Planar straight-line point-set embedding of trees with partial embeddings

2010 ◽  
Vol 110 (12-13) ◽  
pp. 521-523 ◽  
Author(s):  
Alireza Bagheri ◽  
Mohammadreza Razzazi
Keyword(s):  
Straight Line ◽  
Point Set ◽  
Line Point ◽  
Embedding Of Trees

scholarly journals An Improved Robust Method for Pose Estimation of Cylindrical Parts with Interference Features

Sensors ◽  
2019 ◽  
Vol 19 (10) ◽  
pp. 2234 ◽  
Author(s):  
Jieyu Zhang ◽  
Yuanying Qiu ◽  
Xuechao Duan ◽  
Kangli Xu ◽  
Changqi Yang
Keyword(s):  
Laser Scanning ◽  
Robust Method ◽  
Negative Effects ◽  
Profile Fitting ◽  
Straight Line ◽  
Intelligent Measurement ◽  
Cylindrical Parts ◽  
Point Set ◽  
Aerospace Assembly ◽  
Series Of Experiments

Horizontal docking assembly is a fundamental process in the aerospace assembly, where intelligent measurement and adjustable support systems are urgently needed to achieve higher automation and precision. Thus, a laser scanning approach is employed to obtain the point cloud from a laser scanning sensor. And a method of section profile fitting is put forward to solve the pose parameters from the data cloud acquired by the laser scanning sensor. Firstly, the data is segmented into planar profiles by a series of parallel planes, and ellipse fitting is employed to estimate each center of the section profiles. Secondly, the pose of the part can be obtained through a spatial straight line fitting with these profile centers. However, there may be some interference features on the surface of the parts in the practical assembly process, which will cause negative effects to the measurement. Aiming at the interferences, a robust method improved from M-estimation and RANSAC is proposed to enhance the measurement robustness. The proportion of the inner points in a whole profile point set is set as a judgment criterion to validate each planar profile. Finally, a prototype is fabricated, a series of experiments have been conducted to verify the proposed method.

PARAMETRIC POLYMATROID OPTIMIZATION AND ITS GEOMETRIC APPLICATIONS

2002 ◽  
Vol 12 (05) ◽  
pp. 429-443 ◽  
Author(s):  
NAOKI KATOH ◽  
HISAO TAMAKI ◽  
TAKESHI TOKUYAMA
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Transportation Problem ◽  
Minimum Weight ◽  
Planar Point ◽  
Line Arrangement ◽  
Optimal Bound ◽  
Straight Line ◽  
Point Set ◽  
Multiple Levels

We give an optimal bound on the number of transitions of the minimum weight base of an integer valued parametric polymatroid. This generalizes and unifies Tamal Dey's O(k1/3 n) upper bound on the number of k-sets (and the complexity of the k-level of a straight-line arrangement), David Eppstein's lower bound on the number of transitions of the minimum weight base of a parametric matroid, and also the Θ(kn) bound on the complexity of the at-most-k level (the union of i-levels for i = 1,2,…,k) of a straight-line arrangement. As applications, we improve Welzl's upper bound on the sum of the complexities of multiple levels, and apply this bound to the number of different equal-sized-bucketings of a planar point set with parallel partition lines. We also consider an application to a special parametric transportation problem.

scholarly journals THE POINT-SET EMBEDDABILITY PROBLEM FOR PLANE GRAPHS

2013 ◽  
Vol 23 (04n05) ◽  
pp. 357-395 ◽  
Author(s):  
THERESE BIEDL ◽  
MARTIN VATSHELLE
Keyword(s):  
Planar Graph ◽  
Planar Graphs ◽  
Line Drawing ◽  
Np Hard ◽  
Bounded Treewidth ◽  
Straight Line ◽  
Triangulated Graphs ◽  
Point Set ◽  
Fixed Embedding ◽  
Set Of Points

In this paper, we study the point-set embeddability problem, i.e., given a planar graph and a set of points, is there a mapping of the vertices to the points such that the resulting straight-line drawing is planar? It was known that this problem is NP-hard if the embedding can be chosen, but becomes polynomial for triangulated graphs of treewidth 3. We show here that in fact it can be answered for all planar graphs with a fixed combinatorial embedding that have constant treewidth and constant face-degree. We prove that as soon as one of the conditions is dropped (i.e., either the treewidth is unbounded or some faces have large degrees), point-set embeddability with a fixed embedding becomes NP-hard. The NP-hardness holds even for a 3-connected planar graph with constant treewidth, triangulated planar graphs, or 2-connected outer-planar graphs. These results also show that the convex point-set embeddability problem (where faces must be convex) is NP-hard, but we prove that it becomes polynomial if the graph has bounded treewidth and bounded maximum degree.

scholarly journals Counting Triangulations of Planar Point Sets

10.37236/557 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Micha Sharir ◽  
Adam Sheffer
Keyword(s):  
Upper Bound ◽  
Planar Graphs ◽  
Spanning Trees ◽  
Upper Bounds ◽  
Line Graphs ◽  
Point Sets ◽  
Planar Point ◽  
Straight Line ◽  
Point Set ◽  
Spanning Cycles

We study the maximal number of triangulations that a planar set of $n$ points can have, and show that it is at most $30^n$. This new bound is achieved by a careful optimization of the charging scheme of Sharir and Welzl (2006), which has led to the previous best upper bound of $43^n$ for the problem. Moreover, this new bound is useful for bounding the number of other types of planar (i.e., crossing-free) straight-line graphs on a given point set. Specifically, it can be used to derive new upper bounds for the number of planar graphs ($207.84^n$), spanning cycles ($O(68.67^n)$), spanning trees ($O(146.69^n)$), and cycle-free graphs ($O(164.17^n)$).

