Dudeney Dissection of Polygons
JCDCG '98 Revised Papers from the Japanese Conference on Discrete and 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
An energy-driven approach to linkage unfolding
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Hinged dissection of polyominoes and polyforms
Computational Geometry: Theory and Applications - Special issue: The 11th Candian conference on computational geometry - CCCG 99
Hinged dissection of polypolyhedra
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Computational geometry column 50
ACM SIGACT News
Proceedings of the twenty-fourth annual symposium on Computational geometry
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
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We extend linkage unfolding results from the well-studied case of polygonal linkages to the more general case of linkages of polygons. More precisely, we consider chains of nonoverlapping rigid planar shapes (Jordan regions) that are hinged together sequentially at rotatable joints. Our goal is to characterize the familes of planar shapes that admit locked chains, where some configurations cannot be reached by continuous reconfiguration without self-intersection, and which families of planar shapes guarantee universal foldability, where every chain is guaranteed to have a connected configuration space. Previously, only obtuse triangles were known to admit locked shapes, and only line segments were known to guarantee universal foldability. We show that a surprisingly general family of planar shapes, called slender adornments, guarantees universal foldability: roughly, the inward normal from any point on the shape's boundary should intersect the line segment connecting the two incident hinges. In constrast, we show that isosceles triangles with any desired apex angle