• Proceedings of the Korean Operations and Management Science Society Conference
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• 1994.04a
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• pp.691-700
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• 1994

Voronoi diagram of a set of geometric entities on a plane such as points, line segments, or arcs is a collection of Voronoi polygons associated with each entity, where Voronoi polygon of an entity is a locus of point which is closer to the associated entity than any other entity. Voronoi diagram is one of the most fundamental geometrical construct and well-known for its theoretical elegance and the wealth of applications. Various geometric problems can be solved with the aid of Voronoi diagram. For example, the maximum tool diameter of a milling cutter for rough cutting in a pocket can be easily found, and the pocketing tool path can be efficiently generated from Voronoi diagram. In PCB design, the design rule checking can be easily done via Voronoi diagram, too. This paper discusses an algorithm to construct Voronoi diagram of a simple polygon which consists of simple curves such as line segments as well as arcs in a plane with O(nlogn) time complexity by employing the divide and conquer scheme.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.513-518
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• 2007

A polygon-wise constant curvature natural element approximation is presented in this paper for the numerical implementation of the abstract Kirchhoff plate model. The strict continuity requirement in the displacement field is relaxed by converting the area integral of the curvatures into the boundary integral along the Voronoi boundary. Curvatures and bending moments are assumed to be constant within each Voronoi polygon, and the Voronoi-polygon-wise constant curvatures are derived in a selective manner for the sake of the imposition of essential boundary conditions. The numerical results illustrating the proposed method are also given.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1601-1606
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• 1991

We present an algorithm to approximate the Voronoi diagrams of 2D objects bounded by algebraic curves. Since the bisector curve for two algebraic curves of degree d can have a very high algebraic degree of 2 * d$^{4}$, it is very difficult to compute the exact algebraic curve equation of Voronoi edge. Thus, we suggest a simple polygonal approximation method. We first approximate each object by a simple polygon and compute a simplified polygonal Voronoi diagram for the approximating polygons. Finally, we approximate each monotone polygonal chain of Voronoi edges with Bezier cubic curve segments using least-square curve fitting.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.405-409
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• 1997

Voronoi diagrams are applied in varios field such as NC toolpath generation, VLSI design and robot path planning because of their geometric charcteristics. In this paper, Voronoi diagrams are introduced on polygon constructed by line segments only and with constant offset. Bisector curves for two arbitrary objects, which is the combination of line segment and arc, are defined as parametric fuction where the parameter is used as offset. Offset curves are applied on the generation of laser scanning path for the stereolithography and shows a good result from several examples.

• Spatial Information Research
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• v.10 no.3
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• pp.439-453
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• 2002

Researches using DEM are actively progressed in field of water resource, and especially the extraction of watershed and stream based on topographic and hydrologic analysis, is widely used in GIS analysis recently. However, because it is extracted that watershed which is type of sliver polygon and stream which is type of straight line in low topographic region, they're not efficient for application. This study determined buffer zone from stream and tried smooth elevation change to buffer zone in order to efficiently extract abnormal watershed and stream being occurred in low topographic region. Especially, we applied equal-distance assignment model using Voronoi Diagram to determine smooth elevation change. Also, we extracted watershed and stream using stream recognition DEM and origional DEM, and evaluated the efficiency of research through comparing the shape of watershed and stream in low topographic region.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.1B
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• pp.106-116
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• 2010

Sensor deployment makes an effect on not only covering of the interesting area but also reliable data acquisition and efficient resource management of sensor, so that sensors must be deployed at their better place. In traditional static wireless sensor networks, however, it is impossible to deploy the sensors manually when they are distributed in unexploited, hostile, or disaster areas. Therefore, if each sensor has locomotion capability, it can re-deploy itself using the location information of neighbor sensors. In our previous study, we showed that moving sensors to the centroids of their Voronoi polygon is efficient for extending the coverage area. In this paper, we present an improved potential-field-based sensor self-deployment scheme by combining the centroid of Voronoi polygon with the traditional potential-field scheme. Simulation results show that our scheme can achieve higher coverage in shorter time and less movement than the traditional potential-field scheme.

• Journal of Mechanical Science and Technology
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• v.20 no.11
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• pp.1881-1890
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• 2006

In this paper, a Petrov-Galerkin natural element method (PG-NEM) based upon the natural neighbor concept is presented for the free vibration and dynamic response analyses of two-dimensional linear elastic structures. A problem domain is discretized with a finite number of nodes and the trial basis functions are defined with the help of the Voronoi diagram. Meanwhile, the test basis functions are supported by Delaunay triangles for the accurate and easy numerical integration with the conventional Gauss quadrature rule. The numerical accuracy and stability of the proposed method are verified through illustrative numerical tests.

• Structural Engineering and Mechanics
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• v.16 no.6
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• pp.713-730
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• 2003

This paper contains the results of the study on the development of fracture and crack propagation in quasi-brittle materials, such as concrete or rocks, using the Discrete Element Method (DEM). A new discrete element numerical model is proposed as the basis for analyzing the inelastic evolution and growth of cracks up to the point of gross material failure. The model is expected to predict the fracture behavior for the quasi-brittle material structure using the elementary aggregate level, the interaction between aggregate materials, and bond cementation. The algorithms generate normal and shear forces between two interfacing blocks and contains two kinds of contact logic, one for connected blocks and the other one for blocks that are not directly connected. The Mohr-Coulomb theory has been used for the fracture limit. In this algorithm the particles are moving based on the connected block logic until the forces increase up to the fracture limit. After passing the limit, the particles are governed by the discrete block logic. In setting up a discrete polygon element model, two dimensional polygons are used to investigate the response of an assembly of different shapes, sizes, and orientations with blocks subjected to simple applied loads. Several examples involving assemblies of particles are presented to show the behavior of the fracture and the failure process.

• Journal of IKEEE
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• v.11 no.4
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• pp.348-357
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• 2007

Due to the improved performance and cost of personal mobile devices and rapid progress of wireless communication technology, the number of users who utilize these devices is increasing. This trend requires various types of services be available to users. So far, there have been many solutions provided for the shortest path problem. But, technologies which can offer various recommendation services to user depending on user’s current location are focused on Euclidean spaces rather than road network. Thus, in this paper, we extend the previous work to satisfy this requirement on road network database. Our proposed scheme requires pre-computation for the efficient query processing. In the preprocessing step, we first partition the input road network into a fixed number of Voronoi polygons and then pre-compute routing information for each polygon. In the meantime, we select the number of Voronoi polygons in proposition to the scale of road network. Through this selection, the required size of pre-computation is linearly increasing to the size of road network. Using this pre-computated information, we can process queries more quickly. Through experiments, we have shown that our proposed scheme can achieve excellent performance in terms of scheduling time and the number of visited nodes.

• Journal of the Korea Computer Graphics Society
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• v.7 no.2
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• pp.11-19
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• 2001

This paper proposes a colored paper mosaic rendering technique based on image segmentation that can automatically generate torn and tagged colored paper mosaic effect. and 3D effect that come about in human-made mosaic work can be represented by generating shadow using difference of paper thickness. Previous method did not produce satisfactory results due to the ineffectiveness of having to use pieces of the same size. The proposed two methods for determination of paper shape and location that are based on segmentation can subdivide image area by considering characteristics of image. The first method is to generate Voronoi polygon after subdividing the segmented image again using quad tree. And the second method is to apply the Voronoi diagram on each segmentation layer. Through these methods, the characteristic of the image is expressed in more detail than previous colored paper mosaic rendering method and these methods enable to produce image that is closer to human-made mosaic work.