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Monotone polygons using linked list
2015 International Conference on Advances in Computer Engineering and Applications, 2015Two heuristics have been designed to generate a random monotone polygon from a given set of ‘n’ points lying on a 2-Dimensional plane. The first algorithm runs in O(n2) time using constant work space algorithm. The second algorithm is designed using dynamic memory allocation to generate x-monotone in O(n) time with a preprocessing time complexity of O ...
Kamaljit Pati +4 more
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On decomposing polygons into uniformly monotone parts
Information Processing Letters, 1988We present an \(O(n^ 3)\) algorithm for finding a maximum set of independent chords in a circle with n vertices on its circumference. We use this result to partition simple polygons into the minimum number of uniformly monotone polygons. Two or more polygons are uniformly monotone if they are monotone with respect to a common axis.
Liu, Robin, Ntafos, Simeon
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Uniformly monotone partitioning of polygons
Theoretical Computer SciencezbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kim, Hwi, Lee, Jaegun, Ahn, Hee-Kap
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Partitioning Polygons into Tree Monotone and Y -monotone Subpolygons
2003A polygon Q is tree monotone if, for some highest or lowest point p on Q and for any point q interior to Q, there is a y-monotone curve from p to q whose interior is interior to Q. We show how to partition an n vertex polygon P in Θ(n) time into tree monotone subpolygons such that any y-monotone curve interior to P intersects at most two of the ...
Ralph P. Boland, Jorge Urrutia
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GENERALIZING MONOTONICITY: ON RECOGNIZING SPECIAL CLASSES OF POLYGONS AND POLYHEDRA
International Journal of Computational Geometry & Applications, 2005A simple polyhedron is weakly-monotonic in direction [Formula: see text] provided that the intersection of the polyhedron and any plane with normal [Formula: see text] is simply-connected (i.e. empty, a point, a line-segment or a simple polygon). Furthermore, if the intersection is a convex set, then the polyhedron is said to be weakly-monotonic in ...
Bose, P., van Kreveld, M.J.
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Optimal uniformly monotone partitioning of polygons with holes
Computer-Aided Design, 2012Polygon partitioning is an important problem in computational geometry with a long history. In this paper we consider the problem of partitioning a polygon with holes into a minimum number of uniformly monotone components allowing arbitrary Steiner points. We call this the MUMC problem.
Wei, Xiangzhi +2 more
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Separation of two monotone polygons in linear time
Robotica, 1984SUMMARYLet P= (p1, p2, …, pn) and Q= (q1, q2, …, qm) be two simple polygons monotonic in directions θs and φ respectively. It is shown that P and Q are separable with a single translation in at least one of the directions: ,. Furthermore, a direction for carrying out such a translation can be determined in O(m + n) time.
Godfried T. Toussaint +1 more
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A Note on Monotone Polygons Fitted to Bivariate Data
Psychometrika, 1976The monotone regression function of Kruskal and the rank image function of Guttman and Lingoes were fitted to bivariate normal samples and their statistical properties contrasted.
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Euler Polygonal Lines for Itô Equations with Monotone Coefficients
Theory of Probability & Its Applications, 1988See the review in Zbl 0624.60072.
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