Computational geometry: an introduction
Computational geometry: an introduction
Proceedings of the sixth ACM symposium on Solid modeling and applications
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Matching Theory (North-Holland mathematics studies)
Matching Theory (North-Holland mathematics studies)
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
Covering points with orthogonally convex polygons
Computational Geometry: Theory and Applications
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
Perspective: Simple agents learn to find their way: An introduction on mapping polygons
Discrete Applied Mathematics
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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 points, 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 in most models, but for some assumptions allows polynomial-time reconstruction algorithms which we describe.