On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
An output-sensitive algorithm for computing visibility
SIAM Journal on Computing
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Voronoi diagrams and Delaunay triangulations
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Polygon decomposition for efficient construction of Minkowski sums
Computational Geometry: Theory and Applications - Special issue on: Sixteenth European Workshop on Computational Geometry (EUROCG-2000)
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
High-Level Filtering for Arrangements of Conic Arcs
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Retraction: A new approach to motion-planning
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Finding paths for coherent groups using clearance
SCA '04 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation
The visibility--voronoi complex and its applications
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Advanced programming techniques applied to Cgal's arrangement package
Computational Geometry: Theory and Applications
Motion planning in order to optimize the length and clearance applying a Hopfield neural network
Expert Systems with Applications: An International Journal
Efficient and safe path planning for a mobile robot using genetic algorithm
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
Shortest path queries in a simple polygon for 3D virtual museum
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part I
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Real-time density-based crowd simulation
Computer Animation and Virtual Worlds
Kelp Diagrams: Point Set Membership Visualization
Computer Graphics Forum
A navigation mesh for dynamic environments
Computer Animation and Virtual Worlds
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We introduce a new type of diagram called the VV(c)-diagram (the visibility-Voronoi diagram for clearance c), which is a hybrid between the visibility graph and the Voronoi diagram of polygons in the plane. It evolves from the visibility graph to the Voronoi diagram as the parameter c grows from 0 to ∞. This diagram can be used for planning natural-looking paths for a robot translating amidst polygonal obstacles in the plane. A natural-looking path is short, smooth, and keeps--where possible--an amount of clearance c from the obstacles. The VV(c)-diagram contains such paths. We also propose an algorithm that is capable of preprocessing a scene of configuration-space polygonal obstacles and constructs a data structure called the VV-complex. The VV-complex can be used to efficiently plan motion paths for any start and goal configuration and any clearance value c, without having to explicitly construct the VV(c)-diagram for that c-value. The preprocessing time is O(n2 logn), where n is the total number of obstacle vertices, and the data structure can be queried directly for any c-value by merely performing a Dijkstra search. We have implemented a CGAL-based software package for computing the VV(c)-diagram in an exact manner for a given clearance value and used it to plan natural-looking paths in various applications.