• Journal of information and communication convergence engineering
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• v.8 no.1
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• pp.59-63
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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 given 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. Two points of a polygon P are said to be L-visible from each other if they can be joined by a simple chain of at most two rectilinear line segments contained in P completely. An L-visible polygon P is a polygon such that there is a point from which every point of P is L-visible. We present the customized optimal shortest path algorithm for an L-visible polygon. Our algorithm doesn't require triangulating as preprocessing and consists of simple procedures such as construction of convex hulls and operations for convex polygons, so it is easy to implement and runs very fast in linear time.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.9
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• pp.1167-1174
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• 1999

In this paper, we present a new technique for the local decomposition of convex structuring elements for morphological image processing. Local decomposition of a structuring element consists of local structuring elements, in which each structuring element consists of a subset of origin pixel and its eight neighbors. Generally, local decomposition of a structuring element reduces the amount of computation required for morphological operations with the structuring element. A unique feature of our approach is the use of linear integer programming technique to determine optimal local decomposition that guarantees the minimal amount of computation. We defined a digital convex polygon, which, in turn, is defined as a convex structuring element, and formulated the necessary and sufficient conditions to decompose a digital convex polygon into a set of basis digital convex polygons. We used a set of linear equations to represent the relationships between the edges and the positions of the original convex polygon, and those of the basis convex polygons. Further. a cost function was used represent the total processing time required for computation of dilation/erosion with the structuring elements in a decomposition. Then integer linear programming was used to seek an optimal local decomposition, that satisfies the linear equations and simultaneously minimize the cost function.

• Journal of Ocean Engineering and Technology
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• v.18 no.2
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• pp.77-82
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• 2004

The purpose of this study is to develop a nesting algorithm, using a genetic algorithm to optimize nesting order, and modified No Fit Polygon(NFP) methodology to place parts with the order generated from the previous genetic algorithm. Various genetic algorithm techniques, which have thus far been applied to the Travelling Salesman Problem, were tested. The partially mapped crossover method, the inversion method for mutation, the elitist strategy, and the linear scaling method of fitness value were selected to optimize the nesting order. A modified NFP methodology, with improved searching capability for non-convex polygon, was applied repeatedly to the placement of parts according to the order generated from previous genetic algorithm. Modified NFP, combined with the genetic algorithms that have been proven in TSP, were applied to the nesting problem. For two example cases, the combined nesting algorithm, proposed in this study, shows better results than that from previous studies.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.279-289
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• 1999

Given n points in the plane the planar convex hull prob-lem in that of finding which of these points belong to the perimeter of the smallest convex region (a polygon) containing all n points. Here we suggest two kinds of methods. First we present a new sequential method for constructing the pla-nar convex hull O(1.5n) time in the quadratic decision tree model. Second using the sequential method we suggest a new parallel algo-rithm which solve the planar convex hull O(1.5n/p) time on a maspar Machine (CREW-PRAM) with O(n) processors. Also when we run on a maspar Machine we achieved a 37. 156-fold speedup with 64 pro-cessor.

• 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.

• 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.

• International Journal of Automotive Technology
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• v.8 no.2
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• pp.193-201
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• 2007

The present paper deals with the application of the explicit finite element code, PAM-CRASH, to simulate the crash behavior of steel thin-walled tubes with various cross-sections subjected to axial loading. An isotropic elastic, linear strain-hardening material model was used in the finite element analysis and the strain-rate sensitivity of mild steel was modeled by using the Cowper-Symonds constitutive equation with modified coefficients. The modified coefficients were applied in numerical collapse simulations of 11 types of thin-walled polygon tubes: 7 convex polygon tubes and 4 concave polygon tubes. The results show that the thin hexagonal tube and the thick octagonal tube showed relatively good performance within the convex polygon tubes. The crush strengths of the hexagonal and octagonal tubes increased by about 20% and 25% from the crush strength of the square tube, respectively. Among the concave tubes, the I-type tube showed the best performance. Its crush strength was about 50% higher than the crush strength of the square tube.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.245-250
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• 2002

Consider the Convex Polygon Pm={Al , A2, ‥‥, Am} With Vertex points A$\_$i/ = (a$\_$i/, b$\_$i/),i : 1,‥‥, m, interior P$\^$0/$\_$m/, and length of perimeter denoted by L(P$\_$m/). Let R$\_$n/ = {B$_1$,B$_2$,‥‥,B$\_$n/), where B$\_$i/=(x$\_$i/,y$\_$I/), i =1,‥‥, n, denote a regular polygon with n sides of equal length and equal interior angle. Kaiser[4] used the regular polygon R$\_$n/ to approximate P$\_$m/, and the problem examined in his work is to position R$\_$n/ with respect to P$\_$m/ to minimize the area of the symmetric difference between the two figures. In this paper we give the quality of a approximating regular polygon R$\_$n/ to approximate P$\_$m/.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.283-290
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• 2003

Andras Bezdek proved that if a convex n-gon and n points are given, then the points and the sides of the polygon can be renumbered so that at least[${\frac{n}{3}}$] triangles spanned by the ith point and the ith side (i = 1,2,...n) are mutually non-overlapping. In this paper, we show that at least [${\frac{n}{2}}$] mutually non-overlapping triangles can be constructed. This lower bound is best possible.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.823-833
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• 2009

It is well-known that if a convex hyperbolic polygon is constructed as a fundamental domain for a subgroup of the modular group, then its translates by the group elements form a locally finite tessellation and its side-pairing transformations form a system of generators for the group. Such hyperbolically convex polygons can be obtained by using Dirichlet's and Ford's polygon constructions. Another method of obtaining a fundamental domain for subgroups of the modular group is through the use of a right coset decomposition and we call such domains standard fundamental domains. In this paper we give subgroups of the modular group which do not have hyperbolically convex standard fundamental domain containing only inequivalent cusps.