scholarly journals Interactive motion planning using hardware-accelerated computation of generalized Voronoi diagrams

2002 ◽  
Author(s):  
K. Hoff ◽  
T. Culver ◽  
J. Keyser ◽  
M.C. Lin ◽  
D. Manocha
Keyword(s):  
Motion Planning ◽  
Voronoi Diagrams ◽  
Generalized Voronoi Diagrams

Approximating Voronoi Diagrams of Convex Sites in Any Dimension

1998 ◽  
Vol 08 (02) ◽  
pp. 201-221 ◽  
Author(s):  
Jules Vleugels ◽  
Mark Overmars
Keyword(s):  
Computational Complexity ◽  
Motion Planning ◽  
Voronoi Diagrams ◽  
Higher Dimensions ◽  
Three Dimensions ◽  
Primitive Operation ◽  
Generalized Voronoi Diagrams ◽  
Arbitrary Precision ◽  
A Site ◽  
Disjoint Convex

Generalized Voronoi diagrams of objects are difficult to compute in a robust way, especially in higher dimensions. For a number of applications an approximation of the real diagram within some predetermined precision is sufficient. In this paper we study the computation of such approximate Voronoi diagrams. The emphasis is on practical applicability, therefore we are mainly concerned with fast (in terms of running time) computation, generality, robustness, and easy implementation, rather than optimal combinatorial and computational complexity. Given a set of disjoint convex sites in any dimension, we describe a general algorithm that approximates their Voronoi diagram with arbitrary precision. The only primitive operation that is required is the computation of the distance from a point to a site. The method is illustrated by its application to motion planning using retraction. To justify our claims on practical applicability, we provide experimental results obtained with implementations of the method in two and three dimensions.

scholarly journals Incremental Construction of Generalized Voronoi Diagrams on Pointerless Quadtrees

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Quanjun Yin ◽  
Long Qin ◽  
Xiaocheng Liu ◽  
Yabing Zha
Keyword(s):  
Voronoi Diagrams ◽  
Surrounding Area ◽  
Repair Mechanism ◽  
Local Repair ◽  
Order Of Magnitude ◽  
Generalized Voronoi Diagrams ◽  
Incremental Construction ◽  
Coarse To Fine ◽  
Multiple Granularities ◽  
Magnitude Improvement

In robotics, Generalized Voronoi Diagrams (GVDs) are widely used by mobile robots to represent the spatial topologies of their surrounding area. In this paper we consider the problem of constructing GVDs on discrete environments. Several algorithms that solve this problem exist in the literature, notably the Brushfire algorithm and its improved versions which possess local repair mechanism. However, when the area to be processed is very large or is of high resolution, the size of the metric matrices used by these algorithms to compute GVDs can be prohibitive. To address this issue, we propose an improvement on the current algorithms, using pointerless quadtrees in place of metric matrices to compute and maintain GVDs. Beyond the construction and reconstruction of a GVD, our algorithm further provides a method to approximate roadmaps in multiple granularities from the quadtree based GVD. Simulation tests in representative scenarios demonstrate that, compared with the current algorithms, our algorithm generally makes an order of magnitude improvement regarding memory cost when the area is larger than210×210. We also demonstrate the usefulness of the approximated roadmaps for coarse-to-fine pathfinding tasks.

Approximations of 2D and 3D generalized Voronoi diagrams

2008 ◽  
Vol 85 (7) ◽  
pp. 1003-1022 ◽  
Author(s):  
Imma Boada ◽  
Narcís Coll ◽  
Narcís Madern ◽  
J. Antoni Sellarès
Keyword(s):  
Voronoi Diagrams ◽  
Generalized Voronoi Diagrams ◽  
2D And 3D
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