• Journal of KIISE:Computer Systems and Theory
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• v.29 no.12
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• pp.640-647
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• 2002

In this paper, we consider the problems related to the edge visibility on a reconfigurable mesh(in short, RMESH). The following basic problems related to the edge visibility are considered: First, determine if a given polygon is visible from a specific edge, Second, find all edges from which a given polygon is visible. Third, compute the visibility polygon from a specific edge of a given polygon. In this paper, we consider the following problem in order to solve these problems in constant time: given two edges e and f of a simple polygon p, compute the maximal interval of f which is visible from e. We present a constant time algorithm for the problem on an N-N RMESH, where N is the number of vertices of P. Applying the algorithm, we can solve the above three problems in a constant time on a reconfigurable mesh. Specially, we can solve the third problem in a constant time on an N-$N_2$ RMESH.

• Proceedings of the Korean Information Science Society Conference
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• 2001.10a
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• pp.607-609
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• 2001

본 논문에서는 단순 다각형의 두 에지 사이의 가시성 문제를 재구성가능한 메쉬(RMESH) 병렬 모델에서 상수 시간에 해결하기 위한 알고리즘을 고려한다. 두 에지 사이의 가시성은 네 가지 유형, 즉, 완전 가시성(complete visibility), 강 가시성(strong visibility), 약 가시성(weak visibility), 부분 가시성(partial visibility)으로 구분될 수 있다. 논문에서는 에지 가시성에 대한 여러 가지 성질들을 고찰하여 두 에지 사이의 모든 유형에 대한 가시성의 판별과 가시 영역을 구하는 상수 시간 N$\times$N RMESH 알고리즘을 제시한다.

• Proceedings of the Korean Information Science Society Conference
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• 2000.10a
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• pp.548-550
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• 2000

본 논문은 재구성 가능한 메쉬(RMESH) 병렬 모델에서 상수 시간에 구멍이 있는 다각형의 한 점으로부터의 가시성 다각형을 구하는 문제를 고려한다. 알고리즘의 기본 전략은 프로세서의 수에 있어 준-최적인 상수 시간 알고리즘을 사용하여 문제의 크기를 감소시킴으로써 최적인 상수 시간 알고리즘을 얻는 것이다. 이 전략을 사용해 모두 N개의 에지로 구성된 구멍이 있는 다각형에 대한 가시성 다각형을 N$\times$N RMESH에서 상수 시간에 구하는 알고리즘을 제시한다. 이 알고리즘은 다각형들의 집합이 주어져 있을 때 외부의 한 점에서 가시 영역을 구하거나, 선분들의 집합이 주어져 있을 때 평면상의 한 점에서 가시 영역을 구하는 문제도 해결할 수 있다.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2014.05a
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• pp.795-797
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• 2014

The visibility polygon of a simple polygon P is the set of points which are visible from a visibility source in P such as a point or an edge. Since a visibility polygon is the set of points, the set operations such as intersection and union can be executed on them. The intersection(resp. union) of two visibility polygons is the set of points which are visible from both (resp. either) of the corresponding two visibility sources. As previous results, there exist O(n) time algorithms for the set operations of two visibility polygons with total n vertices. In this paper, we present $O(log^2n)$ time algorithms for solving the problems on a reconfigurable mesh with size $O(n^2)$.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.1_2
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• pp.102-111
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• 2004

The visibility polygon of a simple polygon P is the set of points which are visible from a visibility source in P such as a point or an edge. Since a visibility polygon is the set of points, the set operations such as intersection, union, or difference can be executed on them. The intersection (resp. union) of two visibility polygons is the set of points which are visible from both (resp. either) of the corresponding two visibility sources. The difference of two visibility polygons is the set of points which are visible from only a visibility source. Previously, the best known algorithm for the set operations of two polygons with total n vertices takes O(nlogn ＋ k) time, where k is the output size. In this paper, we present O(n) time algorithms for computing the intersection, the union, and the difference of given two visibility polygons, which are optimal.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2009.10a
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• pp.807-810
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• 2009

In this paper, we consider the shortest path problems in a simple polygon. The shortest path between two points inside a 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 cases without very large input size. In this paper, we present the customized shortest path algorithms for specific polygon classes such as star-shaped polygons, edge-visible polygons, and monotone polygons. These algorithms need not triangulating as preprocessing, so they are simple and run very fast in linear time.