Results 1 to 10 of about 10,726 (213)
α-Concave hull, a generalization of convex hull
Theoretical Computer Science, 2017 Bounding hull, such as convex hull, concave hull, alpha shapes etc. has vast applications in different areas especially in computational geometry. Alpha shape and concave hull are generalizations of convex hull. Unlike the convex hull, they construct non-convex enclosure on a set of points.
Saeed Asaeedi +2 more
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On the convex hull and homothetic convex hull functions of a convex body [PDF]
Geometriae Dedicata, 2022 AbstractThe aim of this note is to investigate the properties of the convex hull and the homothetic convex hull functions of a convex body K in Euclidean n-space, defined as the volume of the union of K and one of its translates, and the volume of K and a translate of a homothetic copy of K, respectively, as functions of the translation vector.
Ákos G. Horváth, Zsolt Lángi
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On Sumsets and Convex Hull [PDF]
Discrete & Computational Geometry, 2014 One classical result of Freimann gives the optimal lower bound for the cardinality of A+A if A is a d-dimensional finite set in the Euclidean d-space. Matolcsi and Ruzsa have recently generalized this lower bound to |A+kB| if B is d-dimensional, and A is contained in the convex hull of B.
Károly J. Böröczky +2 more
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A Convex Hull’ Characterization [PDF]
Pure and Applied Mathematics Journal, 2014 Conditions so that a vector belongs to a convex hull are obtained. Multilinear convex functions are considered. If these maps are defined on a convex set, it is obtained the algebraic expression. As an application, infinite games, with linear convex payoff, are studied.
FINESCHI, FRANCO, Quaranta, Giovanni
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Convex Hulls under Uncertainty [PDF]
Algorithmica, 2014 We study the convex-hull problem in a probabilistic setting, motivated by the need to handle data uncertainty inherent in many applications, including sensor databases, location-based services and computer vision. In our framework, the uncertainty of each input site is described by a probability distribution over a finite number of possible locations ...
Pankaj K. Agarwal +4 more
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Convex hulls of spheres and convex hulls of disjoint convex polytopes
Computational Geometry, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Menelaos I. Karavelas +2 more
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Computational Geometry, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Komei Fukuda +2 more
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Convex hulls of spheres and convex hulls of convex polytopes lying on parallel hyperplanes [PDF]
Proceedings of the twenty-seventh annual symposium on Computational geometry, 2011 Given a set $Σ$ of spheres in $\mathbb{E}^d$, with $d\ge{}3$ and $d$ odd, having a fixed number of $m$ distinct radii $ρ_1,ρ_2,...,ρ_m$, we show that the worst-case combinatorial complexity of the convex hull $CH_d(Σ)$ of $Σ$ is $Θ(\sum_{1\le{}i\ne{}j\le{}m}n_in_j^{\lfloor\frac{d}{2}\rfloor})$, where $n_i$ is the number of spheres in $Σ$ with radius ...
Menelaos I. Karavelas, Eleni Tzanaki
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Largest convex hulls for convex-hull disjoint clusters with bounded size
Theoretical Computer Science, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xuehou Tan, Rong Chen
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Dynamic planar convex hull [PDF]
The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings., 2003 In this article, we determine the amortized computational complexity of the planar dynamic convex hull problem by querying. We present a data structure that maintains a set of n points in the plane under the insertion and deletion of points in amortized O(log n) time per operation. The space usage of the data structure is O(n).
Jacob, Riko, Brodal, Gerth
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