scholarly journals Finding the Medial Axis of a Simple Polygon in Linear Time

1999 ◽  
Vol 21 (3) ◽  
pp. 405-420 ◽  
Author(s):  
F. Chin ◽  
J. Snoeyink ◽  
C. A. Wang
Keyword(s):  
Linear Time ◽  
Medial Axis ◽  
Simple Polygon

How to Keep an Eye on Small Things

2021 ◽  
pp. 1-24
Author(s):  
Bengt J. Nilsson ◽  
Paweł Żyliński
Keyword(s):  
Linear Time ◽  
Simple Polygon ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Approximation Factor ◽  
Fpt Algorithm ◽  
Optimal Linear ◽  
Small Things ◽  
Set Of Points ◽  
Better Than

We present new results on two types of guarding problems for polygons. For the first problem, we present an optimal linear time algorithm for computing a smallest set of points that guard a given shortest path in a simple polygon having [Formula: see text] edges. We also prove that in polygons with holes, there is a constant [Formula: see text] such that no polynomial-time algorithm can solve the problem within an approximation factor of [Formula: see text], unless P=NP. For the second problem, we present a [Formula: see text]-FPT algorithm for computing a shortest tour that sees [Formula: see text] specified points in a polygon with [Formula: see text] holes. We also present a [Formula: see text]-FPT approximation algorithm for this problem having approximation factor [Formula: see text]. In addition, we prove that the general problem cannot be polynomially approximated better than by a factor of [Formula: see text], for some constant [Formula: see text], unless P [Formula: see text]NP.

AN APPROXIMATE MORPHING BETWEEN POLYLINES

2005 ◽  
Vol 15 (02) ◽  
pp. 193-208 ◽  
Author(s):  
SERGEY BEREG
Keyword(s):  
Shortest Path ◽  
Optimization Problem ◽  
Linear Time ◽  
Medial Axis ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Geodesic Path ◽  
Minimum Width ◽  
Approximation Factor ◽  
Previous Algorithm

We consider the problem of continuously transforming or morphing one simple polyline into another polyline so that every point p of the initial polyline moves to a point q of the final polyline using the geodesic shortest path from p to q. The width of a morphing is defined as the longest geodesic path between corresponding points of the polylines. The optimization problem is to compute a morphing that minimizes the width. We present a linear-time algorithm for finding a morphing with width guaranteed to be at most two times the minimum width of a morphing. This improves the previous algorithm10 by a factor of log n. We develop a linear-time algorithm for computing a medial axis separator. We also show that the approximation factor is less than two for κ-straight polylines.

scholarly journals Finding the convex hull of a simple polygon in linear time

1986 ◽  
Vol 19 (6) ◽  
pp. 453-458 ◽  
Author(s):  
S.Y. Shin ◽  
T.C. Woo
Keyword(s):  
Convex Hull ◽  
Linear Time ◽  
Simple Polygon
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