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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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We prove three convex hull theorems on triangles and circles. Given a triangle ${\triangle}$ and a point p, let ${\triangle}^{\prime}$ be the triangle each of whose vertices is the intersection of the orthogonal line from p to an extended edge of ${\triangle}$. Let ${\triangle}^{{\prime}{\prime}}$ be the triangle whose vertices are the centers of three circles, each passing through p and two other vertices of ${\triangle}$. The first theorem characterizes when $p{\in}{\triangle}$ via a distance duality. The triangle algorithm in [1] utilizes a general version of this theorem to solve the convex hull membership problem in any dimension. The second theorem proves $p{\in}{\triangle}$ if and only if $p{\in}{\triangle}^{\prime}$. These are used to prove the third: Suppose p be does not lie on any extended edge of ${\triangle}$. Then $p{\in}{\triangle}$ if and only if $p{\in}{\triangle}^{{\prime{\prime}}$.
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참고문헌 (7)
참고문헌 신청
B. Kalantari / A characterization theorem and an algorithm for a convex hull problem, to appear in Annals of Operations Research
B. Kalantari / 2012 / Finding a lost treasure in convex hull of points from known distances / Proceedings of the 24th Canadian Conference on Computational Geometry :271~276
B. Kalantari / 2012 / Solving linear system of equations via a convex hull algorithm / arxiv.org/pdf/1210.7858v1.pdf
B. Kalantari / 2013 / On the Triangle Algorithm for the Convex Hull Membership / 23nd Annual Fall Workshop on Computational Geometry
M. Li / 2013 / Experimental Study of the Convex Hull Decision Problem via a New Geometric Algorithm / 23nd Annual Fall Workshop on Computational Geometry
B. Kalantari / 2012 / Finding a lost treasure in convex hull of points from known distances / Proceedings of the 24th Canadian Conference on Computational Geometry :271~276
B. Kalantari / 2012 / Solving linear system of equations via a convex hull algorithm / arxiv.org/pdf/1210.7858v1.pdf
B. Kalantari / 2013 / On the Triangle Algorithm for the Convex Hull Membership / 23nd Annual Fall Workshop on Computational Geometry
M. Li / 2013 / Experimental Study of the Convex Hull Decision Problem via a New Geometric Algorithm / 23nd Annual Fall Workshop on Computational Geometry
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