Reconstructing sets from interpoint distances (extended abstract)
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Cross-ratios and angles determine a polygon
Proceedings of the fourteenth annual symposium on Computational geometry
Orthogonal polygon reconstruction from stabbing information
Computational Geometry: Theory and Applications
Visibility Algorithms in the Plane
Visibility Algorithms in the Plane
Simple Robots with Minimal Sensing: From Local Visibility to Global Geometry
International Journal of Robotics Research
Reconstructing Polygons from Scanner Data
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Reconstructing visibility graphs with simple robots
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
How simple robots benefit from looking back
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
A polygon is determined by its angles
Computational Geometry: Theory and Applications
An improved algorithm for reconstructing a simple polygon from its visibility angles
Computational Geometry: Theory and Applications
An improved algorithm for reconstructing a simple polygon from the visibility angles
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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We study the problem of reconstructing a simple polygon from angles measured at the vertices of the polygon. We assume that at each vertex, a sensing device returns the sequence of angles between each pair of vertices that are visible. We prove that the sequence of angle measurements at all vertices of a simple polygon in cyclic order uniquely determines the polygon up to similarity. Furthermore, we propose an algorithm that reconstructs the polygon from this information in polynomial time.