The L_infinity (L_1) Farthest Line-Segment Voronoi Diagram

2012 ◽  
Author(s):  
Sandeep Kumar Dey ◽  
Evanthia Papadopoulou
Keyword(s):  
Voronoi Diagram ◽  
Line Segment

BASELINE BOUNDED HALF-PLANE VORONOI DIAGRAM

2013 ◽  
Vol 05 (03) ◽  
pp. 1350021 ◽  
Author(s):  
BING SU ◽  
YINFENG XU ◽  
BINHAI ZHU
Keyword(s):  
Voronoi Diagram ◽  
Half Plane ◽  
Line Segment ◽  
Euclidean Plane ◽  
Voronoi Region ◽  
Point Set ◽  
Set Of Points

Given a set of points P = {p1, p2, …, pn} in the Euclidean plane, with each point piassociated with a given direction vi∈ V. P(pi, vi) defines a half-plane and L(pi, vi) denotes the baseline that is perpendicular to viand passing through pi. Define a region dominated by piand vias a Baseline Bounded Half-Plane Voronoi Region, denoted as V or(pi, vi), if a point x ∈ V or(pi, vi), then (1) x ∈ P(pi, vi); (2) the line segment l(x, pi) does not cross any baseline; (3) if there is a point pj, such that x ∈ P(pj, vj), and the line segment l(x, pj) does not cross any baseline then d(x, pi) ≤ d(x, pj), j ≠ i. The Baseline Bounded Half-Plane Voronoi Diagram, denoted as V or(P, V), is the union of all V or(pi, vi). We show that V or(pi, vi) and V or(P, V) can be computed in O(n log n) and O(n2log n) time, respectively. For the heterogeneous point set, the same problem is also considered.

Topology and context-based pattern extraction using line-segment Voronoi diagram

2015 ◽  
Author(s):  
Sandeep K. Dey ◽  
Panagiotis Cheilaris ◽  
Nathalie Casati ◽  
Maria Gabrani ◽  
Evanthia Papadopoulo
Keyword(s):  
Voronoi Diagram ◽  
Line Segment ◽  
Pattern Extraction

THE ANCHORED VORONOI DIAGRAM: STATIC, DYNAMIC VERSIONS AND APPLICATIONS

2006 ◽  
Vol 16 (04) ◽  
pp. 315-332
Author(s):  
J. M. DÍAZ-BÁÑEZ ◽  
F. GÓMEZ ◽  
I. VENTURA
Keyword(s):  
Fixed Point ◽  
Voronoi Diagram ◽  
Line Segment ◽  
Time Complexity ◽  
Optimization Problems ◽  
Dynamic Version

For a given set S of n points in the plane and a fixed point o, we introduce the Voronoi diagram of S anchored at o. It will be defined as an abstract Voronoi diagram that uses as bisectors the following curves. For each pair of points p, q in S, the bisecting curve between p and q is the locus of points x in the plane such that the line segment [Formula: see text] is equidistant to both p and q. We show that those bisectors have nice properties and, therefore, this new structure can be computed in O(n log n) time and O(n) space both for nearest-site and furthest-site versions. Also, we prove that the dynamic version of this diagram can be built in O(n2λ6s+2(n) log n) time complexity, where s is a constant depending on the function that describes the motion of the points. Finally, we show how to use these structures for solving several locational optimization problems.

ON THE FARTHEST LINE-SEGMENT VORONOI DIAGRAM

2013 ◽  
Vol 23 (06) ◽  
pp. 443-459 ◽  
Author(s):  
EVANTHIA PAPADOPOULOU ◽  
SANDEEP KUMAR DEY
Keyword(s):  
Convex Hull ◽  
Voronoi Diagram ◽  
Line Segment ◽  
Euclidean Plane ◽  
Line Segments ◽  
Polygonal Curve ◽  
Number Of Faces ◽  
Farthest Point ◽  
Construction Algorithms ◽  
Standard Techniques

The farthest line-segment Voronoi diagram illustrates properties surprisingly different from its counterpart for points: Voronoi regions may be disconnected and they are not characterized by convex-hull properties. In this paper we introduce the farthest hull and its Gaussian map as a closed polygonal curve that characterizes the regions of the farthest line-segment Voronoi diagram, and derive tighter bounds on the (linear) size of this diagram. With the purpose of unifying construction algorithms for farthest-point and farthest line-segment Voronoi diagrams, we adapt standard techniques to construct a convex hull and compute the farthest hull in O(n log n) or output sensitive O(n log h) time, where n is the number of line-segments and h is the number of faces in the corresponding farthest Voronoi diagram. As a result, the farthest line-segment Voronoi diagram can be constructed in output sensitive O(n log h) time. Our algorithms are given in the Euclidean plane but they hold also in the general Lp metric, 1 ≤ p ≤ ∞.

Model and algorithm for searching for victims in emergency situations and fires using the Voronoi diagram

2019 ◽  
Vol 86 ◽  
pp. 53-61
Author(s):  
N. G. Topolskiy ◽  
◽  
A. V. Mokshantsev ◽  
To Hoang Thanh ◽  
◽  
...  
Keyword(s):  
Voronoi Diagram ◽  
Emergency Situations

Less is more: Simple stimuli provoke more variable search strategies.

2020 ◽  
Author(s):  
Anna Nowakowska ◽  
Alasdair D F Clarke ◽  
Jessica Christie ◽  
Josephine Reuther ◽  
Amelia R. Hunt
Keyword(s):  
Line Segment ◽  
Search Strategies ◽  
Complex Objects ◽  
Search Behaviour ◽  
Line Segments ◽  
Surface Level ◽  
Efficient Search ◽  
Less Is More ◽  
Dramatic Shift

We measured the efficiency of 30 participants as they searched through simple line segment stimuli and through a set of complex icons. We observed a dramatic shift from highly variable, and mostly inefficient, strategies with the line segments, to uniformly efficient search behaviour with the icons. These results demonstrate that changing what may initially appear to be irrelevant, surface-level details of the task can lead to large changes in measured behaviour, and that visual primitives are not always representative of more complex objects.

Sign in / Sign up

Export Citation Format

Share Document