• Journal of the Korea Institute of Information and Communication Engineering
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• v.14 no.2
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• pp.369-374
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• 2010

The shortest path between two points inside a simple polygon P is a minimum-length path among all paths connecting them which don't pass by the exterior of P. A linear time algorithm for computing the shortest path in a general simple polygon requires triangulating a polygon as preprocessing. The linear time triangulating is known to very complex to understand and implement it. It is also inefficient in case that the input without very large size is given because its time complexity has a big constant factor. In this paper, we present the customized shortest path algorithm for a segment-visible polygon which is a simple polygon weakly visible from an internal line segment. Our algorithm doesn't require triangulating as preprocessing and consists of simple procedures such as construction of convex hulls, so it is easy to implement and runs very fast in linear time.

• Korean Journal of Optics and Photonics
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• v.6 no.1
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• pp.21-25
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• 1995

Q-switched Waveguide $CO_{2}$ laser using polygon mirror were constructed and their output characteristics were measured. Waveguide was made of the beryllium oxide tube of inner diameter of 2 mm, outer diameter of 20 mm, and length of 200 mm. A flat ZnSe output coupler of 80% reflectivity was placed on the 9 mm distance from the end of the waveguide. Convex lens was used to reduce the coupling loss between the polygon mirror and the waveguide. The polygon mirror was located behind of convex lens. With this condition, continuous output of the laser were measured as 1.2 W. In the Q-switched mode. pulse width 120 ns were measured with rotational speed 7,559 RPM. and peak power of up to 250 W. 250 W.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.11
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• pp.130-136
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• 1998

This paper develops an efficient algorithm for the minimum distance calculation between two general polyhedra(convex and/or concave) in three-dimensional space. The polyhedra approximate objects using flat polygons which composed of more than three vertices. The algorithm developed in this paper basically computes minimum distance between two polygons(one polygon per object) and finds a set of two polygons which makes a global minimum distance. The advantage of the algorithm is that the global minimum distance can be computed in any cases. But the big disadvantage is that the minimum distance computing time is rapidly increased with the number of polygons which used to approximate an object. This paper develops a method to eliminate sets of two polygons which have no possibility of minimum distance occurrence, and an efficient algorithm to compute a minimum distance between two polygons in order to compensate the inherent disadvantage of the algorithm. The correctness of the algorithm is verified not only comparing analytically calculated exact minimum distance with one calculated using the developed algorithm but also watching a line which connects two points making a global minimum distance of a convex object and/or a concave object. The algorithm efficiently finds minimum distance between two convex objects made of 224 polygons respectively with a computation time of about 0.1 second.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.315-321
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• 2009

Erd$\"{o}$s posed the problem of determining the minimum number g(n) such that any set of g(n) points in general position in the plane contains an empty convex n-gon. In 1978, Harborth proved that g(5) = 10. We reprove the result in a geometric approach.

• Journal of the Korean School Mathematics Society
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• v.15 no.1
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• pp.183-197
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• 2012

Geometry having long history of mathematics have important role for thinking power and creativity progress in middle school. The regular polygon included in plane geometry was mainly taught convex regular polygon in elementary school and middle school. In this study, we investigated the denotation's extension of regular polygon by mathematical basic knowledge included in school curriculum. For this research, first, school mathematical knowledge about regular polygon was analyzed. And then, basic direction of research was established for inquiry. Second, based on this analysis inductive inquiry activity was performed with research using geometry software(Cabri Geometry II). Through this study the development of enriched learning material and showing the direction of geometry research is expected.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.193-198
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• 2006

Plunge milling is the fastest way to mill away large volumes of metal in the axial direction. The residual volume (inaccessible volume by the plungers) is minimized when selecting a specific direction of filling. This direction is known as the optimal inclination angle for filling of the plunged area. This paper proposes a new algorithm to calculate the optimal inclination angle of filling and to fill the plunged area with multi-plungers sizes. The proposed algorithm uses the geometry of the 2D area of the shape that being cutting to estimate the optimal inclination angle of filling. It is found that, the optimal inclination angle for filling of the plunged area is the same direction as the longer width of the equivalent convex polygon of the boundary contour. The results of the tested examples show that, the residual volume is minimized when comparing the proposed algorithm with the previous method.

• Journal of KIISE:Computer Systems and Theory
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• v.27 no.4
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• pp.416-419
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• 2000

Let G be an n-vertex convex polygon whose vertices are in general position. We consider an illumination problem of locating two floodlights on the boundary of G, which illuminates G and whose larger angle is as small as possible. We present an O($n^2$) time algorithm under the extended real-RAM model.

• Proceedings of the National Institute of Ecology of the Republic of Korea
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• v.3 no.4
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• pp.199-203
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• 2022

The spring home range and habitat use of the spot-billed duck in Korea were studied using GPS-mobile phone-based telemetry (WT-300). The study areas were Anseong-si, Seosan-si, Nonsan-si, and Sejong-si. Analysis was performed using minimum convex polygon (MCP) and kernel density estimation (KDE) spot-billed ducks had an average home range of 70.28 km² (standard deviation [SD]=84.50, n=6), and a core habitat (50%) 2.66 km² (SD=2.60, n=6), according to MCP and KDE, respectively. Wetlands (41.5%) and rice fields (35.7%) were highly used as habitats. The rice field use rate was high during the day, and the wetland utilization rate was high at night. Rice fields and wetlands were the primary habitats in spring.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.10a
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• pp.527-530
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• 1997

An automated process planning system for cold forging of non-axisymmetric parts of comparatively simple shape was developed in this study. Programs for the system have been written with Visual LISP in the AutoCAD using a personal computer and are composed of four main modules such as input module, shape cognition and shape expression module, material diameter determination module and process planning module. The design rules and knowledges for th system are extracted from the plasticity theories. handbook, relevant reference and empirical knowledge of field experts. Generally, in forging, only front view is needed for expression of axisymmetric parts, but non-axisymmetric parts are needed both front view and plane. At the plane, this system cognizes the external shape of non-axisymmetric parts - number of sides of regular polygon and radius of a circle circumscribing the polygon of n sides. At the front view, the system perceives diameter of axisymmetric portions and hight of primitive geometries such as polygon, cylinder, cone, concave, convex, etc.

• Journal of IKEEE
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• v.17 no.1
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• pp.29-35
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• 2013

In this paper, we suggest an improved Convex Hull algorithm considering sort in plane point set. This algorithm has low computational complexity since processing data are reduced by characteristic of extreme points. Also it obtains a complete convex set with just one processing using an convex vertex discrimination criterion. Initially it requires sorting of point set. However we can't quickly sort because of its heavy operations. This problem was solved by replacing value and index. We measure the execution time of algorithms by generating a random set of points. The results of the experiment show that it is about 2 times faster than the existing algorithm.