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
Theoretical Computer Science
Reconstructing a simple polygon from its angles
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
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
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
Reconstructing visibility graphs with simple robots
Theoretical Computer Science
Perspective: Simple agents learn to find their way: An introduction on mapping polygons
Discrete Applied Mathematics
Unsolved problems in visibility graphs of points, segments, and polygons
ACM Computing Surveys (CSUR)
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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 v a sensing device returns a list of angles @a"1,@a"2,..., where @a"i is the angle between the i-th and the (i+1)-th vertices visible to v in counterclockwise (ccw) order starting with the ccw neighbor of v along the boundary. We prove that the angle measurements at all vertices of a simple polygon together with the order of the vertices along the boundary uniquely determine the polygon (up to similarity). In addition, we give an algorithm for reconstructing the polygon from this information in polynomial time.