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
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
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
Computational Geometry: Theory and Applications - Special issue on the 21st European workshop on computational geometry (EWCG 2005)
Creating High-quality Paths for Motion Planning
International Journal of Robotics Research
Geometric algorithms for clearance based optimal path computation
Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems
Flexible Path Planning Using Corridor Maps
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Indicative routes for path planning and crowd simulation
Proceedings of the 4th International Conference on Foundations of Digital Games
Finding a natural-looking path by using generalized visibility graphs
PRICAI'06 Proceedings of the 9th Pacific Rim international conference on Artificial intelligence
A geometric approach to clearance based path optimization
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part I
Navigation queries from triangular meshes
MIG'10 Proceedings of the Third international conference on Motion in games
A Sensor Placement Algorithm for a Mobile Robot Inspection Planning
Journal of Intelligent and Robotic Systems
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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(c)-complex. The VV(c)-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 log n), 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.