Now showing items 1-14 of 14

• #### A polynomial bound for untangling geometric planar graphs ﻿

(2009-12)
Article
Open Access
To untangle a geometric graph means to move some of the vertices so that the resulting geometric graph has no crossings. Pach and Tardos (Discrete Comput. Geom. 28(4): 585–592, 2002) asked if every n-vertex geometric planar ...
• #### Affine invariant triangulations ﻿

(2019)
Conference report
Restricted access - publisher's policy
We study affine invariant 2D triangulation methods. That is, methods that produce the same triangulation for a point set S for any (unknown) affine transformation of S. Our work is based on a method by Nielson [A ...
• #### Affine invariant triangulations ﻿

(2021-11-01)
Article
Restricted access - publisher's policy
We study affine invariant 2D triangulation methods. That is, methods that produce the same triangulation for a point set S for any (unknown) affine transformation of S. Our work is based on a method by Nielson (1993) that ...
• #### Connectivity-preserving transformations of binary images ﻿

(2009-10)
Article
Open Access
A binary image $\emph{I}$ is $B_a$, $W_b$-connected, where $\emph{a,b}$ ∊ {4,8}, if its foreground is $\emph{a}$-connected and its background is $\emph{b}$-connected. We consider a local modification of a $B_a$, $W_b$-connected ...
• #### Every large point set contains many collinear points or an empty pentagon ﻿

(2011-01)
Article
Restricted access - publisher's policy
We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next ...
• #### Flips in higher order Delaunay triangulations ﻿

(2021)
Conference report
Restricted access - publisher's policy
We study the flip graph of higher order Delaunay triangulations. A triangulation of a set S of n points in the plane is order-k Delaunay if for every triangle its circumcircle encloses at most k points of S. The flip graph ...
• #### Hamiltonicity for convex shape Delaunay and Gabriel graphs ﻿

(2019)
Conference report
Restricted access - publisher's policy
We study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Let S be a point set in the plane. The k-order Delaunay graph of S, denoted k-DGC(S), has vertex set S and edge pq provided ...
• #### Hamiltonicity for convex shape Delaunay and Gabriel graphs ﻿

(2020-08)
Article
Open Access
We study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Instead of defining these proximity graphs using circles, we use an arbitrary convex shape $$\mathcal {C}$$ . Let S be a point ...
• #### Hamiltonicity for convex shape Delaunay and Gabriel Graphs ﻿

(Springer, 2019)
Conference report
Restricted access - publisher's policy
We study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Instead of defining these proximity graphs using circles, we use an arbitrary convex shape C. Let S be a point set in the plane. ...
• #### On computing enclosing isosceles triangles and related problems ﻿

(2011-02)
Article
Open Access
Given a set of n points in the plane, we show how to compute various enclosing isosceles triangles where different parameters such as area or perimeter are optimized. We then study a 3-dimensional version of the problem ...
• #### On structural and graph theoretic properties of higher order Delaunay graphs ﻿

(2009-12)
Article
Open Access
Given a set $\emph{P}$ of $\emph{n}$ points in the plane, the order-$\emph{k}$ Delaunay graph is a graph with vertex set $\emph{P}$ and an edge exists between two points p,q ∊ $\emph{P}$ when there is a circle through ...
• #### Pole Dancing: 3D Morphs for Tree Drawings ﻿

(Springer, 2018)
Conference report
Restricted access - publisher's policy
We study the question whether a crossing-free 3D morph between two straight-line drawings of an n-vertex tree can be constructed consisting of a small number of linear morphing steps. We look both at the case in which the ...
• #### Sequences of spanning trees for L-infinity Delaunay triangulations ﻿

(2018)
Conference report
Open Access
We extend a known result about L2-Delaunay triangulations to L∞-Delaunay. Let TS be the set of all non-crossing spanning trees of a planar n-point set S. We prove that for each element T of TS, there exists a length-decreasing ...
• #### Some properties of higher order delaunay and gabriel graphs ﻿

(2010)
Conference report
Open Access
We consider two classes of higher order proximity graphs defined on a set of points in the plane, namely, the k-Delaunay graph and the k-Gabriel graph. We give bounds on the following combinatorial and geometric properties ...