Computational geometry: an introduction
Computational geometry: an introduction
Fundamentals of interactive computer graphics
Fundamentals of interactive computer graphics
Visibility of disjoint polygons
Algorithmica
An efficient and simple motion planning algorithm for a ladder amidst polygonal barriers
Journal of Algorithms
Art gallery theorems and algorithms
Art gallery theorems and algorithms
An Efficient Uniform Cost Algorithm Applied to Distance Transforms
IEEE Transactions on Pattern Analysis and Machine Intelligence
An algorithmic approach to some problems in terrain navigation
Geometric reasoning
Shortest Path Solves Translation Separability of Polygons
Intelligent Autonomous Systems, An International Conference
A Hierarchical Knowledge Structure for Heuristic Path Planning
Intelligent Autonomous Systems 2, An International Conference
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Given a map which describes an obstacle-cluttered environment, a number of different queries can be posed. Such queries may involve point-to-point visibility, shortest paths, general visibility from an arbitrary source-point or perhaps localization. Here, a localization query is defined to be the problem of describing the collection of all points which may be reached by moving away from some arbitrary source-point, in any direction, while not exceeding a given radius. The solutions to localization and general visibility queries are perhaps best presented graphically, i.e., in visual terms. For 2-D maps, this paper describes a unified approach for deriving solutions to the above-mentioned problems, including techniques for producing visual responses when appropriate. The methods described herein are founded upon a data abstraction known as a free-space graph.