scholarly journals Exploring the Outer Boundary of a Simple Polygon

2021 ◽  
Vol E104.D (7) ◽  
pp. 923-930
Author(s):  
Qi WEI ◽  
Xiaolin YAO ◽  
Luan LIU ◽  
Yan ZHANG
1999 ◽  
Vol 09 (06) ◽  
pp. 533-552 ◽  
Author(s):  
EVANTHIA PAPADOPOULOU

This paper presents a simple O(n+k) time algorithm to compute the set of knon-crossing shortest paths between k source-destination pairs of points on the boundary of a simple polygon of n vertices. Paths are allowed to overlap but are not allowed to cross in the plane. A byproduct of this result is an O(n) time algorithm to compute a balanced geodesic triangulation which is easy to implement. The algorithm extends to a simple polygon with one hole where source-destination pairs may appear on both the inner and outer boundary of the polygon. In the latter case, the goal is to compute a collection of non-crossing paths of minimum total cost. The case of a rectangular polygonal domain where source-destination pairs appear on the outer and one inner boundary12 is briefly discussed.


2021 ◽  
Vol 11 (4) ◽  
pp. 1936
Author(s):  
Abdel-Hakim Bouzid

The accurate prediction of liquid leak rates in packing seals is an important step in the design of stuffing boxes, in order to comply with environmental protection laws and health and safety regulations regarding the release of toxic substances or fugitive emissions, such as those implemented by the Environmental Protection Agency (EPA) and the Technische Anleitung zur Reinhaltung der Luft (TA Luft). Most recent studies conducted on seals have concentrated on the prediction of gas flow, with little to no effort put toward predicting liquid flow. As a result, there is a need to simulate liquid flow through sealing materials in order to predict leakage into the outer boundary. Modelling of liquid flow through porous packing materials was addressed in this work. Characterization of their porous structure was determined to be a key parameter in the prediction of liquid flow through packing materials; the relationship between gland stress and leak rate was also acknowledged. The proposed methodology started by conducting experimental leak measurements with helium gas to characterize the number and size of capillaries. Liquid leak tests with water and kerosene were then conducted in order to validate the predictions. This study showed that liquid leak rates in packed stuffing boxes could be predicted with reasonable accuracy for low gland stresses. It was found that internal pressure and compression stress had an effect on leakage, as did the thickness change and the type of fluid. The measured leak rates were in the range of 0.062 to 5.7 mg/s for gases and 0.0013 and 5.5 mg/s for liquids.


2002 ◽  
Vol 12 (04) ◽  
pp. 339-352 ◽  
Author(s):  
SANG-MIN PARK ◽  
JAE-HA LEE ◽  
KYUNG-YONG CHWA

We consider the problem of searching for mobile intruders in a polygonal region with one door by two guards. Given a simple polygon [Formula: see text] with a door d, which is called a room [Formula: see text], two guards start at d and walk along the boundary of [Formula: see text] to detect a mobile intruder with a laser beam between the two guards. During the walk, two guards are required to be mutually visible all the time and eventually meet at one point. We give a characterization of the class of rooms searchable by two guards and an O(n log n)-time algorithm to test if a given room admits a walk, where n is the number of the vertices in [Formula: see text].


2007 ◽  
Vol 45 (3) ◽  
pp. 268-272 ◽  
Author(s):  
E. V. Panov ◽  
S. P. Savin ◽  
J. Büchner ◽  
A. Korth

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