A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
A better upper bound on the number of triangulations of a planar point set

2003
*
Journal of combinatorial theory. Series A
*

We show that a

doi:10.1016/s0097-3165(03)00002-5
fatcat:7yti4f63nncpdcg6z6tncnhjcm
*point**set**of*cardinality n in*the*plane cannot be*the*vertex*set**of*more than 59^n O(n^-6) straight-edge*triangulations**of*its convex hull. ... This improves*the*previous upper bound*of*276.75^n. ... We thank*the*organizers*of*this meeting,*the*University*of*Crete and*the*Anogia Academic Village for*the*invitation and financial support. ...##
###
A lower bound on the number of triangulations of planar point sets

2004
*
Computational geometry
*

We show that

doi:10.1016/j.comgeo.2004.02.003
fatcat:rvtqvkocf5ax5lmirhph2o5c7e
*the**number**of*straight-edge*triangulations*exhibited by any*set**of*n*points*in general position in*the*plane is bounded from below by (2.33 n ). ... We highly appreciate*the*useful remarks and suggestions*of*two anonymous referees. Especially Eq. (7) , which lead to substantial improved bounds, is based*on*their valuable contribution. ... Introduction A*triangulation**of*a finite*planar**point**set*S is a maximal non-crossing straight-edge graph with vertex*set*S. ...##
###
The Number of Triangulations on Planar Point Sets
[chapter]

*
Graph Drawing
*

We give a brief account

doi:10.1007/978-3-540-70904-6_1
dblp:conf/gd/Welzl06
fatcat:p7dyyjh6jrbmncysof7dxahepm
*of*results concerning*the**number**of**triangulations**on*finite*point**sets*in*the*plane, both for arbitrary*sets*and for specific*sets*such as*the*n × n integer lattice. ... yields*the*claimed bound*on**the**number**of**triangulations*. ... In [5] it is shown that*the**set**of*all*triangulations**of*a*point**set*can be enumerated in time O(t · poly(n)), where t is*the**number**of**triangulations*. ...##
###
On the average length of Delaunay triangulations

1984
*
BIT Numerical Mathematics
*

We shall show that

doi:10.1007/bf02136025
fatcat:cjbps7sqnjbsdfj2dh755bsvum
*on**the*average,*the*total length*of*a Delaunay*triangulation*is*of**the*same order as that*of*a minimum*triangulation*, under*the*assumption that our*points*are drawn from a homogeneous ...*planar*Poisson*point*distribution. ... Given a*set*P*of*N*points*, any*triangulation**of*P has*the*same*number**of*triangles, N t = 2(N-1)-Nh, and*the*same*number**of*edges, N e = 3(N-1)-N h, where N h is*the**number**of**points**on**the*convex hull ...##
###
Incremental and batch planar simplification of dense point cloud maps

2015
*
Robotics and Autonomous Systems
*

Our results also show that

doi:10.1016/j.robot.2014.08.019
fatcat:rhfp5xdebvcozcapn6f5bmmg2a
*the*proposed*planar*simplification and*triangulation*algorithm removes more than 90%*of**the*input*planar**points*, leading to a*triangulation*with only 10%*of**the*original quantity ... In this paper we present a method for incremental*planar*segmentation*of*a gradually expanding*point*cloud map and a method for efficient*triangulation*and texturing*of**planar*surface segments. ...*The*polygon-based and*point*-based methods offer a trade-off depending*on**the*desired*number**of*triangles or*the*intended use*of**the*final*triangulation*. ...##
###
Conceptual Framework for Finding Approximations to Minimum Weight Triangulation and Traveling Salesman Problem of Planar Point Sets

2020
*
International Journal of Advanced Computer Science and Applications
*

We provide motivation for our research and introduce

doi:10.14569/ijacsa.2020.0110403
fatcat:kswkleldebbmzmwzchflbwdosi
*the*fields*of**triangulation*and polygonization*of**planar**point**sets*as theoretical bases*of*our approach, namely, we present*the*Isoperimetric Inequality ... We introduce a novel Conceptual Framework for finding approximations to both Minimum Weight*Triangulation*(MWT) and optimal Traveling Salesman Problem (TSP)*of**planar**point**sets*. ...*Triangulations*,*on**the*other hand, represent*the*most intuitive way*one*can partition a*planar**point**set*. ...##
###
Diagonal Flips in Labelled Planar Triangulations

2001
*
Graphs and Combinatorics
*

Recently Komuro gives a linear bound

doi:10.1007/s003730170006
fatcat:lelsaokgirfw7mji5o7t7z77ku
*on**the*maximum*number**of*diagonal flips needed for such a transformation. ... A classical result*of*Wagner states that any two (unlabelled)*planar**triangulations*with*the*same*number**of*vertices can be transformed into each other by a finite sequence*of*diagonal flips. ...*The*graph*of**triangulations*GT (P n )*of*a*point**set*P n is*the*graph whose vertex*set*is*the**set**of**triangulations**of*P n . ...##
###
A QPTAS for the Base of the Number of Triangulations of a Planar Point Set
[article]

2014
*
arXiv
*
pre-print

*The*

*number*

*of*

*triangulations*

*of*a

*planar*n

*point*

*set*is known to be c^n, where

*the*base c lies between 2.43 and 30. ... We present

*the*first quasi-polynomial approximation scheme for

*the*base

*of*

*the*

*number*

*of*

*triangulations*

*of*a

*planar*

*point*

*set*. ... Acknowledgments We thank Victor Alvarez, Artur Czumaj, Peter Floderus, Miroslaw Kowaluk, Christos Levcopoulos and Mia Persson for preliminary discussions

*on*counting

*the*

*number*

*of*

*triangulations*

*of*a

*planar*...

