Topology-oriented incremental computation of Voronoi diagrams of circular arcs and straight-line segments

2009 ◽  
Vol 41 (5) ◽  
pp. 327-338 ◽  
Author(s):  
Martin Held ◽  
Stefan Huber
Keyword(s):  
Voronoi Diagrams ◽  
Line Segments ◽  
Incremental Computation ◽  
Circular Arcs ◽  
Straight Line

Grouping of Straight Line Segments and Circular Arcs for Scene Analysis

1995 ◽  
pp. 163-185
Author(s):  
Jean-Luc Arseneault ◽  
Robert Bergevin ◽  
Denis Laurendeau
Keyword(s):  
Scene Analysis ◽  
Line Segments ◽  
Circular Arcs ◽  
Straight Line

scholarly journals TOPOLOGY-PRESERVING WATERMARKING OF VECTOR GRAPHICS

2014 ◽  
Vol 24 (01) ◽  
pp. 61-86 ◽  
Author(s):  
STEFAN HUBER ◽  
MARTIN HELD ◽  
PETER MEERWALD ◽  
ROLAND KWITT
Keyword(s):  
Input Data ◽  
Two Dimensional ◽  
Statistical Features ◽  
Embedding Capacity ◽  
Vector Graphics ◽  
Line Segments ◽  
Circular Arcs ◽  
Straight Line ◽  
Watermark Embedding ◽  
Topological Correctness

Watermarking techniques for vector graphics dislocate vertices in order to embed imperceptible, yet detectable, statistical features into the input data. The embedding process may result in a change of the topology of the input data, e.g., by introducing self-intersections, which is undesirable or even disastrous for many applications. In this paper we present a watermarking framework for two-dimensional vector graphics that employs conventional watermarking techniques but still provides the guarantee that the topology of the input data is preserved. The geometric part of this framework computes so-called maximum perturbation regions (MPR) of vertices. We propose two efficient algorithms to compute MPRs based on Voronoi diagrams and constrained triangulations. Furthermore, we present two algorithms to conditionally correct the watermarked data in order to increase the watermark embedding capacity and still guarantee topological correctness. While we focus on the watermarking of input formed by straight-line segments, one of our approaches can also be extended to circular arcs. We conclude the paper by demonstrating and analyzing the applicability of our framework in conjunction with two well-known watermarking techniques.

scholarly journals On the generation of spiral-like paths within planar shapes

2017 ◽  
Vol 5 (3) ◽  
pp. 348-357 ◽  
Author(s):  
Martin Held ◽  
Stefan de Lorenzo
Keyword(s):  
Simple Algorithm ◽  
Basic Algorithm ◽  
Line Segments ◽  
Spiral Path ◽  
Curvature Variation ◽  
Circular Arcs ◽  
Straight Line ◽  
Planar Shapes ◽  
Double Spiral ◽  
Step Over

Abstract We simplify and extend prior work by Held and Spielberger [CAD 2009, CAD&A 2014] to obtain spiral-like paths inside of planar shapes bounded by straight-line segments and circular arcs: We use a linearization to derive a simple algorithm that computes a continuous spiral-like path which (1) consists of straight-line segments, (2) has no self-intersections, (3) respects a user-specified maximum step-over distance, and (4) starts in the interior and ends at the boundary of the shape. Then we extend this basic algorithm to double-spiral paths that start and end at the boundary, and show how these double spirals can be used to cover complicated planar shapes by composite spiral paths. We also discuss how to improve the smoothness and reduce the curvature variation of our paths, and how to boost them to higher levels of continuity. Highlights The algorithm computes a spiral path within planar shapes with and without islands. It respects a user-specified maximum step-over distance. Double spirals and composite spiral paths can be computed. Heuristics for smoothing the spirals are discussed. The algorithm is simple and easy to implement, and suitable for various applications.

Nonholonomic path planning among obstacles subject to curvature restrictions

Robotica ◽  
2002 ◽  
Vol 20 (1) ◽  
pp. 49-58 ◽  
Author(s):  
Wilson D. Esquivel ◽  
Luciano E. Chiang
Keyword(s):  
Path Planning ◽  
Shortest Path ◽  
Autonomous Navigation ◽  
Line Segments ◽  
Circular Arcs ◽  
Straight Line ◽  
Smoothing Process ◽  
Planning Methodology ◽  
Final Orientation ◽  
Complete Path

This paper addresses the problem of finding a nonholonomic path subject to a curvature restriction, to be tracked by a wheeled autonomous navigation vehicle. This robot is able to navigate in a structured environment, with obstacles modeled as polygons, thus constituting a model based system. The path planning methodology begins with the conditioning of the polygonal environment by offsetting each polygon in order to avoid the possibility of collision with the mobile. Next, the modified polygonal environment is used to compute a preliminary shortest path (PA) between the two extreme positions of the trajectory in the plane (x, y). This preliminary path (PA) does not yet consider the restrictions on the curvature and is formed only by straight line segments. A smoothing process follows in order to obtain a path (PS) that satisfies curvature restrictions which consist basically of joining the straight line segments by circular arcs of minimum radius R (filleting). Finally, the initial and final orientation of the vehicle are accounted for. This is done using a technique we have called the Star Algorithm, because of the geometric shape of the resulting maneuvers. A final complete path (PC) is thus obtained.

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.

A New and Efficient Method for Curve Drawing using Circular Arcs and Straight Line Segments

1989 ◽  
Vol 6 (5) ◽  
pp. 365-371 ◽  
Author(s):  
S N Biswas ◽  
D Dutta Majumder ◽  
B B Chaudhuri
Keyword(s):  
Efficient Method ◽  
Line Segments ◽  
Circular Arcs ◽  
Straight Line

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 COMPUTATIONAL AND STRUCTURAL ADVANTAGES OF CIRCULAR BOUNDARY REPRESENTATION

2011 ◽  
Vol 21 (01) ◽  
pp. 47-69 ◽  
Author(s):  
OSWIN AICHHOLZER ◽  
FRANZ AURENHAMMER ◽  
THOMAS HACKL ◽  
BERT JÜTTLER ◽  
MARGOT RABL ◽  
...  
Keyword(s):  
Convex Hull ◽  
Medial Axis ◽  
Boundary Representation ◽  
Line Segments ◽  
Circular Boundary ◽  
Original Shape ◽  
Circular Arcs ◽  
Straight Line ◽  
Planar Shapes ◽  
Boundary Approximation

Boundary approximation of planar shapes by circular arcs has quantitative and qualitative advantages compared to using straight-line segments. We demonstrate this by way of three basic and frequent computations on shapes – convex hull, decomposition, and medial axis. In particular, we propose a novel medial axis algorithm that beats existing methods in simplicity and practicality, and at the same time guarantees convergence to the medial axis of the original shape.

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.

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