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This article describes a method for the symbolic representation of a general polygon and shows how expression for union, complement and intersection functions can be derived.
English (United States)
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Method for the Symbolic Representation of a General Polygon
This article describes a method for the symbolic representation of a general
polygon and shows how expression for union, complement and intersection
functions can be derived.
Definitions A 'simple polygon' is defined as an area bounded by a single
perimeter which does not cross itself.
An 'inside/outside polygon' is defined as a simple polygon
(outside polygon) from which zero or more totally contained and
non-intersecting simple polygons (inside polygons) have been removed.
Fig. 1 shows an example of an inside/outside polygon.
The 'complement' of two simple polygons A and B is defined as that part of A
which is not contained in B. Fig. 2 is an example of the complement A,B.
A 'positively-oriented' simple polygon is arbitrarily defined to be counter-
clockwise oriented and represents the area contained within its perimeter.
Conversely, a negatively-oriented polygon is clockwise oriented and represents
the area outside its perimeter.
The Problem In the field of chip design verification it is desirable to be able to
manipulate polygons which represent mask shapes. Therefore, it is necessary
that the compiler implementing the chip design verification program language
should be able to perform the polygon operations inter section, union and
complement, among others, on any simple or inside/ outside polygon, however
complex, transparently to the user.
Union and intersection routines are available to form the basis of the required
functions, but are only able to accept as input pairs of oriented simple polygons,
although inside/outside polygons could be generated from these. The
complement function for simple po...