scholarly journals Approximating the Generalized Voronoi Diagram of Closely Spaced Objects

2015 ◽  
Vol 34 (2) ◽  
pp. 299-309 ◽  
Author(s):  
John Edwards ◽  
Eric Daniel ◽  
Valerio Pascucci ◽  
Chandrajit Bajaj
Keyword(s):  
Voronoi Diagram ◽  
Generalized Voronoi Diagram

Visual Servoing on the Generalized Voronoi Diagram Using an Omnidirectional Camera

2018 ◽  
Vol 94 (3-4) ◽  
pp. 793-804 ◽  
Author(s):  
Romain Marie ◽  
Hela Ben Said ◽  
Joanny Stéphant ◽  
Ouiddad Labbani-Igbida
Keyword(s):  
Voronoi Diagram ◽  
Visual Servoing ◽  
Omnidirectional Camera ◽  
Generalized Voronoi Diagram

BOAT-SAIL VORONOI DIAGRAM AND ITS APPLICATION

2009 ◽  
Vol 19 (05) ◽  
pp. 425-440 ◽  
Author(s):  
TETSUSHI NISHIDA ◽  
KOKICHI SUGIHARA
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Voronoi Diagram ◽  
Water Surface ◽  
Eikonal Equation ◽  
Fast Marching Method ◽  
Fast Marching ◽  
Marching Method ◽  
Generalized Voronoi Diagram

A new generalized Voronoi diagram, called a boat-sail Voronoi diagram, is defined on the basis of the time necessary for a boat to reach on water surface with flow. A new concept called a boat-sail distance is introduced on the surface of water with flow, and it is used to define a generalized Voronoi diagram, in such a way that the water surface is partitioned into regions belonging to the nearest harbors with respect to this distance. The problem of computing this Voronoi diagram is reduced to a boundary value problem of a partial differential equation, and a numerical method for solving this problem is constructed. The method is a modification of a so-called fast marching method originally proposed for the eikonal equation. Computational experiments show the efficiency and the stableness of the proposal method. We also apply our equation to the shortest path problem and the simulation of the forest fire.

3D Reconstruction of Complex Polyhedral Shapes from Contours using a Simplified Generalized Voronoi Diagram

1996 ◽  
Vol 15 (3) ◽  
pp. 397-408 ◽  
Author(s):  
J-M. Oliva ◽  
M. Perrin ◽  
S. Coquillart
Keyword(s):  
3D Reconstruction ◽  
Voronoi Diagram ◽  
Generalized Voronoi Diagram

A Reusable Generalized Voronoi Diagram Based Feature Tree for Fast Robot Motion Planning in Trapped Environments

2021 ◽  
pp. 1-1
Author(s):  
Wenzheng Chi ◽  
Jiankun Wang ◽  
Zhiyu Ding ◽  
Guodong Chen ◽  
Lining Sun
Keyword(s):  
Motion Planning ◽  
Voronoi Diagram ◽  
Robot Motion ◽  
Robot Motion Planning ◽  
Generalized Voronoi Diagram

scholarly journals Lyapunov Function Based Steering Law for Generalized Voronoi Diagram (GVD) Construction by a Mobile Robot

2014 ◽  
Vol 47 (1) ◽  
pp. 103-108
Author(s):  
G.K. Arunkumar ◽  
Srikant Sukumar ◽  
Leena Vachhani
Keyword(s):  
Lyapunov Function ◽  
Mobile Robot ◽  
Voronoi Diagram ◽  
Steering Law ◽  
Generalized Voronoi Diagram
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