Computing polygonal path simplification under area measures

2012 ◽  
Vol 74 (5) ◽  
pp. 283-289 ◽  
Author(s):  
Shervin Daneshpajouh ◽  
Mohammad Ghodsi ◽  
Alireza Zarei
Keyword(s):  
Polygonal Path

Hamiltonian polygonal path in assembly graph of FTTM

2019 ◽  
Author(s):  
Tahir Ahmad ◽  
Noorsufia Abd Shukor ◽  
Amidora Idris ◽  
Zainab Mahamud
Keyword(s):  
Polygonal Path

scholarly journals Polygonal path simplification with angle constraints

2005 ◽  
Vol 32 (3) ◽  
pp. 173-187 ◽  
Author(s):  
Danny Z. Chen ◽  
Ovidiu Daescu ◽  
John Hershberger ◽  
Peter M. Kogge ◽  
Ningfang Mi ◽  
...  
Keyword(s):  
Polygonal Path

Extrema of a Class of Functions on a Finite Set

1974 ◽  
Vol 26 (4) ◽  
pp. 806-819
Author(s):  
Kenneth W. Lebensold
Keyword(s):  
Positive Integer ◽  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Polygonal Path ◽  
Finite Set ◽  
Vertex Set ◽  
The Traveling Salesman Problem ◽  
The Cost ◽  
Special Case ◽  
Class Of Functions

In this paper, we are concerned with the following problem: Let S be a finite set and Sm* ⊂ 2S a collection of subsets of S each of whose members has m elements (m a positive integer). Let f be a real-valued function on S and, for p ∊ Sm*, define f(P) as Σs∊pf (s). We seek the minimum (or maximum) of the function f on the set Sm*.The Traveling Salesman Problem is to find the cheapest polygonal path through a given set of vertices, given the cost of getting from any vertex to any other. It is easily seen that the Traveling Salesman Problem is a special case of this system, where S is the set of all edges joining pairs of points in the vertex set, Sm* is the set of polygons, each polygon has m elements (m = no. of points in the vertex set = no. of edges per polygon), and f is the cost function.

THE CRAB: A CONNECTED FRACTILE OF INFINITE CONNECTIVITY

Fractals ◽  
2011 ◽  
Vol 19 (03) ◽  
pp. 367-377 ◽  
Author(s):  
GILBERT HELMBERG
Keyword(s):  
Hausdorff Dimension ◽  
Hausdorff Metric ◽  
Unit Interval ◽  
Limit Set ◽  
Space Filling ◽  
Polygonal Path ◽  
Space Filling Curve ◽  
Dimension Formula ◽  
Filling Curve ◽  
Similar Copy

In the plane IR2, let A0 be the unit interval on the x-axis, and let A(1) be the polygonal path with nodes (0, 0), [Formula: see text], (½, 0), [Formula: see text], (1, 0). Let S be the operator which, applied to a segment B(0) in IR2, replaces it by a polygonal path B(1) = SB(0), a similar copy of A(1), but with the same endpoints as B(0). Denote by S(n) the n-th iterate of S. The limit set (with respect to the Hausdorff metric) A(∞) = lim n → ∞ S(n)A(0) is a space-filling curve which is the closure of its interior and the union of four half-size copies of itself, intersecting only in their boundaries. Although A(∞) is of infinite connectivity, it is a tile tessellating the plane. It is related to the set of Eisenstein fractions and has a boundary of Hausdorff dimension [Formula: see text]

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