Guard Zone Problem.

Date of Submission

December 1992

Date of Award

Winter 12-12-1993

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Master's Dissertation

Degree Name

Master of Technology

Subject Name

Computer Science


Advance Computing and Microelectronics Unit (ACMU-Kolkata)


Bhattacharya, Bhargab Bikram (ACMU-Kolkata; ISI)

Abstract (Summary of the Work)

In VISI layout. design where the ma for aim is to pack more and more cireultry In mirnlmum ahlparen. the degree of closeuerss more bet.ween two different. modules is limited by the inductive effects of one circuit. another. It. is thus required to separate on different circuit components by a predefined distance δ determined t.his dissertation the modules which by the design rules of the technology. In we Introduce the concept of a guard zone around will be used to prevent the violation of design rules.The guard zone (of width δ) of a polygon Is defined as closed region consisting of straight. lines and circular arcs bounding the polygon so that there exist. no pair of points (p, q), where p lies the polygon and a lies the boundary of on on the guard zone, such that. the euclidian distance between p and a less than In this dissertation, our objective is find the guard of simple polygon having minimum Fig Zone area. 1 demonstrates the guard zone around an isothetie polygon.In addition to VLSI design the concept of guard zone has wide range of applications In graphics, machine tools and defence to name a few.2. PROBLEM DESCRIPTIONThe guard zone problem is an optimization problem of computational geometry, defined as follows.DEFINITION:A guard a simple polygon P of is a closed zone region bounded by straight line segments and circular enclosing t.he polygon P and satisfying the following constraints. 1. For every point. x the boundary of G there does not. exist. any point. p the boundary of P such that. dist(x,p) < δ for given positive value of δ. 2. Area (3) is a minimum.To develop the algorithm for finding the guard zone of a polygon, we now Introduce the following concepts :In our problem we consider polygon a as sequence of vertices, By clockwise traversal, an ordering we mean of the vertices such that. if one travels along the outer boundary of the polygon, then the interior of the polygon will his right lie to throughout.During a clockwise traversal of the polygon, if we encounter a Sequence of consecutive vertices ( а, b, с,) then vertex is convex corner provided there exists at least. one point. p (* b) on ab and a point a ( b) on be such that. the straight line segment. pg lies completely inside the polygon. otherwise b is said to be a concave corner. In the above two cases the angle abc is said to be a right/left turn respectively.The convex hull [2] of a polygon P is the smallest. convex polyeon hounding the given polygon P completeiv. vertices of Q is a subset. of the set of vertices of P, but. all the Note that the set. of edges of Q may not correspond to that of P. Remark: Ir r is convex the edges of Q are edges of P and vice versa. Let α and be the two consecutive vertices of Q such that there exists sequence of vertices ⌈- γ1,γ2..γk > (k≥ 1) Such that the vertices of ⌈ lie bet.ween and 3 in clockwise traversal.


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