Generating random polygons with given vertices
Computational Geometry: Theory and Applications
Linear Programming in Linear Time When the Dimension Is Fixed
Journal of the ACM (JACM)
Closed Object Boundaries from Scattered Points
Closed Object Boundaries from Scattered Points
Matching Theory (North-Holland mathematics studies)
Matching Theory (North-Holland mathematics studies)
Curve and Surface Reconstruction: Algorithms with Mathematical Analysis (Cambridge Monographs on Applied and Computational Mathematics)
Reconstructing Polygons from Scanner Data
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
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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A range-finding scanner can collect information about the shape of an (unknown) polygonal room in which it is placed. Suppose that a set of scanners returns not only a set of points, but also additional information, such as the normal to the plane when a scan beam detects a wall. We consider the problem of reconstructing the floor plan of a room from different types of scan data. In particular, we present algorithmic and hardness results for reconstructing two-dimensional polygons from point-wall pairs, point-normal pairs, and visibility polygons. The polygons may have restrictions on topology (e.g., to be simply connected) or geometry (e.g., to be orthogonal). We show that this reconstruction problem is NP-hard under most models, but that some restrictive assumptions do allow polynomial-time reconstruction algorithms.