The storage and reconstruction of polygon boundaries using circles (original) (raw)

Constructing Approximate Voronoi Diagrams from Digital Images of Generalized Polygons and Circular Objects

International Conference in Central Europe on Computer Graphics and Visualization, 2003

In this paper we present the geometrical construction of an approximate generalized Voronoi diagram for generalized polygons and circular objects based on their minimum geometrical structure that are extracted from the object's digital image. The construction is done in ) (n O time complexity, where n is the number of single points defining the set of objects. An application of

The Use of the Circle Tree for the Efficient Storage of Polygons

University of …, 2003

The circle tree has been proposed as a novel hierarchical spatial data structure, promising optimised storage, access, and multiscale representation. The theory behind the circle tree draws from the fields of 3D computer graphics, spatial database indexing and cartography. The ...

A sweepline algorithm for Euclidean Voronoi diagram of circles

Computer-Aided Design, 2006

Presented in this paper is a sweepline algorithm to compute the Voronoi diagram of a set of circles in a two-dimensional Euclidean space. The radii of the circles are non-negative and not necessarily equal. It is allowed that circles intersect each other, and a circle contains others.

Evaluation of the Precision for Exact Computation of a Circle Voronoi Diagram

2007

An exact computation scheme for incremental construction of a circle Voronoi diagram is represented. The most important test for the incremental addition of a circle is to decide whether or not the new circle intersects the inscribing circle determined by three circles associated with a Voronoi vertex. For this purpose, the decision procedure is introduced using the sign of three polynomial functions. The proposed procedure requires about eight times higher precision than the input precision for the exact decision of the topological structure of a circle Voronoi diagram.

A Maximum Inscribed Circle Algorithm Based on Voronoi Diagrams and Geometry Equations

2018

The aim of this study is to develop an algorithm for the calculation of Maximum Inscribed Circle (MIC) that can be placed within a polygon feature (PF) by using Free and Open Source Software (FOSS) for GIS. Compared with other parameters developed for PFs, there is no simple algorithm for the computation of MIC for different PFs. The algorithm developed in this study for the computation of MIC is based on the Voronoi diagrams and analytical geometry equations. The algorithm developed for the approximation of MIC can be applied to both convex and concave PFs. For the implementation of the algorithm, Eclipse IDE platform and OpenJUMP libraries written in Java is used. What is evident from the various runs of the script produced on the base of the algorithm for a set of regular and irregular PFs is that it is successful in finding MIC.

Comparison of region approximation techniques based on Delaunay triangulations and Voronoi diagrams

2008

Region approximation techniques based on constructions from sample data points, i.e. points whose position is known and which are known to be inside or outside the region of interest, can be advantageous in a variety of applications. This paper compares two different constructions and presents results from a Monte Carlo model that shows that the construction based on mid points of edges in a Delaunay triangulation produces the lowest errors. These errors are some 10% less than those produced by the Voronoi diagram construction which appears to be more widely used at present. A consideration of the basic geometries of the different constructions leads to an expression for approximating the expected error in the case of a random point distribution. The expression takes the form

Computational and Structural Advantages of Circular Boundary Representation

International Journal of Computational Geometry & Applications, 2011

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.

An Exposition of Polygonal Approximation of Circle

2022

In this article, it is attempted to discuss how do we can create an infinite number of circles from a single circle, using its tangents with a pattern ( PX; X≥3 ) and what is the process to reach up into a single point from a given circle. The time to get a new circle from its predecessor circle can be reduced just by changing the pattern. The pattern behind both the radius of the successor circles and predecessor circles is also discussed. Most interestingly, when we apply the P∞ pattern of tangents on the single circle, then all the infinitely many successor circles merge into a single one, almost without taking any time and it takes infinite time to reach up into a single point from the given circle, for that pattern. In the whole process, polygonal approximation and sequences play a vital role.

Reconstruction of a Digital Circle

Since digitization always causes some loss of information, reconstruction of the original figure from a given digitization is a challenging task. Reconstruction of digital circles has already been addressed in the literature. However, an in-depth analysis of an OBQ image of a continuous circle as well as a solution to its domain construction problem is still lacking. In this paper a detailed analysis of digital circles has been carried out. A modified I_R method is formulated to numerically compute the domain of each digital quarter circle for a given radius. Several properties of the OBQ image of a circle reveal that in many cases it is possible to split a digital circle into four digital quarter circles, such that the domains of the individual quarter circles can be combined to obtain the domain of the full circle. Moreover, the domain of a quarter circle is geometrically characterized.