Nonoverlap of the star unfolding
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
A computational algorithm for origami design
Proceedings of the twelfth annual symposium on Computational geometry
Computational geometry column 33
ACM SIGACT News
The complexity of flat origami
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Locked and unlocked polygonal chains in 3D
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Folding and one straight cut suffice
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Folding flat silhouettes and wrapping polyhedral packages: new results in computational origami
Computational Geometry: Theory and Applications
Ununfoldable polyhedra with convex faces
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Folding and Unfolding in Computational Geometry
JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
On the Reachable Regions of Chains
Proceedings of the 8th Canadian Conference on Computational Geometry
A combinatorial approach to planar non-colliding robot arm motion planning
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Straightening polygonal arcs and convexifying polygonal cycles
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Folding and unfolding
Computational Geometry: Theory and Applications - Special issue on the 10th fall workshop on computational geometry
Survey on model-based manipulation planning of deformable objects
Robotics and Computer-Integrated Manufacturing
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We study algorithmic aspects of bending wires and sheet metal into a specified structure. Problems of this type are closely related to the question of deciding whether a simple non-self-intersecting wire structure (a carpenter's ruler) can be straightened, a problem that was open for several years and has only recently been solved in the affirmative. If we impose some of the constraints that are imposed by the manufacturing process, we obtain quite different results. In particular, we study the variant of the carpenter's ruler problem in which there is a restriction that only one joint can be modified at a time. For a linkage that does not self-intersect or self-touch, the recent results of Connelly et al. and Streinu imply that it can always be straightened, modifying one joint at a time. However, we show that for a linkage with even a single vertex degeneracy, it becomes NP-hard to decide if it can be straightened while altering only one joint at a time. If we add the restriction that each joint can be altered at most once, we show that the problem is NP-complete even without vertex degeneracies. In the special case, arising in wire forming manufacturing, that each joint can be altered at most once, and must be done sequentially from one or both ends of the linkage, we give an efficient algorithm to determine if a linkage can be straightened.