##
###
Experimental results on quadrangulations of sets of fixed points

2002
*
Computer Aided Geometric Design
*

We consider

doi:10.1016/s0167-8396(02)00133-4
fatcat:cisaq4vpjzhg5dcocuv6psbs64
*the*problem*of*obtaining "nice" quadrangulations*of**planar**sets**of**points*. ...*on**the*dual graph*of**the**triangulations*. ... A*set**of**points*admits a quadrangulation without Steiner*points*if and only if*the**number**of**points**on**the*convex hull is even. ...##
###
Novel parallel algorithm for constructing Delaunay triangulation based on a twofold-divide-and-conquer scheme

2014
*
GIScience & Remote Sensing
*

To increase

doi:10.1080/15481603.2014.946666
fatcat:jx6l4qc3xfbdfbe2xt4pnt6wcy
*the*efficiency when processing large data*sets*, a novel parallel algorithm is proposed for constructing*the*Delaunay*triangulation**of*a*planar**point**set*based*on*a twofold-divide-and-conquer ... This algorithm automatically divides*the**planar**point**set*into several non-overlapping subsets along*the*x-axis and y-axis directions alternately, according to*the**number**of**points*and their spatial distribution ... Funding This work is supported by*the*National Natural Science Foundation*of*China [grant*number*41371017] and*the*Program for New Century Excellent Talents in University (NCET-13-0280). ...##
###
Planar simplification and texturing of dense point cloud maps

2013
*
2013 European Conference on Mobile Robots
*

Experimental results show that our algorithm removes more than 90%

doi:10.1109/ecmr.2013.6698837
dblp:conf/ecmr/MaWBWM13
fatcat:auu2sw2atfcjfg4kphtx6wtkzy
*of**the*input*planar**points*, leading to a*triangulation*with only 10%*of**the*original amount*of*triangles per*planar*segment, improving ... In this paper we present a method for efficient*triangulation*and texturing*of**planar*surfaces in large*point*clouds. ...*The*polygonbased and*point*-based methods offer a trade-off depending*on**the*desired*number**of*triangles or*the*intended use*of**the*final*triangulation*. ...##
###
Succinct Geometric Indexes Supporting Point Location Queries
[chapter]

2009
*
Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
*

Our first and main result is a succinct geometric index that can answer

doi:10.1137/1.9781611973068.70
fatcat:ocva2u2vwvclxerdvnedmwxqi4
*point*location queries, a fundamental problem in computational geometry,*on**planar**triangulations*in O(lg n) time 1 . ... in*the*data*set*permuted and stored elsewhere as a sequence. ... Denny and Sohler [15] showed how to encode*the*connectivity information*of*a*planar**triangulation*by permuting its vertex*set*:*Point*Location in*Planar**Triangulations*In this section, we show how ...##
###
Succinct geometric indexes supporting point location queries

2012
*
ACM Transactions on Algorithms
*

Our first and main result is a succinct geometric index that can answer

doi:10.1145/2151171.2151173
fatcat:aop6jhrcqrfd3lklm62oewp35u
*point*location queries, a fundamental problem in computational geometry,*on**planar**triangulations*in O(lg n) time 1 . ... in*the*data*set*permuted and stored elsewhere as a sequence. ... Denny and Sohler [15] showed how to encode*the*connectivity information*of*a*planar**triangulation*by permuting its vertex*set*:*Point*Location in*Planar**Triangulations*In this section, we show how ...##
###
A Note On Universal Point Sets for Planar Graphs
[article]

2019
*
arXiv
*
pre-print

We investigate which

arXiv:1811.06482v3
fatcat:s7x2wkd5w5ggpjdkws4szxloqy
*planar**point**sets*allow simultaneous straight-line embeddings*of*all*planar*graphs*on*a fixed*number**of*vertices. ... Moreover, we provide a*set**of*49*planar*11-vertex graphs which cannot be simultaneously drawn*on*any*set**of*11*points*. ... We denote by f p (n)*the*size*of*a minimal n-universal*set*(for*planar*graphs), and by f s (n)*the*size*of*a minimal n-universal*set*for stacked*triangulations*, where stacked*triangulations*(a.k.a.*planar*...##
###
Flips in planar graphs

2009
*
Computational geometry
*

We review results concerning edge flips in

doi:10.1016/j.comgeo.2008.04.001
fatcat:fxq5ql3imzftpoh5naidvy5e3q
*planar*graphs concentrating mainly*on*various aspects*of**the*following problem: Given two different*planar*graphs*of**the*same size, how many edge flips are necessary ... We overview both*the*combinatorial perspective (where only a combinatorial embedding*of**the*graph is specified) and*the*geometric perspective (where*the*graph is embedded in*the*plane, vertices are*points*... [53] show that given two near-*triangulations*defined*on**the*same*set**of*n*points*,*the**number**of*flips sufficient to convert*one*to*the*other is bounded by*the**number**of*intersections between*the*edges ...
« Previous

*Showing results 1 — 15 out of 28,327 results*