 * Maintaining visibility polygon of a fixed point located in the free space of the polygonal domain amid vertex insertions to simple polygons in that polygonal domain. The proposed algorithms are output-sensitive, and the time complexities of algorithms for (weak) visibility polygon maintenance are expressed in terms of change in output complexity .
<clarity>  * Maintaining visibility polygon of a fixed point located in the free space of the polygonal domain amid vertex insertions to simple polygons in that polygonal domain. The proposed algorithms are output-sensitive, and the time complexities of algorithms for (weak) visibility polygon maintenance are expressed in terms of change in output complexity .
 Each of these algorithms require preprocessing the initial simple polygon. And, the algorithms that maintain the visibility polygon (resp. weak visibility polygon) compute the visibility polygon (resp. weak visibility polygon) with respect to the initial simple polygon during the preprocessing phase .