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Let P be a set of n points in the plane. We solve the problem of computing the orientations for which the rectilinear convex hull of P has minimum area in optimal ⇥(n log n) time and O(n) space. Introduction The interest in the rectilinear convex hull of planar point sets arises from the study of ortho-convexity [10], a relaxation of traditional convexity.… (More)

- Carlos Alegría-Galicia, David Orden, Carlos Seara, Jorge Urrutia
- ArXiv
- 2017

Let P be a set of n points in the plane and O be a set of k lines passing through the origin. We show: (1) How to compute the O-hull of P in Θ(n log n) time and O(n) space, (2) how to compute and maintain the rotated hull OHθ(P ) for θ ∈ [0, 2π) in O(kn log n) time and O(kn) space, and (3) how to compute in Θ(n log n) time and O(n) space a value of θ for… (More)

- Renato Barrera, Abraham Alcántara, Carlos Alegría-Galicia, Ana L. Ávila, David Esparza
- 2010 7th International Conference on Electrical…
- 2009

This paper describes a system to enable access to those information systems at the National Autonomous University of Mexico that are related to biodiversity and the environment. This system associates existing Geographic Information Systems, Biodiversity Information Systems, and standard Relational Database Management Systems in a federation. In this way,… (More)

- Carlos Alegría-Galicia, David Orden, Carlos Seara, Jorge Urrutia
- ArXiv
- 2015

We study the Oβ-hull of a planar point set, a generalization of the Orthogonal Convex Hull where the coordinate axes form an angle β. Given a set P of n points in the plane, we show how to maintain the Oβ-hull of P while β runs from 0 to π in Θ(n log n) time and O(n) space. With the same complexity, we also find the values of β that maximize the area and… (More)

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