scholarly journals On connected and regular point sets

1928 ◽  
Vol 34 (5) ◽  
pp. 649-656 ◽  
Author(s):  
R. L. Wilder
Keyword(s):  
Regular Point ◽  
Point Sets

scholarly journals Regular and non-regular point sets: Properties and reconstruction

2001 ◽  
Vol 19 (2-3) ◽  
pp. 101-126 ◽  
Author(s):  
Sylvain Petitjean ◽  
Edmond Boyer
Keyword(s):  
Regular Point ◽  
Point Sets

Potentially regular point sets

1930 ◽  
Vol 16 ◽  
pp. 160-172
Author(s):  
Gordon Whyburn
Keyword(s):  
Regular Point ◽  
Point Sets

Almost empty polygons

2003 ◽  
Vol 40 (3) ◽  
pp. 269-286 ◽  
Author(s):  
H. Nyklová
Keyword(s):  
Exact Results ◽  
Point Sets ◽  
Planar Point ◽  
Convex Position ◽  
Vertex Set ◽  
Point Set ◽  
Empty Polygons

In this paper we study a problem related to the classical Erdos--Szekeres Theorem on finding points in convex position in planar point sets. We study for which n and k there exists a number h(n,k) such that in every planar point set X of size h(n,k) or larger, no three points on a line, we can find n points forming a vertex set of a convex n-gon with at most k points of X in its interior. Recall that h(n,0) does not exist for n = 7 by a result of Horton. In this paper we prove the following results. First, using Horton's construction with no empty 7-gon we obtain that h(n,k) does not exist for k = 2(n+6)/4-n-3. Then we give some exact results for convex hexagons: every point set containing a convex hexagon contains a convex hexagon with at most seven points inside it, and any such set of at least 19 points contains a convex hexagon with at most five points inside it.

An Algorithm for Extracting and Enhancing Valley-ridge Features from Point Sets

2010 ◽  
Vol 36 (8) ◽  
pp. 1073-1083 ◽  
Author(s):  
Xu-Fang PANG ◽  
Ming-Yong PANG ◽  
Chun-Xia XIAO
Keyword(s):  
Point Sets

Multifractal Analysis of Chaotic Point Sets

1992 ◽  
Author(s):  
L. V. Meisel ◽  
M. A. Johnson
Keyword(s):  
Multifractal Analysis ◽  
Point Sets

ON THE GENERAL THEORY OF POINT SETS, II

1986 ◽  
Vol 12 (1) ◽  
pp. 377 ◽  
Author(s):  
Morgan
Keyword(s):  
General Theory ◽  
Point Sets
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