Voronoi Diagram and Delaunay Triangulation: Applications and Challenges in Bioinformatics

2006 ◽  
Author(s):  
Binhai Zhu
Keyword(s):  
Voronoi Diagram ◽  
Delaunay Triangulation

A LINEAR-TIME RANDOMIZED ALGORITHM FOR THE BOUNDED VORONOI DIAGRAM OF A SIMPLE POLYGON

1996 ◽  
Vol 06 (03) ◽  
pp. 263-278 ◽  
Author(s):  
ROLF KLEIN ◽  
ANDRZEJ LINGAS
Keyword(s):  
Voronoi Diagram ◽  
Delaunay Triangulation ◽  
Spanning Tree ◽  
Linear Time ◽  
Randomized Algorithm ◽  
Simple Polygon ◽  
Minimal Spanning Tree ◽  
Expected Time

For a polygon P, the bounded Voronoi diagram of P is a partition of P into regions assigned to the vertices of P. A point p inside P belongs to the region of a vertex v if and only if v is the closest vertex of P visible from p. We present a randomized algorithm that builds the bounded Voronoi diagram of a simple polygon in linear expected time. Among other applications, we can construct within the same time bound the generalized Delaunay triangulation of P and the minimal spanning tree on P’s vertices that is contained in P.

ON SIMULTANEOUS CONSTRUCTION OF VORONOI DIAGRAM AND DELAUNAY TRIANGULATION BY PHYSARUM POLYCEPHALUM

2009 ◽  
Vol 19 (09) ◽  
pp. 3109-3117 ◽  
Author(s):  
TOMOHIRO SHIRAKAWA ◽  
ANDREW ADAMATZKY ◽  
YUKIO-PEGIO GUNJI ◽  
YOSHIHIRO MIYAKE
Keyword(s):  
Voronoi Diagram ◽  
Delaunay Triangulation ◽  
Physarum Polycephalum ◽  
Vegetative State ◽  
Dual Graph ◽  
Data Sets ◽  
Limited Data ◽  
Data Set ◽  
The Given

We experimentally demonstrate that both Voronoi diagram and its dual graph Delaunay triangulation are simultaneously constructed — for specific conditions — in cultures of plasmodium, a vegetative state of Physarum polycephalum. Every point of a given planar data set is represented by a tiny mass of plasmodium. The plasmodia spread from their initial locations but, in certain conditions, stop spreading when they encounter plasmodia originated from different locations. Thus space loci not occupied by the plasmodia represent edges of Voronoi diagram of the given planar set. At the same time, the plasmodia originating at neighboring locations form merging protoplasmic tubes, where the strongest tubes approximate Delaunay triangulation of the given planar set. The problems are solved by plasmodium only for limited data sets, however the results presented lay a sound ground for further investigations.

Voronoi Diagram Generation Algorithm based on Delaunay Triangulation

2014 ◽  
Vol 9 (3) ◽  
Author(s):  
Liping Sun ◽  
Yonglong Luo ◽  
Yalei Yu ◽  
Xintao Ding
Keyword(s):  
Voronoi Diagram ◽  
Delaunay Triangulation ◽  
Generation Algorithm

Procedural Playable Cave Systems Based on Voronoi Diagram and Delaunay Triangulation

2014 ◽  
Author(s):  
Aitor Santamaria-Ibirika ◽  
Xabier Cantero ◽  
Sergio Huerta ◽  
Igor Santos ◽  
Pablo G. Bringas
Keyword(s):  
Voronoi Diagram ◽  
Delaunay Triangulation
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