Dynamic Construction of Voronoi Diagram for a Set of Points and Straight Line Segments

2014 ◽  
Vol 533 ◽  
pp. 264-267
Author(s):  
Xin Liu
Keyword(s):  
Production Process ◽  
Voronoi Diagram ◽  
Voronoi Diagrams ◽  
High Potential ◽  
Line Segments ◽  
Potential Value ◽  
Straight Line ◽  
Traditional Algorithm ◽  
Set Of Points

Voronoi Diagram for a set of points and straight line segments is difficult to construct because general figures have uncertain shapes[. In traditional algorithm, when generator of general figure changes, production process will be extremely complex because of the change of regions neighboring with those generator changed. In this paper, we use dynamicconstruction of Voronoi diagrams. The algorithm can get over all kinds of shortcomings that we have just mentioned. So it is more useful and effective than the traditional algorithm[2]. The results show that the algorithm is both simple and useful, and it is of high potential value in practice.

Discrete Construction of Compoundly Weighted Voronoi Diagram

2013 ◽  
Vol 467 ◽  
pp. 545-548
Author(s):  
Hui Wang
Keyword(s):  
Production Process ◽  
Voronoi Diagram ◽  
Voronoi Diagrams ◽  
High Potential ◽  
Graphic Display ◽  
Potential Value ◽  
Discrete Algorithms ◽  
Traditional Algorithm ◽  
Definition Of

Compoundly weighted Voronoi diagram is difficult to construct because the bisector is fairly complex. In traditional algorithm, production process is always extremely complex and it is more difficult to graphic display because of the complex definition of mathematic formula. In this paper, discrete algorithms are used to construct compoundly weighted Voronoi diagrams. The algorithm can get over all kinds of shortcomings that we have just mentioned. So it is more useful and effective than the traditional algorithm. The results show that the algorithm is both simple and useful, and it is of high potential value in practice.

Activities: Massive Graphs, Power Laws, and the World Wide Web

2003 ◽  
Vol 96 (6) ◽  
pp. 434-439
Author(s):  
L. Charles Biehl
Keyword(s):  
Mathematical Modeling ◽  
World Wide ◽  
Transportation Networks ◽  
Power Laws ◽  
Line Segments ◽  
Massive Graphs ◽  
Straight Line ◽  
Edge Graph ◽  
The World ◽  
Set Of Points

Mathematical modeling has seen many changes over the years. These changes range from the types of situations being modeled to the types of tools used for the modeling. An extremely powerful modeling tool for many situations is the vertex-edge graph (hereafter simply called a graph). In this type of graph, a set of points, called vertices (or nodes), represent objects, people, or other ideas. The nodes can be connected with (not necessarily straight) line segments, called edges (or arcs), to show a relationship between the nodes. Graphs are used to model everything from transportation networks to groups of friends.

scholarly journals THE L∞ VORONOI DIAGRAM OF SEGMENTS AND VLSI APPLICATIONS

2001 ◽  
Vol 11 (05) ◽  
pp. 503-528 ◽  
Author(s):  
EVANTHA PAPADOPOULOU ◽  
D. T. LEE
Keyword(s):  
Voronoi Diagram ◽  
Yield Prediction ◽  
Critical Area ◽  
Vlsi Layout ◽  
Line Segments ◽  
Straight Line ◽  
Computational Bottleneck

In this paper we address the L∞ Voronoi diagram of polygonal objects and present application in VLSI layout and manufacturing. We show that L∞ Voronoi diagram of polygonal objects consists of straight line segments and thus it is much simpler to compute than its Euclidean counterpart; the degree of the computation is significantly lower. Moreover, it has a natural interpretation. In applications where Euclidean precision is not essential the L∞ Voronoi diagram can provide a better alternative. Using the L∞ Voronoi diagram of polygons we address the problem of calculating the critical area for shorts in a VLSI layout. The critical area computation is the main computational bottleneck in VLSI yield prediction.

scholarly journals Weighted Voronoi Diagrams in the Maximum Norm

2019 ◽  
Vol 29 (03) ◽  
pp. 239-250
Author(s):  
Günther Eder ◽  
Martin Held
Keyword(s):  
Simple Formula ◽  
Voronoi Diagrams ◽  
Incremental Algorithm ◽  
Maximum Norm ◽  
Worst Case ◽  
Line Segments ◽  
One Dimensional ◽  
Straight Line ◽  
Dimensional Version ◽  
The One

We consider multiplicatively weighted points, axis-aligned rectangular boxes and axis-aligned straight-line segments in the plane as input sites and study Voronoi diagrams of these sites in the maximum norm. For [Formula: see text] weighted input sites we establish a tight [Formula: see text] worst-case bound on the combinatorial complexity of their Voronoi diagram and introduce an incremental algorithm that allows its computation in [Formula: see text] time. Our approach also yields a truly simple [Formula: see text] algorithm for solving the one-dimensional version of this problem, where all weighted sites lie on a line.

scholarly journals Use of otoliths to estimate size at sexual maturity in fish

2000 ◽  
Vol 43 (4) ◽  
pp. 437-440 ◽  
Author(s):  
Carlos Sérgio Agostinho
Keyword(s):  
Sexual Maturity ◽  
Line Segments ◽  
Alternative Method ◽  
Straight Line ◽  
Size At Sexual Maturity

The viability of an alternative method for estimating the size at sexual maturity of females of Plagioscion squamosissimus (Perciformes, Sciaenidae) was analyzed. This methodology was used to evaluate the size at sexual maturity in crabs, but has not yet been used for this purpose in fishes. Separation of young and adult fishes by this method is accomplished by iterative adjustment of straight-line segments to the data for length of the otolith and length of the fish. The agreement with the estimate previously obtained by another technique and the possibility of calculating the variance indicates that in some cases, the method analyzed can be used successfully to estimate size at sexual maturity in fish. However, additional studies are necessary to detect possible biases in the method.

scholarly journals An Automatic Measurement Method for Absolute Depth of Objects in Two Monocular Images Based on SIFT Feature

2017 ◽  
Author(s):  
Lixin He ◽  
Jing Yang ◽  
Bin Kong ◽  
Can Wang
Keyword(s):  
Automatic Measurement ◽  
Depth Estimation ◽  
Depth Information ◽  
Scale Invariant ◽  
Line Segments ◽  
Sift Feature ◽  
Novel Approach ◽  
Straight Line ◽  
Object Depth ◽  
Scale Invariant Feature

It is one of very important and basic problem in compute vision field that recovering depth information of objects from two-dimensional images. In view of the shortcomings of existing methods of depth estimation, a novel approach based on SIFT (the Scale Invariant Feature Transform) is presented in this paper. The approach can estimate the depths of objects in two images which are captured by an un-calibrated ordinary monocular camera. In this approach, above all, the first image is captured. All of the camera parameters remain unchanged, and the second image is acquired after moving the camera a distance d along the optical axis. Then image segmentation and SIFT feature extraction are implemented on the two images separately, and objects in the images are matched. Lastly, an object depth can be computed by the lengths of a pair of straight line segments. In order to ensure that the best appropriate a pair of straight line segments are chose and reduce the computation, the theory of convex hull and the knowledge of triangle similarity are employed. The experimental results show our approach is effective and practical.

scholarly journals Low-level Grouping of Straight Line Segments

1991 ◽  
Author(s):  
A. Etemadi ◽  
J. P. Schmidt ◽  
G. Matas ◽  
J. Illingworth ◽  
J. Kittler
Keyword(s):  
Line Segments ◽  
Low Level ◽  
Straight Line

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.

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