scholarly journals Computing Convex Hulls by Automata Iteration

2008 ◽  
pp. 112-121 ◽  
Author(s):  
François Cantin ◽  
Axel Legay ◽  
Pierre Wolper
Keyword(s):  
Convex Hulls

scholarly journals Continuous Maps from Spheres Converging to Boundaries of Convex Hulls

2021 ◽  
Vol 9 ◽  
Author(s):  
Joseph Malkoun ◽  
Peter J. Olver
Keyword(s):  
Convex Hull ◽  
Convex Geometry ◽  
Gauss Map ◽  
Parameter Family ◽  
Convex Hulls ◽  
Dimensional Sphere ◽  
Continuous Maps ◽  
Dimensional Boundary

Abstract Given n distinct points $\mathbf {x}_1, \ldots , \mathbf {x}_n$ in $\mathbb {R}^d$ , let K denote their convex hull, which we assume to be d-dimensional, and $B = \partial K $ its $(d-1)$ -dimensional boundary. We construct an explicit, easily computable one-parameter family of continuous maps $\mathbf {f}_{\varepsilon } \colon \mathbb {S}^{d-1} \to K$ which, for $\varepsilon> 0$ , are defined on the $(d-1)$ -dimensional sphere, and whose images $\mathbf {f}_{\varepsilon }({\mathbb {S}^{d-1}})$ are codimension $1$ submanifolds contained in the interior of K. Moreover, as the parameter $\varepsilon $ goes to $0^+$ , the images $\mathbf {f}_{\varepsilon } ({\mathbb {S}^{d-1}})$ converge, as sets, to the boundary B of the convex hull. We prove this theorem using techniques from convex geometry of (spherical) polytopes and set-valued homology. We further establish an interesting relationship with the Gauss map of the polytope B, appropriately defined. Several computer plots illustrating these results are included.

A Practical Solution for Privacy-Preserving Approximate Convex Hulls Problem

2009 ◽  
Author(s):  
Dong Li ◽  
Liusheng Huang ◽  
Wei Yang ◽  
Youwen Zhu ◽  
Yonglong Luo ◽  
...  
Keyword(s):  
Privacy Preserving ◽  
Convex Hulls ◽  
Practical Solution

Convex hulls of objects bounded by algebraic curves

Algorithmica ◽  
1991 ◽  
Vol 6 (1-6) ◽  
pp. 533-553 ◽  
Author(s):  
Chanderjit Bajaj ◽  
Myung -Soo Kim
Keyword(s):  
Algebraic Curves ◽  
Convex Hulls

scholarly journals Computable representations for convex hulls of low-dimensional quadratic forms

2010 ◽  
Vol 124 (1-2) ◽  
pp. 33-43 ◽  
Author(s):  
Kurt M. Anstreicher ◽  
Samuel Burer
Keyword(s):  
Quadratic Forms ◽  
Convex Hulls ◽  
Low Dimensional

Polynomially convex hulls with piecewise smooth boundaries

1986 ◽  
Vol 276 (1) ◽  
pp. 97-104 ◽  
Author(s):  
Franc Forstnerič
Keyword(s):  
Piecewise Smooth ◽  
Convex Hulls ◽  
Polynomially Convex

Convex hulls of finite sets of points in two and three dimensions

1977 ◽  
Vol 20 (2) ◽  
pp. 87-93 ◽  
Author(s):  
F. P. Preparata ◽  
S. J. Hong
Keyword(s):  
Three Dimensions ◽  
Convex Hulls ◽  
Finite Sets
Sign in / Sign up

Export Citation Format

Share Document