• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.05a
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• pp.859-865
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• 2007

This paper presents a method to analyze the unbalance response of a high speed polygon mirror scanner motor supported by sintered bearing and flexible supporting structures by using the finite element method and the mode superposition method. The appropriate finite element equations for polygon mirror are described by rotating annular sector element using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. The rotating components except for the polygon mirror are modeled by Timoshenko beam element including the gyroscopic effect. The flexible supporting structures are modeled by using a 4-node tetrahedron element and 4-node shell element with rotational degrees of freedom. Finite element equations of each component of the polygon mirror scanner motor and the flexible supporting structures are consistently derived by satisfying the geometric compatibility in the internal boundary between each component. The rigid link constraints are also imposed at the interface area between sleeve and sintered bearing to describe the physical motion at this interface. A global matrix equation obtained by assembling the finite element equations of each substructure is transformed to a state-space matrix-vector equation, and both damped natural frequencies and modal damping ratios are calculated by solving the associated eigenvalue problem by using the restarted Arnoldi iteration method. Unbalance responses in time and frequency domain are performed by superposing the eigenvalues and eigenvectors from the free vibration analysis. The validity of the proposed method is verified by comparing the simulated unbalance response with the experimental results. This research also shows that the flexibility of supporting structures plays an important role in determining the unbalance response of the polygon mirror scanner motor.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.23 no.9
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• pp.1146-1151
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• 2019

Histogram H is an x-monotone rectilinear polygon with a horizontal edge, called by a base, connecting the leftmost vertical edge and the rightmost vertical edge. Here the rectilinear polygon is a polygon with only horizontal and vertical edges and the x- monotone polygon P is a polygon in which every line orthogonal to the x-axis intersects P at most twice. Walking counterclockwise on the boundary of a histogram H yields a sequence of left turns and right turns at its vertices. Conversely, a given sequence of the turns at the vertices can be realized by a histogram. In this paper, we consider the problem of finding a histogram to realize a given turn sequence. Particularly, we will find the histograms to minimize its area and its bounding box. It will be shown that both of the problems can be solved by linear time algorithms.

• Asia-Pacific Journal of Business
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• v.9 no.2
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• pp.1-13
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• 2018

Physics simulation is an important part of many interactive 2D applications and collision detection and response is key component of this simulation. While methods for reducing the number of collision tests that need to be performed has been well researched, methods for performing the final checks with collision primitives have seen little recent development. This paper presents a new collision primitive, the n-arc, constructed from piecewise circular curves or biarcs. An algorithm for performing a collision check between these primitives is presented and compared to a convex polygon primitive. The n-arc is shown to exhibit similar, though slightly slower, performance to a polygon when no collision occurs, but is considerably faster when a collision does occur. The goodness of fit of the new primitive is also compared to a polygon. While the n-arc often gives a looser fit in terms of area, the continuous tangents of the n-arcs makes them a good choice for organic, soft or curved surfaces.

• Journal of KIISE:Computer Systems and Theory
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• v.27 no.6
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• pp.541-548
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• 2000

An area light source in the three dimensional space shines past a scene polygon, to generate two types of shadow volumes for each scene polygon, i.e., one with partial occlusion and the other with the complete occlusion. These are called, penumbra and umbra, respectively. In this paper, consider the problem for computing the umbra of a convex polygon from convex quadric light sources such as circles, ellipses, spheres, ellipsoids and cylinders. First, we give characteristics of the boundary surfaces of the umbra and then propose an algorithm for generating the umbra using them.

• 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.

• IEMEK Journal of Embedded Systems and Applications
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• v.3 no.2
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• pp.119-125
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• 2008

This paper presents the polygon-based Q-leaning and Cascade Support Vector Machine algorithm for object search with multiple robots. We organized an experimental environment with ten mobile robots, twenty five obstacles, and an object, and then we sent the robots to a hallway, where some obstacles were lying about, to search for a hidden object. In experiment, we used four different control methods: a random search, a fusion model with Distance-based action making (DBAM) and Area-based action making (ABAM) process to determine the next action of the robots, and hexagon-based Q-learning and dodecagon-based Q-learning and Cascade SVM to enhance the fusion model with DBAM and ABAM process.

• East Asian mathematical journal
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• v.31 no.4
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• pp.483-503
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• 2015

While some studies have examined the concave and convex regular polygons respectively, very little work has been done to integrate and restructure polygon shapes. Therefore, this study aims to systematically reclassify the regular polygons on the through a comprehensive analysis of previous studies on the convex and concave regular polygons. For this study, the polygon's consistency with respect to the number of sides and angles was examined. Second, the consistency on the number of diagonals was also examined. Third, the size of the interior and exterior angels of regular polygons was investigated in order to discover the consistent properties. Fourth, the consistency concerning the area in regular polygons was inspected. Last, the consistency of the central figure number in the "k-th" regular polygons was examined. Given these examinations, this study suggests a way to create a concave regular polygon from a convex regular polygon.

• Spatial Information Research
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• v.23 no.3
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• pp.23-33
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• 2015

Most data used for urban planning is aggregated by administrative district. Thus, a fundamental limit to analysing the changes of micro-geographical units exists. The object of this study is to estimate spatial development patterns based on characteristic city indicators. Gangnam, an area that was analysed, was divided into hexagon polygons. The development density and characteristic city indicators were input into each polygon. Moreover, this study analysed the influence of characteristic city indicators on development density using multinomial regression analysis. According to the results, distance between a polygon and both a road and a bus stop led to a decrease of development density in the polygon. However, distance between a polygon and a river led to an increase of development intensity. The method of this analysis and the results can be used to disaggregate the zonal data in the urban planing area.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.53-60
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• 2010

The concept of discrete curvature is a discretization of the curvature. Many literatures introduce discrete curvatures derived from arc length of circular arcs. We propose a new concept of discrete curvature of a polygon at each vertex, which is derived from area of fan shapes. We estimate the error of the discrete curvature and compare the discrete curvature with old one.