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하종성 又石大學校 1994 論文集 Vol.16 No.-
A polyhedron P is said to be strongly monotone with respect to a direction d when the polygon defined by intersecting P with each plane parallel to d is always monotone. In this paper, we show that the strong monotonicity of p can be characterized using unit normal vectors of pocket surfaces and lid surfaces of P that are obtained by applying geometric operations such as convex hull and regularized difference. Finally, we formulate the strong monotonicity of a polyhedron as a known geometric problem on a unit sphere: find all great circles not intersecting any of spherical polygons derived from unit normal vectors.
삼차원 중력 제조에서 구상의 알고리즘을 이용한 주입성의 결정
하종성 又石大學校 1998 論文集 Vol.20 No.-
It is essential for the automation of gravity casting to determine an orientation of a designed 3D model so that a liquid can completely fill its mould. In this paper. we first consider the properties of 3D fillability that are different to them of 2D in order to extend the results of Bose et al.[3] on the fillability of 2D gravity casting. For determining the minimum k fillability of a given polyhedron, we compute the spherical convex hull of a set of points that are the mappings of the vectors from a convex vertex to its adjacent vertices on the sphere. An orientation with the minimum k-fillability is obtained in O(nlogn+mnlogm) time by determining a hemisphere minimally containing the spherical convex hulls of convex vertices. where m and n are the numbers of convex vertices and all vertices. respectively. We also show that the strong and weak monotonicities are sufficient conditions on the l-fillability of polyhedrons.
구 볼록 다각형들의 최대 교차를 찾기 위한 효율적인 구 분할 방식
하종성 한국CDE학회 2001 한국CDE학회 논문집 Vol.6 No.2
The maximum intersection of spherical convex polygons are to find spherical regions owned by the maximum number of the polygons, which is applicable for determining the feasibility in manufacturing problems such mould design and numerical controlled machining. In this paper, an efficient method for partitioning a sphere with the polygons into faces is presented for the maximum intersection. The maximum intersection is determined by examining the ownerships of partitioned faces, which represent how many polygons contain the faces. We take the approach of edge-based partition, in which, rather than the ownerships of faces, those of their edges are manipulated as the sphere is partitioned incrementally by each of the polygons. Finally, gathering the split edges with the maximum number of ownerships as the form of discrete data, we approximately obtain the centroids of all solution faces without constructing their boundaries. Our approach is analyzed to have an efficient time complexity Ο(nv), where n and v, respectively, are the numbers of polygons and all vertices. Futhermore, it is practical from the view of implementation since it can compute numerical values robustly and deal with all degenerate cases.
구 볼록 다각형 들의 분리 및 교차를 위한 간선 기반 알고리즘의 구현
하종성,천은홍,Ha, Jong-Seong,Cheon, Eun-Hong 한국정보과학회 2001 정보과학회논문지 : 시스템 및 이론 Vol.28 No.9
본 논문에서는 구상에서 주어진 볼록 다각형의 집합$\Gamma$=${P_1...P_n}$의 최대 또는 최소 교차를 결정하기 위하여 다각형의 간선으로 구를 면으로 분할하는 문제를 고려한다. 이 문제는 $\Gamma$의 최대 부분집합을 포함하는 반구를 $\Gamma$를 분리하는 대원을, $\Gamma$를 이분하는 대원을 $\Gamma$를 최소 또는 최대 부분집합을 교차하는 대원을 각각 찾는 다섯가지 기하적 문제를 공통적으로 관련이 있다. 구다각형의 최대 및 최소 교차를 효율적으로 구하기 위하여 우리는 간선 기반 분할의 방식을 취하는데 이 방식에서는 구가 각 다각형에 의해 증분적으로 분할되면서 면이 아닌 면을 구성하는 간선의 소유권이 처리된다. 마지막에는 최대수의소유권을 가지는 분할된 비정렬 간선들을 모아 해가 되는 면들의 경계를 구성하지 않고 그들의 중심을 근사적으로 얻는다. 최대 교차를 찾는 우리의 알고리즘은 효율적인 시간복잡도 O(nv)를 가지는 것으로 분석된다. 여기서 n는 v은 각각 다각형과 모든 장점의 개수들이다. 더구나 견고하게 수치를 계산하고 모든 degeneracy 경우를 다루기 때문에 구현의 관점에서도 실제적이다. 유사한 방식을 사용하여 일반적인 교차의 모든 경계는 O(nv+LlogL)시간에 구성할 수 있다. 여기서 L은 해로 출력되는 간선의 개수이다. In this paper, we consider the method of partitioning a sphere into faces with a set of spherical convex polygons $\Gamma$=${P_1...P_n}$ for determining the maximum of minimum intersection. This problem is commonly related with five geometric problems that fin the densest hemisphere containing the maximum subset of $\Gamma$, a great circle separating $\Gamma$, a great circle bisecting $\Gamma$ and a great circle intersecting the minimum or maximum subset of $\Gamma$. In order to efficiently compute the minimum or maximum intersection of spherical polygons. we take the approach of edge-based partition, in which the ownerships of edges rather than faces are manipulated as the sphere is incrementally partitioned by each of the polygons. Finally, by gathering the unordered split edges with the maximum number of ownerships. we approximately obtain the centroids of the solution faces without constructing their boundaries. Our algorithm for finding the maximum intersection is analyzed to have an efficient time complexity O(nv) where n and v respectively, are the numbers of polygons and all vertices. Furthermore, it is practical from the view of implementation, since it computes numerical values. robustly and deals with all the degenerate cases, Using the similar approach, the boundary of a general intersection can be constructed in O(nv+LlogL) time, where : is the output-senstive number of solution edges.