scholarly journals A Survey and Comparative Study for Connecting 2D points

2020 ◽  
pp. 10-18
Author(s):  
Jijith K ◽  
Philumon Joseph
Keyword(s):  
Research Effort ◽  
Reconstruction Algorithms ◽  
Point Sets ◽  
Science And Engineering ◽  
Engineering Research ◽  
Good Shape ◽  
Sampling Conditions ◽  
Point Set ◽  
Local Sampling ◽  
Surface Curve

Reconstruction from noisy point sets has many ap-plications in the areas of science and engineering. Research effort in reconstructing shape from noisy point sets. Reconstruction on planar point including shape, surface, curve and manifold recon-struction. Good algorithms are required to create a good shape from a given point set. Better local and global sampling conditions form the base of these algorithms. Reconstruction from noisy point set is not extensively studied and therefore the researchers do not have a successful algorithm. Reconstruction from the stage is begun before many decades and these activities are now being extended for a few days. Extending any older reconstruction algorithms needs a good understanding and comparison of all previous algorithms. This survey is spamming on different reconstruction algorithms, various local sampling conditions, extension of different works and their working conditions and reconstruction implementation from point sets. Survey begins after 1997 and compares various extension works. The sampling condition for all these algorithms contributes significantly to the construction of algorithms, thus different local sampling conditions are investigated. During this study, all algorithms for reconstruction are tabulated and different parameters for these algorithms are compared. This survey is concluding with several promising directions for the future works on reconstruction.

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.

scholarly journals Fixed poin sets in digital topology, 1

2020 ◽  
Vol 21 (1) ◽  
pp. 87 ◽  
Author(s):  
Laurence Boxer ◽  
P. Christopher Staecker
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Digital Images ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Point Sets ◽  
Fixed Point Set ◽  
Complete Computation ◽  
Point Set ◽  
Fixed Point Sets

<p>In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topological fixed point theory, and we obtain results that often differ greatly from standard results in classical topology.</p><p>We introduce several measures related to fixed points for continuous self-maps on digital images, and study their properties. Perhaps the most important of these is the fixed point spectrum F(X) of a digital image: that is, the set of all numbers that can appear as the number of fixed points for some continuous self-map. We give a complete computation of F(C<sub>n</sub>) where C<sub>n</sub> is the digital cycle of n points. For other digital images, we show that, if X has at least 4 points, then F(X) always contains the numbers 0, 1, 2, 3, and the cardinality of X. We give several examples, including C<sub>n</sub>, in which F(X) does not equal {0, 1, . . . , #X}.</p><p>We examine how fixed point sets are affected by rigidity, retraction, deformation retraction, and the formation of wedges and Cartesian products. We also study how fixed point sets in digital images can be arranged; e.g., for some digital images the fixed point set is always connected.</p>

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