scholarly journals The complex moment problem: determinacy and extendibility

2019 ◽  
Vol 124 (2) ◽  
pp. 263-288 ◽  
Author(s):  
Dariusz Cichoń ◽  
Jan Stochel ◽  
Franciszek Hugon Szafraniec
Keyword(s):  
Partial Solution ◽  
Positive Definite ◽  
Lattice Points ◽  
Moment Sequence ◽  
Representing Measure ◽  
Straight Line Passing ◽  
Straight Line ◽  
Plane Algebraic Curve ◽  
Line Passing ◽  
Point Set

Complex moment sequences are exactly those which admit positive definite extensions on the integer lattice points of the upper diagonal half-plane. Here we prove that the aforesaid extension is unique provided the complex moment sequence is determinate and its only representing measure has no atom at $0$. The question of converting the relation is posed as an open problem. A partial solution to this problem is established when at least one of representing measures is supported in a plane algebraic curve whose intersection with every straight line passing through $0$ is at most one point set. Further study concerns representing measures whose supports are Zariski dense in $\mathbb{C} $ as well as complex moment sequences which are constant on a family of parallel “Diophantine lines”. All this is supported by a bunch of illustrative examples.

scholarly journals Edge-Removal and Non-Crossing Configurations in Geometric Graphs

2010 ◽  
Vol Vol. 12 no. 1 (Graph and Algorithms) ◽  
Author(s):  
Oswin Aichholzer ◽  
Sergio Cabello ◽  
Ruy Fabila-Monroy ◽  
David Flores-Peñaloza ◽  
Thomas Hackl ◽  
...  
Keyword(s):  
Extremal Problem ◽  
General Position ◽  
Geometric Graph ◽  
Perfect Matchings ◽  
Geometric Graphs ◽  
Line Segments ◽  
Straight Line ◽  
Edge Removal ◽  
International Audience ◽  
Point Set

Graphs and Algorithms International audience A geometric graph is a graph G = (V, E) drawn in the plane, such that V is a point set in general position and E is a set of straight-line segments whose endpoints belong to V. We study the following extremal problem for geometric graphs: How many arbitrary edges can be removed from a complete geometric graph with n vertices such that the remaining graph still contains a certain non-crossing subgraph. The non-crossing subgraphs that we consider are perfect matchings, subtrees of a given size, and triangulations. In each case, we obtain tight bounds on the maximum number of removable edges.

scholarly journals Orthogeodesic point-set embedding of trees

2013 ◽  
Vol 46 (8) ◽  
pp. 929-944 ◽  
Author(s):  
Emilio Di Giacomo ◽  
Fabrizio Frati ◽  
Radoslav Fulek ◽  
Luca Grilli ◽  
Marcus Krug
Keyword(s):  
Point Set ◽  
Embedding Of Trees

Feature-Based Identification and Reconstruction of Regular Curves and Surfaces

2012 ◽  
Vol 184-185 ◽  
pp. 206-209
Author(s):  
Tie Li Ye ◽  
He Li ◽  
Qing Liang Zeng
Keyword(s):  
Line Segment ◽  
Cylindrical Surface ◽  
Straight Line Segment ◽  
Geometric Feature ◽  
Surface Point ◽  
Regular Curve ◽  
Curves And Surfaces ◽  
Straight Line ◽  
Feature Based ◽  
Point Set

Based on the preprocessed measuring data, this paper proposes a method for identification and reconstruction of regular curves and surfaces including straight line(segment), circle(arc), four-sided plane and right cylindrical surface. Considering the geometric feature of each kind of regular curve or surface, the paper studies the corresponding algorithm for identifying the curve or surface point set, reconstructs the curve or surface and gives the parameter equation.

scholarly journals Drawing Hamiltonian Cycles with no Large Angles

10.37236/2356 ◽  
2012 ◽  
Vol 19 (2) ◽  
Author(s):  
Adrian Dumitrescu ◽  
János Pach ◽  
Géza Tóth
Keyword(s):  
Hamiltonian Cycle ◽  
Hamiltonian Cycles ◽  
Point Sets ◽  
Convex Position ◽  
Straight Line ◽  
Open Region ◽  
Point Set ◽  
Rectifiable Curves ◽  
Element Set

Let $n \geq 4$ be even. It is shown that every set $S$ of $n$ points in the plane can be connected by a (possibly self-intersecting) spanning tour (Hamiltonian cycle) consisting of $n$ straight-line edges such that the angle between any two consecutive edges is at most $2\pi/3$. For $n=4$ and $6$, this statement is tight. It is also shown that every even-element point set $S$ can be partitioned  into at most two subsets, $S_1$ and $S_2$, each admitting a spanning tour with no angle larger than $\pi/2$. Fekete and Woeginger conjectured that for sufficiently large even $n$, every $n$-element set admits such a spanning tour. We confirm this conjecture for point sets in convex position. A much stronger result holds for large point sets randomly and uniformly selected from an open region bounded by finitely many rectifiable curves: for any $\epsilon>0$, these sets almost surely admit a spanning tour with no angle larger than $\epsilon$.

scholarly journals Point-Set Embedding of Trees with Edge Constraints

2008 ◽  
pp. 113-124 ◽  
Author(s):  
Emilio Di Giacomo ◽  
Walter Didimo ◽  
Giuseppe Liotta ◽  
Henk Meijer ◽  
Stephen Wismath
Keyword(s):  
Point Set ◽  
Embedding Of Trees
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