• 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 $O(n^2)$.

• 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.

• 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.

• Journal of the Korea Computer Industry Society
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• v.3 no.1
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• pp.35-44
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• 2002

The watchman routes which an watchman patrols the interior of given polygon moving along the route are classified to minimum length or minimum links. The watchman route with minimum links has minimum changes of direction and a weakly visible polygon consists of two chains which have mutually weakly visibility. In this paper, we present an Ο($n^2$) time algorithm for finding the watchman route with minimum links in the weakly visible polygons, where n is the number of vertices of a given polygon.

• The KIPS Transactions:PartA
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• v.15A no.5
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• pp.295-300
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• 2008

In this paper, we consider a characterization of a Guard Sufficiency Set(GSS) in the hierarchy of simple polygons. we propose the diagonals of a arbitrary triangulation of a polygon as a GSS when guards see the diagonals with completely visibility and both sides of the diagonal. we show that this can be a GSS in convex polygons, unimodal polygons, spiral polygons but this can not be a GSS in star-shaped polygons, monotone polygons, completely external visible polygons.

• 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.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.20 no.2
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• pp.401-407
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• 2016

We can consider the following problems for two given points p and q in a simple polygon P. (1) Compute the set of points of P which are visible from both p and q. (2) Compute the set of points of P which are visible from either p or q. They are corresponding to the problems which are to compute the intersection and the union of two visibility polygons. In this paper, we consider algorithms for solving these problems on a reconfigurable mesh(in short, RMESH). The algorithm in [1] can compute the intersection of two general polygons in constant time on an RMESH with size O($n^3$), where n is the total number of vertices of two polygons. In this paper, we construct the planar subdivision graph in constant time on an RMESH with size O($n^2$) using the properties of the visibility polygon for preprocessing. Then we present O($log^2n$) time algorithms for computing the union as well as the intersection of two visibility polygons, which improve the processor-time product from O($n^3$) to O($n^2log^2n$).

• 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.

• Journal of the Korea Computer Graphics Society
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• v.5 no.2
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• pp.9-23
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• 1999

Visibility preprocessing is a useful method to reduce the complexity of scenes to be processed in real-time, and so enhances the overall rendering performance for interactive visualization of virtual environments. In this paper, we propose an efficient visibility preprocessing method. In the proposed method, we assume that navigatable areas in virtual environments are partitioned into rectangular parallelpiped cells or sub-worlds. To preprocess the visibility of each polygon for a given partitioned cell, we should determine at least the area-to-area visibility. This is inherently a four-dimensional problem. We efficiently express four-dimensional visibility information on two-dimensional spaces and keep it within a ternary tree, which is conceptually similar to a BSP(Binary Space Partitioning) tree, by exploiting the characteristics of conservative visibility. The proposed method is able to efficiently handle more general environments like urban scenes, and remove invisible polygons jointly blocked by multiple occluders. The proposed method requires O(nm) time and O(n+m) space. By selecting a suitable value for m, users can select a suitable level of trade-off between the preprocessing time and the quality of the computational result.

• Journal of KIISE:Computer Systems and Theory
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• v.29 no.5
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• pp.274-283
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• 2002

A weakly visible polygon is an n-gon in the plane and consists of two mutually weakly visible chains. In this paper, we present an $O(n^2)$ time algorithm that finds a shortest watchman route among the routes with minimum links where a watchman patrols the inside of weakly visible polygons.