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Concept

Line–line intersection

Publications associées (20)

Additive and geometric transversality of fractal sets in the integers

Florian Karl Richter

By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...

2024

Fully solvable finite simplex lattices with open boundaries in arbitrary dimensions

Fabrizio Minganti

Finite simplex lattice models are used in different branches of science, e.g., in condensed-matter physics, when studying frustrated magnetic systems and non-Hermitian localization phenomena; or in chemistry, when describing experiments with mixtures. An n ...

Amer Physical Soc2023

Region Extraction in Mesh Intersection

Annalisa Buffa, Pablo Antolin Sanchez, Emiliano Cirillo

Region extraction is a very common task in both Computer Science and Engineering with several applications in object recognition and motion analysis, among others. Most of the literature focuses on regions delimited by straight lines, often in the special ...

2023

A finite element framework based on bivariate simplex splines on triangle configurations

Xiaodong Wei

Recently, triangle configuration based bivariate simplex splines (referred to as TCB-spline) have been introduced to the geometric computing community. TCB-splines retain many attractive theoretic properties of classical B-splines, such as partition of uni ...

ELSEVIER SCIENCE SA2019

X-Ray Nanotomography of Individual Pulp Fibre Bonds Reveals the Effect of Wall Thickness on Contact Area

Arttu Ilari Miettinen

Fibre bonds play an essential role in various properties of paper. Much research has focused on their strength, but the determination of the actual contact area also provides a challenge. Many of the research methods rely on optical tools, which are restri ...

Nature Research2019

Ordered Graphs And Large Bi-Cliques In Intersection Graphs Of Curves

János Pach, Istvan Tomon

An ordered graph G(

COMENIUS UNIV2019

Ordered graphs and large bi-cliques in intersection graphs of curves

János Pach, Istvan Tomon

An ordered graph G(

ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD2019

A lower bound on opaque sets

János Pach

It is proved that the total length of any set of countably many rectifiable curves whose union meets all straight lines that intersect the unit square U is at least 2.00002. This is the first improvement on the lower bound of 2 known since 1964. A similar ...

ELSEVIER SCIENCE BV2019

Distinct distances between points and lines

Frank de Zeeuw, Adrian Claudiu Valculescu

We show that for m points and n lines in R-2, the number of distinct distances between the points and the lines is Omega(m(1/5)n(3/5)), as long as m(1/2)

Elsevier Science Bv2018

Improving Spatial Data Processing by Clipping Minimum Bounding Boxes

Anastasia Ailamaki, Eleni Tzirita Zacharatou, Darius Sidlauskas

The majority of spatial processing techniques rely heavily on the idea of approximating each group of spatial objects by their minimum bounding box (MBB). As each MBB is compact to store (requiring only two multi-dimensional points) and intersection tests ...

IEEE2018

Algebraic and topological methods in combinatorics

Adrian Claudiu Valculescu

The present thesis deals with problems arising from discrete mathematics, whose proofs make use of tools from algebraic geometry and topology. The thesis is based on four papers that I have co-authored, three of which have been published in journals, and o ...

EPFL2017

Many disjoint edges in topological graphs

Andres Jacinto Ruiz Vargas

A monotone cylindrical graph is a topological graph drawn on an open cylinder with an infinite vertical axis satisfying the condition that every vertical line intersects every edge at most once. It is called simple if any pair of its edges have at most one ...

Elsevier Science Bv2017

Bisector Energy and Few Distinct Distances

Frank de Zeeuw

We define the bisector energy E(P) of a set P in R-2 to be the number of quadruples (a, b, c, d) is an element of P-4 such that a, b determine the same perpendicular bisector as c, d. Equivalently, E(P) is the number of isosceles trapezoids determined by P ...

Springer2016

On the Richter-Thomassen Conjecture about Pairwise Intersecting Closed Curves

János Pach

A long-standing conjecture of Richter and Thomassen states that the total number of intersection points between any n simple closed Jordan curves in the plane, so that any pair of them intersect and no three curves pass through the same point, is at least ...

Cambridge Univ Press2016

Simple topological graphs : empty triangles and disjoint edges

Andres Jacinto Ruiz Vargas

This thesis is devoted to the understanding of topological graphs. We consider the following four problems: 1. A \emph{simple topological graph} is a graph drawn in the plane so that its edges are represented by continuous arcs with the property that any t ...

EPFL2016

Coloring Intersection Graphs of Arc-Connected Sets in the Plane

Bartosz Maria Walczak, Michal Lason

A family of sets in the plane is simple if the intersection of any subfamily is arc-connected, and it is pierced by a line L if the intersection of any member with L is a nonempty segment. It is proved that the intersection graphs of simple families of com ...

Springer2014

Crowding and grouping: how much time is needed to process good Gestalt?

Michael Herzog, Mauro Manassi

In crowding, perception of a target is deteriorated by flanking elements. Crowding is usually explained by pooling models where target and flanker signals are averaged. We show here that crowding is rather determined by grouping and good Gestalt. We determ ...

2013

Consistent Digital Line Segments

Doemoetoer Palvoelgyi

We introduce a novel and general approach for digitalization of line segments in the plane that satisfies a set of axioms naturally arising from Euclidean axioms. In particular, we show how to derive such a system of digital segments from any total order o ...

2012

Quantum fluctuations of one-dimensional free fermions and Fisher-Hartwig formula for Toeplitz determinants

We revisit the problem of finding the probability distribution of a fermionic number of one-dimensional spinless free fermions on a segment of a given length. The generating function for this probability distribution can be expressed as a determinant of a ...

2011

Tangencies between families of disjoint regions in the plane

János Pach

Let C be a family of n convex bodies in the plane, which can be decomposed into k subfamilies of pairwise disjoint sets. It is shown that the number of tangencies between the members of C is at most O(kn), and that this bound cannot be improved. If we only ...

2010