human-interpretable unfolding motion

    Origami Folding and Unfolding


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    Plan Folding Motion for Rigid Origami via Discrete Domain Sampling (2014 Fall)
    • Valid configurations form a manifold in lower dimensional space
    • Sampling in discrete domain
    • Try linear and nonlinear connectors among valid configurations
    • Able to find paths in different homotopic classes for multi-DOF origami
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    Folding and Unfolding Origami Tessellation by Reusing Folding Path (2014 Fall)
    • Taking advantage of symmetry property of the crease pattern
    • Gather crease lines into groups based on their folding behaviour to reduce DOF
    • Reusing folding path found on essential crease pattern to fold large origami tessellation
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    Folding Rigid Origami with Closure Constraints (2013 Fall)
    • We developed an adaptive randomized search method to fold rigid origami
    • The folding path found was deformation bounded and collision free
    • Download Rigid Origami Folder

    Publications


    Polyhedra Net Folding and Unfolding


    Volume Compaction via Thick Polyhedral Surface Stacking, Yue Hao and Jyh-Ming Lien, Proceedings of Pacific Graphics 2019, Special Issue of the Eurographics journal, Computer Graphics Forum (CGF), Oct 2019
    Web Site / Paper(pdf) / Poster(pdf) / BibTeX
    Computational Laser Forming Origami of Convex Surfaces, Yue Hao and Jyh-Ming Lien, Proceedings of the ACM Symposium on Computational Fabrication (SCF), Jun 2019
    Web Site / Paper(pdf) / Slides(pdf) / Poster(pdf) / BibTeX
    Creating Foldable Polyhedral Nets Using Evolution Control, Yue Hao and Yun-Hyeong Kim and Zhonghua Xi and Jyh-Ming Lien, Proceedings of the Robotics: Science and Systems Conference (RSS), Jun 2018
    Web Site / Paper(pdf) / Slides(pdf) / Poster(pdf) / BibTeX
    Synthesis of Fast and Collision-free Folding of Polyhedral Nets, Yue Hao and Yun-Hyeong Kim and Jyh-Ming Lien, Proceedings of the ACM Symposium on Computational Fabrication (SCF), Jun 2018
    Web Site / Paper(pdf) / BibTeX
    Super Compaction and Pluripotent Shape Transformation via Algorithmic Stacking for 3D Deployable Structures, Zhonghua Xi and Yu-Ki Lee and Young-Joo Lee and Yunhyeong Kim and Huangxin Wang and Yue Hao and Young-Chang Joo and In-Suk Choi and Jyh-Ming Lien, CoRR, 2018
    Paper (pdf) / BibTeX
    Disjoint Convex Shell and its Applications in Mesh Unfolding, Yun-Hyeong Kim and Zhonghua Xi and Jyh-Ming Lien, Symposium on Solid and Physical Modeling (SPM), also appears in Journal of Computer-Aided Design, Jun. 2017
    Web Site / Paper(pdf) / BibTeX
    Compact Folding of Thick Origami via Stacking, Zhonghua Xi and Huangxin Wang and Yue Hao and Jyh-Ming Lien and In-Suk Choi, Department of Computer Science, George Mason University, (Technical Report), 2017
    Web Site / Paper(pdf) / BibTeX
    Polyhedra Fabrication Through Mesh Convexification: A Study of Foldability of Nearly Convex Shapes, Zhonghua Xi and Jyh-Ming Lien, International Design and Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE), ASME, Aug. 2017
    Web Site / Paper(pdf) / BibTeX
    Learning to Segment and Unfold Polyhedral Mesh from Failures, Zhonghua Xi and Yun-Hyeong Kim and Young J. Kim and Jyh-Ming Lien, Shape Modeling International (SMI); also appears in Journal of Computers & Graphics, Jun. 2016
    Web Site / Paper(pdf) / BibTeX
    Continuous Unfolding of Polyhedra - a Motion Planning Approach, Zhonghua Xi and Jyh-Ming Lien, 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Sep. 2015
    Web Site / Paper(pdf) / BibTeX



    Origami Folding and Unfolding


    Folding and Unfolding Origami Tessellation by Reusing Folding Path, Zhonghua Xi and Jyh-Ming Lien, Department of Computer Science, George Mason University, (Technical Report), 2015
    Web Site / Paper (pdf) / BibTeX
    Plan Folding Motion for Rigid Origami via Discrete Domain Sampling, Zhonghua Xi and Jyh-Ming Lien, Department of Computer Science, George Mason University, (Technical Report), 2015
    Web Site / Paper (pdf) / BibTeX
    Folding and Unfolding Origami Tessellation by Reusing Folding Path, Zhonghua Xi and Jyh-Ming Lien, 2015 IEEE International Conference on Robotics and Automation (ICRA), May. 2015
    Web Site / Paper (pdf) / BibTeX
    Plan Folding Motion for Rigid Origami via Discrete Domain Sampling, Zhonghua Xi and Jyh-Ming Lien, 2015 IEEE International Conference on Robotics and Automation (ICRA), May. 2015
    Web Site / Paper (pdf) / BibTeX
    Folding Rigid Origami with Closure Constraints, Zhonghua Xi and Jyh-Ming Lien, International Design and Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE), ASME, Aug. 2014
    Web Site / Paper (pdf) / BibTeX
    Differentiating Bending From Folding In Origami Engineering Using Active Materials, Carlye Lauff and Timothy W. Simpson and Mary Frecker and Zoubeida Ounaies and Saad Ahmed and Paris von Lockette and Rebecca Strzelec and Robert Sheridan and Jyh-Ming Lien, International Design and Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE), ASME, Aug. 2014
    Web Site / Paper (pdf) / BibTeX
    Determine Distinct Shapes of Rigid Origami, Zhonghua Xi and Jyh-Ming Lien, The 6th International Meeting on Origami in Science, Mathematics and Education (6OSME), Aug. 2014
    Web Site / Abstract (pdf) / BibTeX


    Origami Software


    See Origami software page

    Videos




    Related Links




    Acknowledgement


    This work was supported in part by NSF EFRI-1240459 and CNS-1205260.

    List of MASC Research Pages / List of MASC Origami Pages
    Computer Science @ George Mason University