• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.569-608
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• 1994

The subject matter of this survey has to do with holomorphic maps from a compact Riemann surface to projective space, which are also called algebrac curves; the theory we survey lies at the crossroads of function theory, projective geometry, and commutative algebra (although we should mention that the present survey de-emphasizes the algebraic aspect). Algebraic curves have been vigorously and continuously investigated since the time of Riemann. The reasons for the preoccupation with algebraic curves amongst mathematicians perhaps have to do with-other than the usual usual reason, namely, the herd mentality prompting us to follow the leads of a few great pioneering methematicians in the field-the fact that algebraic curves possess a certain simple unity together with a rich and complex structure. From a differential-topological standpoint algebraic curves are quite simple as they are neatly parameterized by a single discrete invariant, the genus. Even the possible complex structures of a fixed genus curve afford a fairly complete description. Yet there are a multitude of diverse perspectives (algebraic, function theoretic, and geometric) often coalescing to yield a spectacular result.

• 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.

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.19-29
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• 1999

B. Gr nbaum defined the arrangements of simple curves and got many combinatorial properties. In this paper, we studied the existence of (n,r,t,k)-arrangements and the existence of digon-free(n,r,t,k)-arrangements, which is a generalized version of Gr nbaum`s definition.

• Steel and Composite Structures
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• v.39 no.3
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• pp.243-259
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• 2021

In the present paper, a Monte Carlo-based framework is developed to investigate the accuracy and reliability of analytical fragility curves of steel moment-resisting frames and simple SDOF systems. It is also studied how the effectiveness of incremental dynamic analysis (IDA) and multiple stripes analysis (MSA) approaches, as two common nonlinear dynamic analysis methods, are influenced by the number of records and analysis stripes in fragility curves producing. Results showed that the simple SDOF systems do not provide accurate and reliable fragility curves compared with realistic steel moment-resisting structures. It is demonstrated that, the effectiveness of nonlinear dynamic analysis approaches is dependent on the fundamental period of structures, where in short-period structures, IDA is found to be more effective approach compared with MSA. This difference between the effectiveness of two analysis approaches decreases as the fundamental period of structures become longer. Using of 2 or 3 analysis stripes in MSA approach leads to significant inaccuracy and unreliability in the estimated fragility curves. Additionally, 15 number of ground motion records is recommended as a threshold of significant unreliability in estimated fragility curves, constructed by MSA.

• Proceedings of the KIEE Conference
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• 1996.11a
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• pp.3-5
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• 1996

The Preisach model needs density function or Everett function for the sample material to calculate the hysteresis characteristics. To obtain these functions, many experimental data obtained from the first order transition curves are required. However, it is not simple task to measure the curves. In this paper, a simple generalized technique to get the Everett function using saturation hysteresis loop and two first order transition curves is proposed. These three data makes three equations for the proposed Everett function model and we can get three variables by those equations. From the simulation, we got acceptable results.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.8
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• pp.114-121
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• 1995

This paper describes a method which uses rail curves for blending surfaces. Blending surface between the free form surfaces which have the flexible shapes and are widely used today is investigated. The rail curves give blending surface continuty through Pointwise interpola- tion. It is the point in this paper that the blending surfaces give a good flexibility to modeling of base free form surfaces. Using rail curves for simple base surfaces, complicated models can be designed. Also this blending surfaces can be used for path generation in compoud surfaces.

• 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.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.577-584
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• 2004

In a 4-valent multi 3-gon graph, every cut-through curve forms a simple closed circuit. Hence it is a weak arrangement of simple curves that is defined by Branko Grunbaum. In this paper, we study the edge properties of the 4-valent multi 3-gon graphs from the point of view of arrangement, and we show that they are 3 colorable.

• Journal of the Korean Society for Nondestructive Testing
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• v.23 no.6
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• pp.605-615
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• 2003

In practice, it is common to manufacture reference blocks containing simple reflectors to obtain distance-amplitude correction (DAC) curves. However, the construction or DAC curves in this manner requires the use of a large number of specimens with appropriate curvatures and reference reflectors located at various depths. Therefore, less costly and quantitative procedures are strongly needed. To address such a need, in this study, we have developed model-based transfer curves to relate a DAC curve obtained in a particular reference configuration with that for a completely different configuration. An example of transferring DAC curves, using the proposed transfer curves, is given.

• Journal of Korea Multimedia Society
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• v.7 no.4
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• pp.579-591
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• 2004

This paper presents a new arc segmentation method which extracts curves from simple drawing consisted of straight lines and curves and segments them into circular arcs. First, it finds center points and finds line segments and curve segments by tracing connected center points. Next, it expands the segment by searching neighbor segment at the two endpoints. Next, it removes straight lines and segments the extracted curves into circular arcs by using the recursive subdivision method. The proposed method has been compared with previous vectorization software and vector based arc segmentation method. Experimental results show that the proposed method produces more correct results for the curves which contain intersection with other lines or curves.