Origami Related Work

Developed an intrinsic necessary and sufficient condition for single vertex origami crease patterns to be able to fold rigidly for both pre-assigned and unassigned cases. Also proposed the minimal forcing sets for rigid origami models.

construct crease patterns whose rigid-foldable configuration spaces are disjoint

Generalize the geometric condition for enabling rigid motion in general quadrilateral mesh origami that preserve developability, flat-foldability and finite rigid-foldability.

Proposed a Matrix based mathematical model for rigid origami. Show the necessary condition for multi-vertex non-flat origami. Self-intersection free and continuous folding motion is not guaranteed.

Show the necessary and sufficient condition for origami to fold flat locally.

The authors proposed the extended crease pattern which is a directed graph. By graph rewriting they obtain the unfolding sequence of an origami. Their method can only handle flat foldable origamis.

The author proposed an interactive simulator for rigid origami model which generates folding motion of origami by calculating the trajectory by projection to the constrained space based on rigid origami model. Though this method can simulate the folding/unfolding process efficiently, global self-intersection avoidance and stacking order problems are not considered in his work.

Balkcom proposed a simulation method based on the ideas of virtual cutting and combination of forward and inverse kinematics using a rigid origami model. Although this approach is computationally efficient, it cannot guarantee the correct mountain-valley assignment for each crease, i.e., a mountain fold can become a valley fold or vice versa.

The author simulate origami folding by a sequence of simple folding steps, including bending, folding up, and tucking in. It is easy to reconstruct an animation from a sheet of paper to the final model. However, the simplicity of folding steps limits the types of origami models that could be represented in the system. Consequently, this method is not suitable for many complex origami models whose folding process cannot be represented as simple folding steps such as the Miura pattern.

Propose a method for transform a 3D model into a box with continuous folding motion. The model is first voxelized and a spanning tree is generated and evaluated. The motion is obtained by both unfolding the original model and the box to close unfolded states.

Balkcom proposed a simulation method based on the ideas of virtual cutting and combination of forward and inverse kinematics using a rigid origami model. Although this approach is computationally efficient, it cannot guarantee the correct mountain-valley assignment for each crease, i.e., a mountain fold can become a valley fold or vice versa.

Song et al. presented a probabilistic-roadmap-method (PRM) based framework for studying folding motion. However, their kinematic representation of origami is a tree-structure model whose folding angle of each crease line is independent of other crease lines. Although tree-structure model greatly simplifies the folding map that can be easily defined along the path from base to each face, this model is not applicable to represent the majority of the origami, such as the Miura crease pattern, due to their closure constraints.

Introduced a method for building self-folding machines and demonstrated three capabilities of the composite:
- producing complex shapes
- producing dynamic mechanisms
- assembling autonomously

They proposed a new type of self-reconfiguration system called self-folding sheet. They first construct the corresponding folded state for a given crease pattern and angle assignment then continuously unfold the paper using local repulsive energies (via a modification of ROS). By reversing the unfolding sequence, they obtained the path starting from a flat sheet and ending with the desired folded state.

Initial study of the dynamics of folding/unfolding a waterbomb crease pattern.

Develop comprehensive kinematic synthesis for rigid origami of thick panels which have the identical motion to that of zero-thickness origami. The authors provide the models for 4, 5, 6 crease lines single vertex. Multi-vertex without rotation symmetry is not discussed.

Proposed a method for constructing the geometry of the thick origami whose folding behavior is exactly the same to when folding paper with zero thickness. Maximum folding angle is limited by the thickness of the panel.

Propose a method for transform a 3D model into a box with continuous folding motion. The model is first voxelized and a spanning tree is generated and evaluated. The motion is obtained by both unfolding the original model and the box to close unfolded states.

Mathematically model the waterbomb crease pattern and show the condition for folding a flat sheet of paper to a unify radius tube.

Generalize the geometric condition for enabling rigid motion in general quadrilateral mesh origami that preserve developability, flat-foldability and finite rigid-foldability.

proposed a method to unfold arbitrary 3D mesh (include non-convex ones) to flat via minimum spanning tree, edge weight is defined by combine two heuristics and user input. Since overlapping is hard to avoid especially for non-convex mesh. The authors try to minimize of the number of extra cuts to remove overlaps. Finally, 2d bin-packing algorithm is used to pack the unfolding onto paper sheets.

Prove any serpentine unfolding can be continuously bloomed. Proposed an algorithm to refine any non-overlapping unfolding to have a continuous blooming.

Proposed a new heuristic approach to unfolding 3d meshes without shape distortions. The method is inspired from topological surgery which could unfolding the 3D mesh into a single connected component.
Source code: project page

Proposed an algorithm called source unfolding to unfold any convex polyhedra without overlapping.

Proposed 19 different heuristics for unfolding a 3D polyhedron to a net. One heuristic is shown to be able unfold arbitrary polyhedron with probability 1.

Approximate the mesh by traingle strips with no internal vertices. Subdivide the mesh into parts based on features, each part is futhur segmented to zonal regions, triangles are grouped based on topological distances from the part boundaries. Triangle strips are generated by simplifying the mesh.

Propose a method for transform a 3D model into a box with continuous folding motion. The model is first voxelized and a spanning tree is generated and evaluated. The motion is obtained by both unfolding the original model and the box to close unfolded states.