Separation of two monotone polygons in linear time

Robotica ◽  
1984 ◽  
Vol 2 (4) ◽  
pp. 215-220 ◽  
Author(s):  
Godfried T. Toussaint ◽  
Hossam A. El Gindy
Keyword(s):  
Linear Time ◽  
Simple Polygons ◽  
Monotone Polygons

SUMMARYLet P= (p1, p2, …, pn) and Q= (q1, q2, …, qm) be two simple polygons monotonic in directions θs and φ respectively. It is shown that P and Q are separable with a single translation in at least one of the directions: ,. Furthermore, a direction for carrying out such a translation can be determined in O(m + n) time. This procedure is of use in solving the FIND-PATH problem in robotics.

A LINEAR-TIME ALGORITHM FOR COVERING SIMPLE POLYGONS WITH SIMILAR RECTANGLES

1996 ◽  
Vol 06 (01) ◽  
pp. 79-102 ◽  
Author(s):  
REUVEN BAR-YEHUDA ◽  
EYAL BEN-HANOCH
Keyword(s):  
Image Compression ◽  
Linear Time ◽  
Simple Polygon ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Equivalent Problem ◽  
Orthogonal Polygon ◽  
Simple Polygons ◽  
Minimum Number ◽  
Incremental Update

We study the problem of covering a simple orthogonal polygon with a minimum number of (possibly overlapping) squares, all internal to the polygon. The problem has applications in VLSI mask generation, incremental update of raster displays, and image compression. We give a linear time algorithm for covering a simple polygon, specified by its vertices, with squares. Covering with similar rectangles (having a given x/y ratio) is an equivalent problem.

Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons

Algorithmica ◽  
1987 ◽  
Vol 2 (1-4) ◽  
pp. 209-233 ◽  
Author(s):  
Leonidas Guibas ◽  
John Hershberger ◽  
Daniel Leven ◽  
Micha Sharir ◽  
Robert E. Tarjan
Keyword(s):  
Shortest Path ◽  
Linear Time ◽  
Shortest Path Problems ◽  
Simple Polygons ◽  
Linear Time Algorithms
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